Optical coherent transients and hole burning of the 7F0 - 5D0 transition in Eu(OH)3
by Michael Stephen Otteson
A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy i n
Physics
Montana State University
© Copyright by Michael Stephen Otteson (1984)
Abstract:
The narrowest inhomogeneous optical linewidth ever seen in a solid has been observed in Eu(OH)^.
This transition is quadratically enhanced in a magnetic field and the results are explained completely in
terms of second order perturbation theory and the coupling of crystal field energy levels.
Optical coherent transients are reported here for the first time in this optically pure, stoichiometric
material. The optical dephasing time, T2 is shown to be greater than 2 microseconds for the 7F0-5D0
zero phonon transition.
Hole burning, attributed to optical pumping of nuclear— qua drupole levels, has been used' to measure
the qua drupole splittings in the excited, 5D0 , state. Due to the small magnetic moment, conventional
magnetic resonance techniques have failed to make this measurement in all Europium compounds. The
new technique developed and used in these hole burning measurements yields the quadrupole coupling
coefficients, |P| = 11.6 MHz and |P| = 4.5 MHz for the 153 isotope and the 151 isotope, respectively.
The qualitative behavior of line narrowing in Doubly-resonant two—photon-absorption induced
four—wave mixing is explained in terms of the anomalous dispersion. The implications of this
dispersion regarding the measurement of the homogeneous linewidth and hyperfine levels hidden
within the inhomogeneous profile are discussed with regard to the particular example of LiTbF4. OPTICAL. COHERENT TRANSI ENTS AND HOLE BURNI NG
OF THE 7F 0 - 5 D0 TRANS I TI ON
IN E u ( O H ) g
• by
Michael
Stephen
Otteson
A thesis submitted in p a r tia l fu lfillm en t
of t h e r e q u i r e m e n t s f o r t h e d e g r e e
of
Doctor
of
Philosophy
in
Physics
MONTANA STATE UNI VE RS I T Y
Bozeman,Montana
November
1984
APPROVAL
of
a thesis
Michael
submitted
Stephen
by
Otteson
This
t h e s i s h a s b e e n r e a d by e a c h member of t h e t h e s i s
committee
a n d h a s b e e n f o u n d t o be
satisfactory
regarding
content,
English usage,
format,
citations,
bibliographic
style,
and c o n s i s t e n c y ,
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C o l l e g e of G r a d u a t e S t u d i e s .
Date
Approved
for
the
Major
Department
Date
I/
Approved
for
the
College
of
Graduate
// Date
Graduate
Dean
Studies
© 1985
MICHAEL STEPHEN OTTESON
All R igh ts R eserved
iii
STATEMENT OF PERMISSION TO USE
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U.S.
a
doctoral
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iv
VI TA
Michael
Stephen Otteson
S t ou gh t on,
Wisconsin.
He i s
Otte son.
was
the
b o r n on A p r i l 3 ,
1951
son of O t t o C. and J e a n
in
M.
Educated
in
the Wisconsin p ublic
school
system,
he
g r a d u a t e d from D e e r f i e l d High School i n 1969.
He
attended
University
of
W i s c o n s i n —O s h k o s h a n d g r a d u a t e d w i t h a
B. S.
degree
i n p h y s i c s and a p p l i e d m a t h e m a t i c s i n 1973
and
the
M. S . d e g r e e i n 1 97 (> .
He r e c e i v e d t h e M . S . d e g r e e i n p h y s i c s
from Montana S t a t e U n i v e r s i t y i n Bozeman, Montana i n 1979.
V
ACKNOWLEDGEMENTS
The
author
several
has
people
been
w ishes
to
the
Dr .
Rufus
been very
helpful
Thanks a re
Jungst
in
and
apparatus ;
ing
m anuscript,
over
Cone,
this
due
Mr.
also
and t o
the years
this
the
Mr.
in
parents
for
machining
of
his
his
h e lp and
to
Mr.
and
Tom
building
successfully
supply­
e x p e r i m e n t a l work.
R.
M.
Macfarlane
and s u g g e s tio n s .
extend a very
Thompson,
Foremost
guidance has
equipm ent;
the
of
preparation.
t h a n k Dr.
discussions
to
thesis.
Al B e l d r i n g
needed in
to
contributions
assistance
and i t s
Ma r k B a l d w i n f o r
w ishes
his
the
whose s c i e n t i f i c
Knick
he w i s h e s
K a r e n L.
and
thesis
to
of
electronic
nitrogen
stim ulating
Ms.
L.
To n y
and t o
Finally,
friend,
in
also
Mr.
The a u t h o r
f o r ma ny
preparation
building
the l i q u i d
acknowledge
encouragement
advisor,
expertise
the
to
warm t h a n k s
for
her help
for
their
in
to
his
preparing
the
encouraging support
vi
TABLE OF CONTENTS
Chapter
Page
APPROVAL. . ......................................................................................
STATEMENT OF PERMI S S I ON TO U S E ....................................
V I T A .............................................
ACKNOWLEDGEMENTS. . . . .. ...................................................
TABLE OF CONTENTS .
L I S T OF T A B L E S ..................................
L I S T OF F I GURES ...........................................................................
ABSTRACT. .........................................................
i i
iii
iv
v
vi
vii
ix
xii
1
I NTRODUCTI ON........................................
2
RARE EARTH S P E C T R A.....................................................................
F r e e I o n ........................... . ........................................ .
. .
C r y s t a l F i e l d .................................................
.
. .
E u 3 "1" i o n i n E u ( O H ) 3 ..........................................................
4
5
8
9
3
SPECTRAL HOLE BURNI NG ..........................................................
Hole B u r n i n g i n Rare E a r t h s .
..
. . . .
N u c l e a r Qu a d r u p o l e H a m i l t o n i a n .
.
. . . .
E s t i m a t e of Q u a d r u p p l e S p l i t t i n g
i n Eu ( OH) 3 .............................................................................
O p t i c a l D e p h a s i n g T i m e .......................................
13
14
18
4
,
.
.
.............................
OPTI CAL PHASE SWI TCHI NG ....................... ........................
S i n g l e P h a s e S w i t c h . ....................................................
D o u b l e P h a s e S w i t c h ..........................................................
I
22
23
.
26
27
30
5
SAMPLES AND EXPERI MENTAL APPARATUS........................
S a m p l e s ....................................................................
L a s e r and G e n e r a l A p p a r a tu s . . . . . . .
Hole B u r n i n g - E x p e r i m e n t a l D e t a i l s . . . .
Phase S w it c h i n g - E x p e r i m e n t a l D e t a i l s . . .
37
37
38
40
42
6
EXPERI MENTAL R E S U L T S ...............................................................
46
Line w i d t h .
. .
Isotope Shift
.....................................................................
Q u a d r a t i c M ag n etic F i e l d Dependence . . .
Enhancement . . . . . . . . . . . . . . .
O scillator Strength .
. Electronic
Magnetic
Magnetic
Zeeman S h i f t . . . . . . . . .
F i e l d P a r a l l e l to c - a x i s . . .
F i e l d P e r p e n d i c u l a r t o c —a x i s .
46
48
53
54
61
64
67
72
vii
TABLE OF C O N T E N T S - c o n t i n u e d
Chapter
Page
M e a s u r e m e n t of
D e p h a s i n g Ti me
O p t i c a l D e p h a s i n g Ti me .
i n Eu ( OH) g ..............................
.
H o l e B u r n i n g i n E u (OH) 3 ...................................
Q u a d r u p o l e S p l i t t i n g s ..............................................
M a g n e t i c F i e l d E f f e c t s ....................................
M a g n e t i c F i e l d P e r p e n d i c u l a r t o c —a x i s .
Magnetic F i e l d P a r a l l e l to c -a x is . . .
Hole
L i f e t i m e s a n d L i n e w i d t h s .. . . .
7
8
76
79
85
87
92
CONCLUSI ONS . ................................................................................
N a r r o w L i n e w i d t h ...........................................................
105
I s o t o p e S h i f t ...........................................................................
E l e c t r o n i c Zeeman S h i f t . .
Q u a d r a t i c E n h a n c e m e n t .............................................. .
107
D e p h a s i n g T i m e ................................................................
Quadrupole S p l it ti n g s . . . .
FOUR- WAVE MI XI NG AND HYP ERF I NE S P L I T T I N G S
I N L i T b F 4 AND T b ( O H ) 3 ...............................................
I n t r o d u c t i o n ................................................................................
T h e o r y a n d E x p e r i m e n t s . ..............................................
S i m u l a t i o n S t u d i e s .....................................................
121
C o n c l u s i o n s ................................................................................
94
99
104
105
105
106
107
108
109
10 9
114
12 8
A P P E N D I C E S ..................................................................................
131
Appendix
I ....................................................................................
13 2
Appendix
1 1 ..............................................................................
13 4
Appendix
I I I ..... ........................................................................
13 6
REFERENCES
CI TED.
.
139
viii
L I S T OF TABLES
Table
I
Page
S e l e c t i o n r u l e s and c r y s t a l quantum
n u m b e r s f o r e v e n —e l e c t r o n i o n s
i n Cgj 1 s y m m e t r y ............................. .......................................
12
ix
L I S T OF FI GURES
Figure
1
Page
Energy le v e l diagram fo r t r i v a l e n t rare
e a r t h i o n E u r o p i u m ..........................................................
2
Phase
3
N o n l i ne a r
transient,
T >>
4
Nonlinear
transient,
T <<
5
I l l u s t r a t i o n of n o n l i n e a r t r a n s i e n t
f o r jt/ 2 p h a s e S h i f t w i t h i n c r e a s i n g
delay time T . . . . .
........................................
34
S c h e m a t ic diagram of Hole b u r n i n g
e x p e r i m e n t .................................................................................
41
Schematic
transient
Phase switched
....................................................
45
7
5
E x p e r i m e n t a l l i n e s h a p e of
F q ---- > D q
t r a n s i t i o n i n Eu ( OH) 3 ....................................................
51
B e s t f i t s u p e r p o s i t i o n o f t wo g a u s s i a n
p e a k s . . . .
.............................................. . . . . .
52
A b s o r p t i o n of Eu(OH)g
magnetic f ie ld .
55
6
7
8
9
10
Switching
resonance diagram.
7
d i a g r a m of
experiment
.
.
28
. .
.
32
, T2 .....................
a 50
kG
Absorption
12
Ma x i mu m a b s o r p t i o n
13
Ma x i mu m
14
Absorption
15
S i m u l t a n e o u s a b s o r p t i o n s p e c t r u m of
Eu ( OH) g a n d I 2 v a p o r ....................................................
69
Ze e ma n s h i f t of a b s o r p t i o n s p e c t r u m
i n E u ( O H ) 3 , B l l c ...............................................................
70
Zeeman s h i f t of f l u o r e s c e n c e e x c i t a t i o n
s p e c t r u m i n E u ( O H ) 3 , B I I c .........................................
71
17
absorption
.
.
.
57
coefficient,
B I Ic
.
.
58
coefficient,
Bj _c .
.
.
59
coetticient,
a ( m) ,
32
11
16
coefficient,
in
T^.
. .
a(ia),
B I Ic
Bj _c .
. . .
60
X
L I S T OF F I G U R E S - c o n t i n u e d
Figure
18
19
20
21
22
Page
Zeeman s h i f t of f l u o r e s c e n c e e x c i t a t i o n
s p e c t r u m , Bj _ c .........................................................
74
Zeeman s h i f t of
B k. . . . . . .
absorption spectrum,
..................................................................
75
T ransient signal following phase s h i f t
o f it r a d i a n s i n i o d i n e v a p o r ....................... .....
78
Phase swiched t r a n s i e n t s i g n a l
Eu ( OH) ^ ................................................................
81
Semi-log
switched
in
p l o t of n o n l i n e a r p h a s e
t r a n s i e n t s i g n a l i n E u ( OH) g
.
81
Hole b u r n i n g i n Eu(OH)g, r e a d and b u r n
c y c l e ..................................................................................................
86
24
Average
s c a n s .........................................
88
25
A v e r a g e o f 16 r e a d s c a n s
( No h o l e b u r n i n g ) ...............................................................
88
26
Ratio
d a t a . .....................................................................
91
27
E i g e n v a l u e s of Q u a d r u p o l e H a m i l t o n i a n
p l o t t e d a s a f u n c t i o n o f y B / P ..................................
95
153
Quadrupole l e v e l s p l i t t i n g s of
Eu
B k,
| P | = 1 1 . 6 MH z ..........................................................
97
Q u a d r u p o l e l e v e l s p l i t t i n g s o f "*"^*Eu
B l c , | P | = 4 . 5 MHz ..........................................................
98
23
28
29
30
31
>32
Side
burn
of
of
16
read
.
hole f re q e n c ie s r e l a t i v e to l a s e r
f r e q u e n c y , B I I c ....................................................
100
S p l i t t i n g s o f qua d r u p o I e l e v e l s , * ^ E u
Bi I c ..............................................................................................
101
S p l i t t i n g s of qua d r u p o l e l e v e l s , *
Eu
B l c ........................................................................................................
102
L I S T OF F I GU R E S —c o n t i n u e d
Figure
Page
33
Four-wave
34
S c h e m a t i c d i a g r a m of f o u r - w a v e m i x i n g
e x p e r i m e n t ..............................................................
112
E x c i t e d s t a t e s i d e n t i f i e d b y t wo p h o t o n
f l u o r e s c e n c e e x c i t a t i o n ............................
115
Experimental
LiTbF4 . .
120
35
36
37
38
39
40
41
mixing
signal
absorption
Model s i m u l a t i o n s of
signal, gaussian f i t
in LiTbF^.
. . .
Ill
coefficient
four-wave
.
mixing
123
S u p e r p o s i t i o n f i t of f o u r h y p e r f i n e
l e v e l s ............................................................................................
124
Mode l s i m u l a t i o n s
signal, hyperfine
125
o f f o u r —w a v e m i x i n g
f i t ...................................................
C o m p a r i s i on o f i n v e r s e F u l l W i d t h a t
H a l f Ma x i mu m o f f o u r —w a v e m i x i n g
s i g n a l ..................................................................... .....
12 6
Mode l s i m u l a t i o n s o f
s i g n a l , L = 1 . 0 cm .
130
four-wave
. . . .
mixing
xii
Ab s t r a c t
Th e n a r r o w e s t i n h o m o g e n e o u s o p t i c a l I i n e w i d t h e v e r s e e n
i n a s o l i d h a s b e e n o b s e r v e d i n E u ( OH ) ^ .
This t r a n s i t i o n is
q u a d r a t i c a l Iy
enhanced in a m a g n e tic f i e l d and th e
results
are
explained
completely
in
terms
of
second
order
p e r t u r b a t i o n t h e o r y and t h e c o u p l i n g of c r y s t a l f i e l d e n e r g y
levels.
Optical
coherent t r a n s i e n t s are rep o rted here for
the
f i r s t time in t h i s o p t i c a l l y p u r e ,
stoichiometric m aterial.
The o p t i c a l d e p h a s i n g t i m e ,
^2’
s h o wn t o be g r e a t e r t h a n
2 m i c r o s e c o n d s f o r t h e ^ F q- ^ Dq z e r o p h o n o n t r a n s i t i o n .
Hole b u r n i n g , a t t r i b u t e d t o o p t i c a l pumping of nuclear^qua d r u p o l e l e v e l s ,
has been used' to measure the
qua d r u p o l e
splittings
in the e x c ited ,
^Dq ,
state.
Due t o t h e s m a l l
m a g n e t i c moment,
conventional magnetic resonance techniques
have
failed
to
ma k e
this
measurement
in
all
Europium
compounds.
The
ne w
t e c h n i q u e developed, and used in
these
hole
burning
measurements y ie ld s
t h e qua d r u p o l e
coupling
coefficients,
IP I
= 1 1 . 6 MHz a n d I P I = 4 . 5 MHz f o r t h e 1 5 3
i s o t o p e and t h e 151 i s o t o p e , r e s p e c t i v e l y .
The
q u a l i t a t i v e b e h a v i o r of l i n e n a r r o w i n g in
Doublyresonant
t w o —p h o t o n - a b s o r p t i o n i n d u c e d f o u r —w a v e m i x i n g
is
explained
in
terms
of
the
anomalous
dispersion.
The
i m p l i c a t i o n s o f t h i s d i s p e r s i o n r e g a r d i n g t h e m e a s u r e m e n t of
the homogeneous I i n e w i d t h and h y p e r f i n e l e v e l s h i d d e n w i t h i n
the
inhomogeneous p r o f i l e are d i s c u s s e d w ith r e g a r d to
the
p a r t i c u l a r example of L i T b F ^ .
I
Chapter
I
I NTRODUCTI ON
The
which
rare
make
practical
is
earth
it
dominantly
state
is
study
of
general,
rare
earth
have
narrow
efficiency
and
the
variety
lattice
small
A
of
to
the
emission
fact
of
has
as
that
host
The
general
is
a
ground
of
such
the
as
can
to
singlet
begin
the
be
a
electronic
electronic
field
as
s t a t e 1 which
from which
singlet
well
nonmagnetic
nature
practical
solid
for
state
s o me
they
the
hyperfine
state
described
be
ma k e
trivalent
GHz h a v e
linewidths
easily
the
in
a
europium
action.
of
rare
rare
and
These
attractive
ion
earths
a quantum
features,
as
a
laser
host
Absorption
l i n e — widths
in
of
in
into
a
earth
characteristics
trivalent
incorporated
them v e r y
been measured
discussion
in
The
transitions.
can
laser
interest
lasers.
absorption
lattices,
particular
is
position
crystal
and
displayed
3.5
state,
as
properties
manner.
for
1.0
established
the
the
several
a spectroscopic
interactions
of
there
ions
near
m aterials.
as
due
exhibits
singlet
order
straightforward
In
J =O
The
Because
perturbations
in
attractive
higher
structure.
more
a ^Fq ,
an
,
The w e l l
state.
also
Eu
interesting
sense.
electronic
ion,
E u P ^ O-^q 4 a t
properties
the
1.6
and
spectra
K.
s o me
are
2
presented
and
Chapter
explanation
study
of
Chapter
new
of
method
the
of
results
transition
of
are
first
resolved
One
added
of
in
experimentally
The
shape
along
of
with
in
laser
used
before
the
stimulated
by
of
narrowest
In
the
the
167
absorption
of
this
Eu(OH)g and
field.
measured
theory
other
The
the
and
in
change
explained
the
second
the
change
Zeeman
in
terms
and
third
6
the
of
the
is
the
optical
compounds
quadratic
small
work,
of
Eu0
full
profile
possibility
contributions
dynamic
MHz
chapter
a solid.
the
5
F q--- Dq
inhomogeneous
in
of
7
the
shift
s t r e n g t h and
perturbation
the
explicated
of
value
solid.
isotope
major
of
is
any
and
detail
magnetic
oscillator
Chapter
The m e a s u r e d
in
the
.5
was
this
using
CW d y e
chapter
in
explained
is
the
work
used
dephasing
linewidth
FWHM,
optical
the
characteristics
order
this
the o p t i c a l
understanding
external
in
linewidth
discussed
and
6.
chapter
a description
is
switching
details
observed in
experimental
optical
in
maxi mum,
ever
burning
in
in Eu(OH)g.
half
of
by
techniques
described
interest
measurements
followed
hole
phase
Experimental
Initial
width
Optical
are
is
experimental
optical
study
discussion
at
t wo
This
measurement
of
4.
this
width
2.
E u (OH)g .
3 and
chapter
in
in
in
an
in
the
shift
are
of
second
parts
of
6 respectively.
measurement
of
an
optical
dephasing
time
in
Eu(OH)g
3
is
difficult
strength
because
associated
material.
Th e
the
intrinsically
with
the
^ F q <-----> ^D q t r a n s i t i o n
development
ne w
technique
for
the
interest
in
different
of
measuring
making
as
an
of
a
measurement
particular
the
experimental
application
dephasing
these
time
measurements
The
use
of
are
splittings
complement
the
nuclear
resonance
techniques.
of
burning
the
previous
coupling
the
is
ne w
technique
In
ular
fine
Chapter
type
potential
in
of
use
hole
is
of
make
detail
in
the
splittings
this
and
of
and
last
The
measure
Chapter
of
the
section
used
the
given
qua d r u p o I e
experiment
along
the
s o me
quadrupole
and
i n. Eu ( OH) 3
a
6.
partic­
with
in measuring
linewidths.
of
of
Chapter
for
to
mor e
isotopes,
of
6.
nuclear
explanation
measurements
is
phase
concerning
a discussion
experiment
homogeneous
to
of
nuclear
europium
these
ma n y
4.
been
use
an
with
explanation
type
the
3,
the
f o u r —w a v e m i x i n g
of
by
of
a
results
measure
Measurement
to
a ne w
to
recently
Chapter
each
expected
switching
as
in
optical
four
this
renewed
type
Chapter
part
resonance
used
8
in
burning
presented
for
of
in
has
conclusions
in
only
measurements.
constants
described
In
this
the
phase
obtained
magnetic
process
and
given
discussed
has
of
oscillator
switching
transients
E u ( OH) g a n d
results
standard
method
optical
spectral
phase
description
are
of
in
hyperfine
hole
coherent
A
switching
optical
measurements
m aterials.
such
of
small
the
hyper­
4
Chapter
2
RARE EARTH SPECTRA
Typically
consists
of
the
groups
approximately
are
groups
are
quantum
relatively
The
S,
good
ionic
crystals
lines
are
atoms
or
as
narrow
3 GHz ,
solids
at
low
the
possible
to
study
of
of
4f
In
fact,
spectra
observed
those
This
in
the
earths
optical
spectra
separated
about
of
each
of
as
with
of
symbols
each
crystal
within
by
group
200
cm- * .
dominant
of
a
group,
J
by
a
the
group
characterized
for
a
states
set
of
remains
a
number.
of
eigenfunctions
rare
ago. 5
in
means
spectra
the
of
narrow
imply
that,
the
The
or
rare
cases
these
of
in
of
free
Ang­
m aterials
in
features
principle,
a
these
0.01
spectral
in
in
solid
it
with
is
an
ions.
earth
energy
suddenly
ions
spectra
widths
These
atoms
earth
I n many
interactions
free
l a n t h a n i d e 1c o n t r a c t i o n ;
the
the
in
are
lines
range
long
rare
obtained
sharp
by
yet
temperature.
by
ions
groups
observed
occur
exhibited
sharp
J ,
earth
energy
states
molecules.
or
The
of
L,
were
strom,
accuracy
an
absorption
free
the
labeled
quantum
sharp
rare
these
component.
admixtures
numbers
and
over
then
of
lines;
c m- ^
spread
Russell-Saunders
contains
of
1000
generally
These
spectrum
ions
and
drops
at
are
spatial
the
a
result
extension
start
of
the
5
lanthanide
electron
series.
by
The
another
4 f - electron
contraction.
As
increase
nuclear
in
effective
of
the
entire
f-shell
outer
the
the
rare
to
and
increases,
of
the
earth
ions
do
the
4f
in
it
chemical
with
each
number,
the
a reduction
contraction
is
xenon
not
this
causes
this
Ai-
to
series
e le c tro n
and
shells
and
the
of
shell
one
contributes
which
Because
inner
participate
electronic
ions
in
with
n electrons
a
solid
lutecium.
levels
of
H =
where
of
also
of
shielded
by
structure.
interact
the
the
As
a
appreciably
electrons
have
little
bonding.
Ion
The
for
an
environment
tendency
Free
as
shielding
through
charge
charge
closed
consequence
proceeds
Afn shell.*
behaves
5s^p°
with
one
nuclear
im perfect
in
The
( - h 2 / 2m)
the
nucleus,
The
consists
firs t
symmetric
and
of
the
the
n=l
that
structure
for
of
! ; ( r j_)
parts
therefore
itj
electrons,
the
of
do
spin-orbit
the
not
the
electrons
up t o
the
4f
n=l 4
energy
£(r i )si ' I i
i=l
screened
coupling
expression
remove
of
earth
as
e2/ r . ,
J
Z^e
rare
cerium
determines
Z % 2/ r ,
i=l
number
two
xenon
t r i v a l ent
i o n c a n be w r i t t e n
y
i=l
and
of
4f shell,
Hamiltonian
an i s o l a t e d
N is
the
configuration
any
are
of
charge
function.
spherically
the
6
degeneracies
mutual
coulomb
respectively,
structure
Hq f o r
of
the
>> H go
°r
H g 0 >> H ^
total
must
electrons.
are
responsible
4f
which
two
f it
the
the
free
or
neither
H1
HC
of
two
level
terms
as
spin-orbit
be
considered.
to
scheme
these
the
the
LS c o u p l i n g
coupling
into
energy
these
cases
terms,
interaction
ion
a n d H go f o r
lim iting
j-j
two
spin-or b it
Russ e 1 1 - Saunder s ,
in which
last
Labeling
interaction,
are
the
for
electrons.
there
earths
and
The
applies,
c a n be
cases,
used.
so
the
Hamiltonian,
be
diagonalized
approach
from
energy
by
in
4f
interaction
coulomb
Hg
rare
the
the
interactions,
The
of
is
a basis
level
Dieke
and
called
set
to
=
+
determine
intermediate
of
diagram
H SO'
the
coupling
Russell-Saunders
for
trivalent
C rossw hite, 7 is
energy
shown
and u s u a l l y
states.
europium,
in
levels.
Figure
The
as
I.
This
starts
general
determined
7
Eu3*(4f6)
S
D1
2
5D O
Figure
I :
Energy
level diagram
e a r t h ion Europium.
for
the
trivalent
rare
8
Crystal
Field
Whe n
the
experiences
the
charge
lap
effects
are
ion
an
inhomogeneous
also
by
a one
which
removes
free
ion.
For
crystal
smaller
m ultiplets.
the
the
free
earth
field
have
the
So
the
the
the
crystal
crystal
potential.
the
field
field
produced
and
crystal
degeneracy
of
potential
as
a
are
the
produced
the
splittings
over­
the
called
of
by
effects
experimentally
separation
ion
These
splittings
shown
the
Covalency
remaining
ions,
been
crystal
potential
potential
the
energy
a
crystal.
to
of
into
electric
electron
s o me
rare
than
in
contribute
field
treating
introduced
distribution
modeled
the
is
to
free
by
be
ion
obtained
perturbation
by
of
ion.
The
crystal
field
Hamiltonian
V -
I
Bt q
Vt I
is
usually
written
as
U l l 7 l l Z1 )
k, q, i
where
the
fitting
parameters,
the
symmetry,
specify
symmetry
must
be
only
four
as
8
many
the
field
as
27
crystal
this
real.
real
Hamiltonian
f or m
crystal
for
is
,
treated
energy
complex
field
reduced
The
are
field
parameters
equivalent
as
levels.
constants
potential.
to
for
27
f
With
Bg Q,
electrons
time
needed
Bgg,
c a n be
which
specified
and
to
reversal
constants
is
in
considering
w o u l d be
symmetry
B^q ,
parameters
Before
independent
Cgj 1
E ^ Q,
free
the
written
by
total
in
the
9
H where
Hq i s
nomials
of
the
even
Matrix
<B2 0 V2 °
free
calculated
the
doubly
Then
basis
of
the
matrix
the
Hq ,
crystal
spherical
b SO v C0
field
tensor
elements
crystal
states
Hamiltonian,
+
i o n H a m i l t o n i a n 9 and
using
reduced
K o s t e r . 11
+ B4 0 V4 °
+ B6 6 V6 6 >
the
are
poly­
d e g r e e . 10
elements
be
using
H0 +
operator
tabulated
field
energies
corresponding
and
operators
to
diagonalizing
by
are
can
methods
and
Nielson
and
obtained
the
the
V
free.
matrix
of
by
ion
H
on
a
computer.
Eu^ + I o n
in
E u ( OH) ^
This
was
F a u l h a b e r . 12
following
In
the
state
the
in
four
the
to
is
determine
-54
the
I
The
and
cm 1
from
to
of
and
Co n e
are
and
given
the
^Dq a t
± 8 cm
+ 3 6 cm
absorption
^Dq ,
not
very
the
= -Tl
B4 0
were
and
position
^F^
by
parameters
B66 = 6 1 7
s t a t e , ^Fq,
forbidden
from
field
Faulhaber,
D manifold
fluorescence
absorption
about
Cone
the
E u (OH)g
constants.
+ 3 cm *
by
in
crystal
+ 11
ground
transition
fitted
Eu^+
B2 0 = 2 1 1
paper
between
for
W
O
Il
the
The
on
by
done
the
lowest
reported
weak.
But
77K to
at
within
excited
because
they
^Dq a b s o r p t i o n
^Dq s t a t e
transitions
by
4.2K
an
were
that
able
comparing
with
accuracy
the
of
c m- ^ .
energy
level
separations,
from
the
paper
by
Cone
10
and
Fauthaber
explanations
given
as
I2
of
,
which
the
phenomena
observed
J Z
numbers
H = 0
=
1151 cm
this
later
crystal
are
"
=
1753
5dO —
5dI
= 0
=
1771 cm
5D0 “
5D2
U = 0
=
4230 cm
matrix
elements
field
q.
J Z
p
ma y b e
above.
Also,
work
I
a
O
energy
separations
similarly
varies
these,
shift
with
J z = p(mod
label
are
energy
the
These
states
given
measurements
level
339
|i
=
4 4 0 .5
0
^ F
section
increase
of
of
will
also
the
the
be
^Fq to
square
cm-
I
—I
cm
of
q
—
chapter
^D1
6 to
absorption
the
magnet i c
the
in
cm.
^F 1 (i= 0 , I and
—
second
the
of
q
made
separations.
=
=
quantum
q) .
(1=1
function
as
Zeeman
to
selection
crystal
17226 . 8
in
coefficient
observed
used
of
the
=
quadratic
the
level
that
differences,
be u s e d
satisfy
set
such
the
Il
7 p I
a
O
calculate
to
n
1
0
O
in
O
-
energy
will
are
complimenting
- 7F1
must
implies
introduced
numbers
I
k
r-
I ,
This
corresponding
The
cm - I
= I
quantum
( i = 0 ,
in
in
5dI
crystal
this
necessary
5dO
crystal
r U l e
be
follows.
7pO -- ?F2
The
will
field.
used
to
^Dq
transition
which
magnetic
field
of
the
calculate
Th e s e
the
strength.
In
a
calculation
of
the
expected
nuclear
qua d r u p o I e
11
splittings,
it
is
separations.
the
^Fq
For
—— ^ Fg
calculation
just
an
of
and
in
the
Chapter
In
^Fq
as
of
state
tions
are
all
have
dipole
selection
the
out
rules
weak
level
energies
used
this
in
of
the
calculation
in
given
of
are
the
it
last
The
conclusions
are
the
of
is
does
section
for
with
in
the
J
E u ( OH) 3
4 f 11
configura­
unless
The
first
electric
the
magnetic
order
=
0
is
magnetic
the
4fn
to
and
J '
magnetic
=
0
dipole
dipole
below.
considerable
for
importance,
transitions
rules
rules
in
crystal
of
the
enable
nature
takes
these
in
a
with
I
the
the
interesting
t h e o r y , 13
rule
valid
between
is
parity.
symmetry
selection
about
of
parity
still
Table
transition
deals
state
opposite
selection
with
transition
levels
the
techniques
and
the
in
rules
connected
which
by
consistent
levels,
which
the
and
rules
a
t h e ' J u d d —O f e l t
tr a n s ition
consideration.
concept
are
given
of
intensity
spectroscopic
between
by
This
character
draw
energy
splittings,
^ Dq e x c i t e d
between
Selection
to
results
and
admixtures
the
t r a n s i t i on.
directly
states
qua drup o le
existence
forbidden
states
energy
use
difference
Although
the
pointed
transitions
all
the
experimental
dipole
selection
the
^ D q ------^ ^ 2
3.
to
6.
ground
explains
necessary
estimate,
Chapter
itself,
because
in
this
estimate
reinforce
again
of
place.
symmetries
between
t wo
spectra
are
crystal
the
the
in
under
experimenter
energy
levels
The m a t h e m a t i c a l
is
group
theory.
12
Group
theory
originally
available
The
as
developed
in
tables
selection
Eu( OB) 3
are
applied
rules
shown
in
for
for
to
by
all
rare
earth
B e t h e , 14
of
the
but
now
different
Eu^ + , w i t h
Table
crystal
Cg j i s i t e
spectra
it
is
readily
s y m m e t r i e s . 15
s y m m e t r y , 1 * in
I.
H'
I
I
I
I
I
I
I
I
I
I
I
I
2
I
e a
eo
m jt
m Jt
mo
m it
m n
e cr
ea
ecr
m Jt
m cr
ea
e Jt
m Jt
2
ecr
m it
e a
mcr
m Jt
e Jt
I
m it
eo
e Jt
m Jt
mo
ea
-I
m Jt
e a
m jt
e Jt
eo
mcr
P
0
3
0
m<y
e it
3
e Jt
-2
-2
was
-I
T a bl e I . S e l e c t i o n r u l e s and c r y s t a l quantum numbers
f o r e v e n - e l e c t r o n i o n s i n Cgj 1 s y m m e t r y ;
m, m a g n e t i c d i p o l e t r a n s i t i o n ; e , e l e c t r i c d i p o l e
tr a n s ition.
13
Chapter
3
SPECTRAL HOLE BURNING
A
short,
given
general
in
this
saturation
holes
The
latter
description
chapter
and
long
parts
of
calculation
in
using
description
of
Wh e n a
is
saturation,
resonant
laser
frequency
On
the
the
energy
inhomogeneous
other
levels
electromagnetic
line,
a nd no
The
strongly
are
atoms
is
or
one
in
the
is
only
emphasis
on
solids.
focus
on
one
an
would measure
and
a
short
broadened,
supplied
those
be
at
a
energy
and
single
levels
saturated.
A
at
'hole'
line.
a homogeneously
immediately
intensity
falls
broadened
by
the
line,
saturating
throughout
the
produced.
ions
another
in
a
liquid
and w i t h
hole
disappears
very
relatively,
rapid
relaxation
rates
The
be
width measurements.
saturation
solids.
will
will
earth
techniques
will
affected
power,
hole
with
hand,
rare
parameters
power
cause
in
in
inhomogeneous Iy
to
appears
all
line
burning
particular
holes
burning
homogeneous
line
a
hole
chapter
the
electromagnetic
frequency
the
of
hole
spectral
sufficient
lived
this
approximate
Eu(OH) 3
with
of
density
which
is
or
solid
vibrational
quickly
modes.
because
frequently
obtainable
interact
in
Thus
of
a
the
encountered
in
a
an
solid
is
14
advantage
scale
however.
linearly
increase
in
which
is
rates
burning
in
scale
This
as
kind
combination,
m aterials.
hole
can
in
different
mechanisms,
list
s ome,
of
modification
population
storage
one
of
nuclear
o r more
one
which
is
of
the
,
17
responsible
is
than
relatively
m o me n t
it
rapid
use
of
does
not
limit
a result
on
is
hole
hole
is
in
relaxa­
saturation
the
of
a
hole
burning
not
the
variety
particular
should
I 8
,
2 0
long
but
and
lived
holes
it
A
photo-
metastable
populations*1’22.
present
of
solid.
include
saturation . ,
may be
for
nonlinear
dipole
solids
an
burned.
level
hyperfine
above
the
photochemistry
t wo
mean
s a me
the
mechanisms
,
of
burning,
should
saturation
depending
these
19
be
a
solids
physical
pumping
It
because
burning
of
limits
however,
that
the
hole
These
i n many
and
as
which
power
smaller
solid
of
Hole
fourth
solids,
in
such
efficiency.
the
much
effects,
density
i n many
general,
only
the
burning
typically
gases.
tion
with
hole
interactions
Nonlinear
optical
In
is
in
solids,
the
last
rare
earth
rare
earth
solids
The
strong
p u mp
laser
such
that
materials.
Hole
Burning
Two
in
level
Rare. Earths
saturation
requires
the
use
of
interacts
with
the
t wo
ground
and
excited
in
the
intensity
in
the
as
well
particular
as
t wo
hole
lasers.
level
the
system.
burning
system
states
dipole
Wh e n
in
depends
coupling
a weak
on
the
the
population
p u mp
laser
the
levels
between
probe
laser
interacts
15
with
the
absorbing
s a me
t wo
power
of
interacting
strong
by
with
p u mp
transparent.
is
scanned
Saturated
to
the
state
than
the
as
the
This
of
is
levels
are
levels
show
separations
Simultaneously,
width
an
is
of
the
the
in
is
the
saturated
to
be
more
absorption
profile.
this
type
c a n be
in
used
rare
earth
lim itations
the
transfer
the
most
in
from
cases
optical
As
will
rare
be
is
the
ground
broadened
much
narrower
and
redistributed
resonant
nonresonant
of
earth
transition,
these
level
ground
popula­
population, between
regions
excited
or
removed
pumping
corresponding
antiholes
process
population
pumping.
depleted
the
with
inhomogeneousIy
the
level
during
holes
of
with
optical
by
is
frequency
their
burning
depopulated,
hyperfine
from
and
it
probe
linewidth
selectively
hyperfine
enhanced
transitions
hole
selectivity
are
will
lived
the
of
the
full
chapter.
associated
state
a result
tions
this
inhomogeneous
ground
state
measurements
in
as
inhomogeneous
spectroscopy
resonant
appears
detected
homogeneous
population
transition.
absorption
then
long
level
the
sample
the
unless
case,
is
later
profile
also
A hole
the
feel
are
the
the
will
that
so
These
addressed
solids,
that
absorption
it
inhomogeneous
ions
In
through
compounds.
system
beam
measure
In
the
the
p u mp b e a m .
the
level
to
state
increased
in
process.
the
the
Now
spectral
energy
hyperfine
spectral
the
line
level
levels.
absorption
,16
will
appear
at
difference
hyperfine
By
energies
combinations
using
this
important,
usually
of
the
is
a
much
method,
broadened
because
less
than
inhomogeneousIy
solid
atomic
state
ground
and
the
s um
excited
spectral
resolution
spectral
line
the
observed
hyperfine
the
Full
Width
broadened
analogue
and
state
of
is
at
the
achieved.
In
Ma x i mu m,
other
D o p p l e r —f r e e
This
splittings
Half
line.
within
are
FWHM,
words
this
spectroscopy
in
physics.
Hole
burning
has
compounds
because
as
major
experimental
nuclear
magnetic
resonance,
Nuclear
which
electrons
of
field
that
is
ions,
be
this
or
gauss.
applied
in
no
by
nuclear
resonance
earths,
as
they
not
do
magnetic
moments
tings
me a s u r e d
can
be
in
form
is
have
electron
ion.
in m a t e r i a l s
possible
be
experiment
of
in
nuclear
the
rare
Nuclear
hyperfine
paramagnetic
oft he
external
compounds.
the
In
fromthe
any
resonance
measurements
from
s o me
paramagnetic.
than
3+
qua d r u p o I e
particular
greater
been
Eu
conventional
n u c l e u s w h i c h ma y
diamagnetic
determined
are
field resulting
a nuclear
direct
moments
this
in
there
nuclear
weakly
the
This
out
observed only
internal
at
interest
doing
and
on
very
field
reason
in
NMR,
usually
the
a
a million
for
E l l i o t t 2* pointed
diamagnetic
can
particular
experiments
creates
order
of
difficulties
resonance
are
been
resonance,
NQR,
paramagnetic
and
of
to
splittings.
i n h o m o g e n e o u s Iy
is
corresponding
split­
resonance
17
experiments,
estimate
4f
b u t moments
of
the
average
<r- ^>,
in
where
this
r
is
way
the
depend
on an
radius
of
the
electron.
Europium
does
which
produces
state
since
conventional
have
sensitivity.
(IMHz),
tuneable
making
these
hyperfine
structure
that
qua d r u p o I e
Since
are
so
narrow
most
attractive
use
of
examples
this
because
of
due
the
to
direct
has
the
the
techniques
earth
lanthanide
to
lucky
been
linewidth,
existence
of
It
and
is
Zeeman
r : La F^
’
,
investigated.
detected
have
nuclear
been
EuP^
q
used
3O
absorption
they
hyperfine
Except
possible.
coincidence
the
state
hyperfine
contraction,
detect
for
the
P
in
optical
spectroscopy.
not
means
burning
been
optically
splittings
rare
candidates
inhomogeneous
and
ODNQR,
in
the
hole
burning,
have
of
excited
using
and
linewidth,
effects**,
hole
and
because
narrow
and
ground
nucleus,
another
transition
burning
resonance,
the
of
the
used
of
Ground
P r ^ + : LaBrg * 9
hole
be
measured
use
electronic
at
provided
Stark
“
2
and
YAlOg: Eu^t * *
moment,
has
been
the
the
time,
qua d r u p o I e
measure
all
Through
of
field
development
measurements.
P r ^ + :LaCig * 8 ,
small
The
lasers
have
techniques.
the
no m a g n e t i c
splittings*^'**.
e f f e c ts *7
Since
a non-degenerate
NMR a n d NQR c a n n o t
limited
by
determined
for
to
and
lines
are
the
structure
t wo
isolated
possible
i n Ho^+
of
three
things,
a
a very
large
magnetic
nuclear
only
one. i s o t o p e ,
^ ^ H0 . 3
very
11
has
also
been
hyperfine
observed
splitting
inhomogeneous
4
to
sites
in
as
very
a
identify
in
650
the
other
which
tensor
ground
earth
the
m aterials.
interesting
because
ground
nuclear
state
to
of
a
the
large
narrow
quadrupole
particular
hyperfine
have
splittings
complemented
obtained
measurements
of
excited
compounds
E lliott's
this
of
the
would
in
have
also
the
ma n y
states
is
the
qua drup 0 1e
of
rare
particularly
p re d ic tio n *3
tensor
in
perturbed
the
measurements
the
used
sites.
magnitude
and
been
of
understanding
the
europium
of
a
shown a u s e f u l n e s s
of
compounds
states
also
also
individual
the
affect
In
has
and
splittings
has
resonance
deal
contributions
GEz
has
These, e x p e r i m e n t a l
great
in
the
earth
paramagnetic
a
it
measurements
m aterials.
added
burning
and
of
P r ^ + and Eu^+ r a r e
electron
2.7
identification
s ome
burning
of
hyperfine
m aterial,
of
CaF2 : P r ^ + w h i c h
MHz . 33
hole
sensitive
perturbations
Hole
of
spectral
this
0.01%
constant
width
Recently
EuVO^
in
be
that
the
anomalously
small.
Nuc t e a r
Quadrupole
The
tensor
large
between
difference
^Dq a nd
contribution
to
mechanisms.
Since
for
a pure
to
admixtures
Hamiltonian
the
J = O
electric
no
first
level,
of
q
the
excited
in
magnitude
s t a t e s * 0 ' 31
field
order
is
the
of
quadrupole
into
field
the
quadrupole
attributed
gradient
observed
states
of
t wo
coupling
F q and
the
important
gradients
7
to
5
exists
are
Dq
due
wa ve
19
functions
and
a
contribution
caused
by
the
crystalline
lattice.
The
of
t wo
contributions
opposite
the
4f^
from
c m- ^
the
in
the
contribution
to
denominator
coupling
which
and
configuration.
results
4230
s i g n , 3 5 ’ 36
to
The
level,
^Fq from
1151
from
with
the
an
splitting,
excited
of
is
the
smaller
has
than
an
smaller
of
the
energy
qua d r u p o I e
lattice
contribution
of
which
denominator
which
the
are
states
for
energy
state
2
So
the
the
expansion,
a result
cancels
qua d r u p o I e
contribution
cm- ^ .
^Fq is
nearly,
are
perturbation
of
for
^T> 2
the
contribution
due
to
the
^Fg,
admixture.
To
to
derive
the
first
an e x p r e s s i o n
qua drup 0 1e
described
by
tensor,
the
spin
H = P[IZ2 - H I
where
each
m o me n t
of
P is
each
parameter,
of
Cgj 1 s i t e
The
spin
the
t wo
Hamiltonian
* -
the
qua drup ole
is
contributions
splittings
are
Hamiltonian:
to
the
europium
Vy y ) / V z z ,' h a s
symmetry,
different
+ I) /3 + q (I x 2 + Iy2 )/3]
as
in
respective
isotopes.
a value
Eu( OH) g ,
quadrupole
The
asymmetry
between
Vx x = Vy y
( 1 / 3 ) I (I
J * 1 “ P4 £ U )
+ 1)1
+ Pp<j + p I a t
0
and
then
H = P [ I z2 -
where
the
proportional
q = ( Vx x -
For
for
+ p 4 f <2) •
and
I.
q = 0.
20
In
the
above
total
the
expression,
q u a d r u p o Ie
order
in
nuclear
coupling
which
qua d r u p o I e
term
they
is
quadrupole
the
nuclear
to
the
be
however
E u ( OH) 3 .
^iat
lattice.
The
polarization
leads
to
an
closed
tronic
charge
,
is
of
a result
cloud
through
of
the
of
is
J =O
interactions
of
effect
is
experimentally
it
the
effect.
small
induce
which
moment.
of
a
in
turn
The
last
the
admixtures
crystal
in
crystalline
to
distortion
the
a
term
shells
with
in
is
This
tend
quadrupole
state
order
magnetic
by
charges
in
observed
negligibly
caused
the
first
quadrupole
electronic
the
a
so
the
lattice
the
moment.
interaction
external
the
from
the
explained
term
is
I *J ,
contribution
enhancement
P^ £ ^ ^
states
t^e
of
term,
J=2
this
of
be
to
experiments.
which
square
i s
dominant
qua d r u p o I e
distinguished
Fortunately
P will
resonance
unrelated
cannot
contributions
**4 f ^ ^
the
interaction
proportional
the
constant
pseudoquadrupole
to
of
appear.
which
electric
each
elec­
of
the
field.
3 7
The
P4 f (1)
first
= -
order
[ 3 e 2 Q/ 4 1 ( 2 1
x
The
quantity
actual
term
-
theorem
by
an
expectation
is
I)]
given
(I
-
by
Rq )
< r - 3 > 4 f <J I I o l I J >
<J I I a l I J >
Wigner-Eckart
interaction
4f
results
to
operator
value
from
application
the
equivalent,
for
JU
+ D ]
.
evaluate
of .r ~ 3
[3 J z2 -
4f
of
crystal
and
<r ~ 2 > 4 f
electrons
in
the
field
is
the
the
ion.
21
The
expectation
cubed,
<r
value
of
given
by
^ >q> i s
<r ^ > Q = ( I where
Rq i s
term,
f ^^
splitting
The
been
the
,
for
i s zero,
a J
estim ated
by
which
The
last
just
factor.
there
authors
en tirely
tribute
with
to
the
two te rm s
Plat
first
no
order
quadrupole
constant,
to
be
less
in
the
has
than
0.052
contribution
sum.
constant
can
now
be
written
as
terms
thing
to
nuclear
different
be
negligible
(
im portant
This
can
interaction
Pla t
The
radius
l e v e l . 24
coupling
t wo
inverse
<r ^ > 4 f .
because
an
quadrupole
of
Rq )
several
is
compared to the
s um
= 0
q u a d r up o l e
Sternheimer
p seu doqu a drupoIe
M H z 3 6 ' 37
the
atomic
the
2)
+ P4 f
notice
is
electric
that
these
quadrupole
two
parts
coupling
con­
constant
signs.
= -[30(1
-
Y==)
A2 0 I
/
1(21
-
I)
P 4 f ( 2 ) = [ 6 e 2 QA2 °< r 2 > 4 f ( l - C T 2 ) < r ~ 3 > 4 f ( 1 - R q )
x I <20 I I a l I 0 0 > I 2 ] / I ( 2 1 - 1 ) ( E 2 0 - E 0 0 )
Here
the
y „
ground
large,
is
state
Yco = - 8 0 ,
cancels
the
excited
state
the
Sternheimer
where
*
second
^Dq ,
the
the
for
antishielding
contribution
order
Yro
factor
from
contribution
should
be
small
the
lattice.
parameter
Y00
the. l a t t i c e
from
or
P4 f '
even
In
.
equal
is
nearly
In the
to
I,
22
so
that
the
the
second
order
E s t imat e of
values
measurements
the
t wo
an
Splitting
from
for
of
Co n e
isotopes
of
Eu
(I
-
where
A2 0
ct2
)
F a u l h a b e r 1 2 and
have
S ulfate, 37
been
coupling
each
the
of
the
made,
ya
where
one
constant
isotopes
P
can
for
have
a
T00)
state
P implies
ct2
)
= 45.7
—I
^Fq t h i s
gives
= -18.6
a P of
cm *
= 81
cm
pIat
-I
= 101
cm- 2
e OO = 1 1 5 1
quadrupole
E 11
N
O
a
-
"
I
c m- 1
P4 f <2>
which
of
= O .27
A2 ® = 1 9 3 . 4
Plat
the
result
-3
aQ
= 7.41
-
E2 0 -
Q,
and
< r 2 > = E1 0
A2 0 < r 2 > ( I
(I
with
the
I = 5/2.
< r - 3 >4 f
ground
be
E u ( OH) 3
qua d r u p o I e
A2 0 < r 2 > = 1 6 9 . 2
the
only
Ethyl
these ' values
(3/5)
For
in
Europium
approximate
of
will
contribution.
parameters
a2
calculate
splitting
Qnadruoo Ie
Using
and
qua dr up o l e
17.3
Q
MHz
Q
moment,
+
p4
-3.2
£ <2)
MHz
MHz
in
barns.
m - 1 -3 O
for
' Eu a n d - 1 . 2
MHz f o r
Eu,
a first
approximation
of
the
excited
state,
,
23
qu ad ru p o Ie
= 0.
coupling
With
the
constant
energy
E2 0
one
one
obtains
The
(21455
E0 0
for
^^^Eu
coupling
the
it
0 + 4.71
is
It
should
be
as
they
the
are
are
in
shall
The
see
burning
4.5
MHz
chapter
for
^^^Eu
hole
dephasing
method,
single
the
frequency,
a
Q
' Eu
so
is
the
MHz
isotope
is
no
very
values
are
as
predicted
and
is
an
MHz
for
s a me
in
the
Ethyl
especially
good,
true
or
however,
these
P = 11.6
discussed
approximate
<r + ^ > , < r - ^ > 4 £ , ( I - Y00) ,
measurements
for
and
quadrupole
P = 4.5
just
parameters
is
barns
respectively.
this
the
2.45
t wo
MHz
in
Sulfate
for
in
estimates
because
as
constants
we
using
and
for
the
Y 00
last
section
of
6.
Spectral
this
that
—I
for
This
B u rn ing Measurement
optical
so
cm 1
Q MHz.
because
techniques
17225)
Q MHz = 4 . 7 1
no m e a n s
measured
ym = I ,
2)
that
the
agreement
the
151
Eu( OH) g .
state
cm
barns
noted
by
(
-
P = 11.5
the
because
excited
exist.
moment
are
and
— 02)
+ P,4 f
T
Q = 0.95
isotope
(I
with
P
153
and
Ho I e
jrI a t
constants
calculation
hole
P
quadrupole
assume
difference
4230
and
can
width
H,
0f
burning
time
or
where
can
also
transverse
sample
which
Dephas ins
is
T i me
be
to
relaxation
prepared
induces
used
by
time
The
in
the
T2 .
irradiation
a polarization
H = 2 ( Awy+AtOj-) .
measure
the
observed
In
at
a
sample
hole
width
is
then
given
by
convolution
I i n e w i d t h , Awg,
and
dye
instrumental
lasers
of
the
ments
is
the
laser
of
where
=(2/
the
difficult
to
following
make
the
the
by
goes
strictly
to
the
CW
bandwidth
measure­
width
is
then
in
but
are
For
deconvolution
valid
zero,
which
Ao i j .
So f o r
time
lim it,
only
the
in
hole
it
can
be
given
by
the
limit
is
often
reliable
the
display
limit
the
difficulty,
will
true
for
is
diffusion
due
will
ma y
affect
be
faster
depth
read
the
gives
of
one
a
hole
than
to
has
lower
burn
as
been
time
One
the
a function
the
and
of
on
the
slightly
power,
the
and
important
n o n r a d i a t ive
on
to
of
time
scales
measure
the
involves
the
use
of
other
monitor
or
time.
but
optical
is
no
width.
broadening
This
required
successful*',
limit
the
and w i d t h
solution
hole
zero
radiative
depth
the
a hole.
spectrum
technique
the
be
homogeneous
however,
to
still
of
spectral
lasers,
only
is
homogeneous
10 MHz ,
interactions.
t wo
this
5 or
dependent
or
is
MHz.
time
transfer
width
I
dephasing
This
hole
important
which
.
and
The m o s t
because
The
Atoj
instrumental
measurements
low p o w e r
will
hole
the
power
broadened
light,
jtH)
than
the
reasons.
the
power
and
laser
linewidth
greater
negligible.
T 2 = (xrAtojj)
In
widths
of
linewidth,
approximately
necessary,
considered
instrumental
itself,
hole
not
the
a
to
In
in
s o me
most
dephasing
cases,
cases,
time
it
T2 .
25
In
any
(2/nH)
case,
is
if
always
a hole
true.
width,
H,
can
be m e a s u r e d ,
T2
26
Chapter
4
OPTI CAL PHASE SWI TCHI NG
Since
the
discovery
techniques
such
b u r n i n g 4 *,
laser
s w i t c h i n g 44
dephasing
be
time
used
free
all
in
these
to
used
variety
methods
measure
photon
the
to
of
of
transient
dephasing
time
optical
dephasing
time,
T2 ,
the
spontaneous
emission
time
T^,
interact
neighboring
with
environment.
This
T2 s u c h
at
than
that,
the
optical
dephasing
interactions
of
step
this
in
general.
low
diagonal
which
coherence
the
however,
the
atoms
affects
the
or
time
can
lead
time.
development
T^.
is
This
of
a
sample
it
the
the
With
s o me
gas
a rarefied
s imply
=
or
or
related
to
2T^.
Iu
ions
the
rest
usually
interest
understanding
strongly
of
dephasing
or
is
optical
the
time
much
less
in
the
understand
lengthening
and
optical
in
better
lasers
frequency
can
and
is
hole
spectroscopy
atoms
ions
ruby,
optical
T2
So
to
to
is
coherence
temperatures,
lifetime
and
in
m aterials.
the
solids,
,
4 o
measure
where
stoichiometric
echo
decay
switching43,
been
a
the
induction
frequency
have
restrictions
all
as
of
the
shortening
an
important
devices
in
27
Single
P h a se
Switch
Optical
phase
approach
to
changing
the
absorbing
switching4*
coherent
phase
medium,
switched
established
in
the
sample
has
again
at
original
the
before
place,
First
consider
the
laser
field
by
the
emitted
laser
beam a t
mixing
of
as
local
the
After
the
sample
s a me
sample
sample
phase
the
the
wa s
the
laser
are
relaxes
detected.
interaction
of
the
results
laser
is
Once
sample
as
a
sample
the
collinearly
This
an
which
switch,
propagates
with
and
is
polarization
the
through
switch.
the
signal
frequency.
signal
as
rapidly
in
is
small
with
the
homodyne
beam w h i c h
serves
oscillator.
I
et
a sudden
is
by
the
the
Genack
laser.
the
By
polarization
sample
and
transient
powerful
passing
phase
the
frequency
where
and
polarization
the
a
stage
ne w
laser
sample
equilibrium,
driven
phase
taken
of
light
into
preparation
to
the
a
spectroscopy.
laser
phase
to
switch
back
the
the
phase
the
transient
of
relative
is
aI ,
phase
in
shift,
instantaneously
E(t)
a calculation
expressed
shifted
= 2Esin[®t+«j»(t)]
by
of
the
an
the
sample
laser
amount
response
field
<f> a t
whose
t =0
as
= - i [ E + e i<*, t - E " e _ i ( 0 t ]
with
One m u s t
then
solve
the
optical
Bloch
equations
for
the
28
sample
polarization
equations
can
be
P -(t ) corresponding
written
to
E±(t).
The
Bloch
as
(±iA-l/T2 )pi + 2(p 2 i/fi2 )NWE+
P-
2.2
NW
where
- N( W- W0 ) / T 1
a
single
! / T 2 . is
as
off
shown
in
d e s c r ib e s the
Wq i s
field,
ground
Figure
the
2:
frequency
resonance
Figure
2.
degree
H12
is
excited
the
component,
from
N is
of
equilibrium
and
and
(E+P " + E 'P + )h
the
driving
the
of
dipole
the
homogeneous
field
density
population
value
of
of
width
by an a m o u n t A
m olecules,
W
inversion,
W = (P22- P 11) .
inversion
with
m atrix
element
no
laser
between
the
state.
The d a s h e d l i n e i s a s i n g l e f r e q u e n c y c o m p o n e n t
in
the
inhom ogeneous
line
which
is
off
resonance from the l a s e r f i e l d a t fre q u e n c y u
b y a n a m o u n t A.
29
A Laplace
The
result
profile
transform
is
to
then
obtain
can
be
used
integrated
the
signal
over
to
solve
the
equation
inhomogeneous
2 . 2 . 4$
line
S(t),
A n 3 7 2 ( Mn Z c ) W0 NL^ 2 / [ A q ( I + ^ 2 T1 T2 ) 17 2 1 =S ( 0 )
, t<0
S(t) C
2.3
k s ( 0 ) +4 Tr37 2 U n Z c ) (W0 ZA0 ) N L y t T1 T2 S i n 2 C <}>/2) g ( t )
, t>0
g ( t ) = ( l / ( 1 —e / 2 ) ) e x p ( - 2 t / T 2 ) ( —e / ( l —e ) ) e x p ( —2 t / T 2 ) +
( E/ ( l - e ) ( 2 - s ) ) e x p ( - t / T 1 ) ,
for
excitation
at
inhomogeneous
equation
is
length
of
density
matrix
the
width,
2.3,
index
the
go
to
zero
The
refraction
sample.
divided
of
greater
by
the
than
flopping
sample,
off-diagonal
The
line
diagonal
when
the
I/T 2.
In
frequency,
and
L
element
element
is
i s
the
of
the
given
is
in
signal
when th e p h a s e
proportional
to
the
a nonlinear
effect
switch
by_
laser
and
o c c u rs , AS=
intensity
the
linear
squared,
effects
A0---in
the
signal
after
the
phase
switch
can
as
AS = 4 Ti3 7 2 ( Wn Z c ) (W0 ZA0 ) NL Xt T1 T2 S i n 2 C 4 > / 2 ) g ( t ) .
In
n
e = ( T 2 ZT1 ) .
change
be w r i t t e n
much
the
is
as
is
a Gaussian
of
The c h a n g e
S0 t h i s
A0 ,
of
Rabi
parameter
^ 4,
center
^ = 2 E | i 1 2 / b. i s t h e
the
S(0+) - S ( 0 " ) ,
the
general,
the
decay
of
the
n o n lin ear
signal
2.4
is
30
com plicated
the
because
lim it
it
T g ^ T ^ ,
depends
or
on
e -----> 0 ,
both
g(t)
and
Tg.
But
s im p lifie s
to
in
the
expression
g (t ) = exp(-2t/T2)
and
the
Tg.
signal
The
at
I ow
lim it
a
rate
a result
time
the
of
when
optically
this
time
The
the
from
Do u b I e
An
the
Phase
a time
a
T after
shift
and
<f> i s
at
twice
in
with
burned
parameter,
many
at
the
the
rate
switching.
For
ground
the
at
homogeneous
state
probing,
and
hole
During
width
for
burned
add
so
and
of
inhomogeneous
t=0,
rates
the
dephasing
homogeneous
into
solids
twice
superposition.
occurs
from
in
phase
the
relaxation
one
one
decays
prepares
then
the
The
signal
a coherent
is
only
appropriate
process
hole
I / Tg,
as
times
in
the
together,
one
the
signal
decays
r a t e . 46
experim ental
double
second
the
time
functional
given
by47
phase
phase
firs t
dephasing
The
in
by
Swit ch
of
dipole
(Tg/Tj).
state
relaxation
known
application
step
laser
alternative
switching,
decay
probes
preparation
twice
The
the
stage.
very
the
two
phase
laser
is
and
saturation
preparation
and
the
tran sitio n ,
t >0
the
I / Tg.
t <0 ,
a
characterized
<< T^
excited
profile.
at
Tg
is
tem peratures
dephasing
is
decay
application
switching
switch
of
switch.
Tg,
independent
of
,
On e
A Sg
of
on
can
the
the
phase
involves
opposite
phase
dependence
4 7
of
the
polarity
then
at
obtain
ratio,
e =
variables
T
31
AS 2 ( T , <f>) = AS1 C[ l - 4 e x p ( - 2 T / T 2 ) c o s 2 (<J>/2) ] - 2 g ( T ) ( l - 2 c o s 2 (<#)/2] ,
so
by
setting
one
then
(j>= n / 2 ,
so
that
[ l - 2 c o s 2 ( (j)/ 2 ) ]
= 0,
obtains
AS2 ( T , T r m = A S 1 [ [ 1 - 2 e x p ( - 2 T / T 2 ) ] ] .
By
considering
AS 2 ( T ) ,
where
T is
radians,
one
can
transient
signal
T >> T 1 , T 2 t h e
have
in
than
4.
is
T1
In
or
time
less
~ -AS1 ,
after
the
3
the
and
with
switch
second
phase
the
expected
t wo.
extreme
response
the
AS2
phase
second
=
of
transient
shift
change
cases.
the
This
is
in
jt/
w ill
2
the
First
sample
response
AS1 .
of
if
w ill
be
because
as
the
a p p r o a c h e d i n a t i m e T w h i c h i s much g r e a t e r
than
the
it
where
first
of
transient
zero
The
than
time
regarding
second
example,
scale,
different
AS2
is
T2 .
this
much
to
second
visualize
by
Figure
steady state
the
f irs t
decayed
shown
the
2.5
the
T1 or
lim iting
time
AS1
phase
just
is
the
is
second
shown
phase
T 2 , T < < T 1 , T 2 . On t h a t
nonlinear
was
of
case
polarization
before
the
switch.
the
change
first
in
the
cannot
phase
in
Figure
switch
kind
be
of
much
switch,
nonlinear
T
so
signal
32
* ( * ) a V( r )
Figure
3:
S c h e m a t i c r e p r e s e n t a t i o n of n o n l i n e a r t r a n s i e n t
absorption.
T, t h e d e l a y b e t w e e n t h e t w o p h a s e
s h i f t s , i s much g r e a t e r t h a n
or
.
Figure
4:
S c h e m a t ic r e p r e s e n t a t i o n of n o n l i n e a r t r a n s i e n t
a b s o r p t i o n . T , t h e d e l a y b e t w e e n t h e t wo p h a s e
s h i f t s , i s m u c h l e s s t h a n T j o r %2 .
33
From
change
go
in
the
last
the
nonlinear
through
solving
the
for
equation
expression
which
zero
two
a second
nonlinear
for
is
easily
A $2 c h a n g e s
interm ediate
seen
sign
time
T q = T w h e n AS2 = 0
relates
phase
it
signal
some
2.5
which
Figures,
the
shift
dephasing
of
jr/ 2
radians
so
Tq
one
time
to
gives
that
it
=
the
must
T.
By
obtains
the
no
time
at
change
in
signal.
T0 = ( T2 / 2 ) I n (2)
With
by
this
method,
varying
occurs.
simply
an
one
the
The
related
can measure
time
time
to
at
which
when
the
2.6
the
the
a
second
null
dephasing
optical
n/2
occurs,
time,
dephasing
phase
T =
with
time
switch
Tq ,
is
then
T^ g i v e n b y
T2 = ( 2 / l n ( 2 ) ) T q ( jt/ 2 ) .
An
illustration
of
the
top
second
of
the
The
fast
the
n/2
power
bottom
of
achieved
it
the
the
a voltage
amplitude
large,
to
phase
sim plicity
The
can
shown
switch,
of
beam.
may be
is
phase
dephasing
applying
laser
this
figure
experimental
of
of
and
tim es
step
amount
the
at
be
T,
is
of
the
an
of
Th e
5 where
increasing
method
in the
phase
electro-optic
phase
shift
step.
70 v o l t s .
very
Since
is
Typically
is
time
from
lies
the
in
its
measurement
switched
modulator
in
proportional
n radian
the v o lta g e
fast.
the
figure.
applicability
voltage
made
Figure
sw itching
T2 •
to
in
step
by
the
to
shifts
is
not
34
NULL METHOD FOR MEASUREMENT OF T2
Figure
5
The t r a n s i e n t a b s o r p t i o n due t o t h e t h i r d o r d e r
effect
is
illu stra te d
for
increasing
delay
tim es b e tw e e n the f i r s t and second phase s h i f t .
When
null
occurs
in
second
phase
sh ift
T = ( 2 / ln2)T2 .
35
A v e l o c i t y —m a t c h e d
switch
the phase
can
as
be
used
to
fast
in a time
as
300
generate
through
the
is
simple
that
in
the
sample
intensity
detected
pulses
there
for
switching
The
for
of
on
all
plays
an
im portant
laser
stability
are
so
the
upper
lim it
is
approximately
is
that
of
if
the
in
the
The
phase
need
to
on
the
and
echo
to
which
pulser
transm itted
a
change
occurs.
discrim inate
photon
used
time
light
switch
detection
then
the
rate
will
just
display
Two
other
measurements
phase
rapid
time
This
against
technique
bandwidth
role
and
the
2
a
of
in
is
the
nor
is
frequency
is
with
no
the
of
is
also
re stric tio n
upper
the
which
lim it,
is
measurement.
measurement
of
the
dephasing
The
frequency
and
the
is
transient
frequency
In
switching
or
be
signal
of
met
upper
the
described
at
the
time
during
twice
a case
double
nonlinear,
this
stages,
such
stability
must
for
bandwidth,
changing,
probing
valid.
the
reason
the
Mos t
MHz
longer
for
it
a I
co n d itio n s
expressions
but
suited
to
of
phase
the
ideally
stabilized
laser
decay
The
sets
microseconds.
the
is
transients,
duration
actively
for
switching
scales.
preparation
dephasing
the
the
no
of
for
lasers
One,
m onitored,
then
rise
depending
is
larger
longer
CW d y e
earlier,
step
step.
as
measurement
course
the
voltage
optical
valid
lim it
to
is
transients.
method
the
modulator
picoseconds
is
the
equal
when
there
preparation
a need
extracavity
the
the
result
laser.
when
phase
transient
making
switching.
response
36
require
an
absorption
higher
be
optically
coefficient
order
neglected
in
The
true,
power
signal
will
decay
not
true
is
second
and
dephasing
apparent
from
"X
are
be
measured
is
twice
the
w ill
the
anywhere
modern
sample
nonlinear
of
the
that
dipole
is
a
then
these
nonlinear
phase
betw een
day
CW d y e
and
than
If
the
a
so
that
packets
rate,
this
is
but
in
if
the
homogeneous
to
the
and a f a s t e r
conditions,
aL<<!
and
transients
can
picoseconds
lasers.
can
transient
hole
the
switched
100
the
signal,
c o n trib u tio n
two
o is
polarizability
burn
homogeneous
If
length,
dephasing
wider
in
where
X2 T ^ T 2 < < 1 .
w ill
r e s u lt
time.
aL < <I ,
negligible,
which
maintained
with
is
la se r
different
dephasing
the
condition
at
the
expansion
profile
this
microseconds
to
broadening
inhomogeneous
w idth
the
sample,
and L i s
corrections
AS(t).
it
thin
and
2
37
Chapter
5
SAMPLES AND EXPERI MENTAL APPARATUS
Different
eliminate
the
crystal.
All
chapters
were
A short
which
of
in
the
in
chapter
system
the
E u ( OH) 3 w e r e
of
in
the
hole
of
three
samples
is
describe
burning
and
this
to
anomalous
the
following
in
individual
by
samples.
a
section
electronics,
The
last
the
particular
phase
study
single
followed
the
experiment.
in
a
reported
system,
respectively
used
studying
each
the
laser
this
of
results
observed
details,
used
of
possibility
description
dewars
this
samples
t wo
switching
and
sections
use
of
the
in
the
experiments.
S amp I e s
The
in
the
Eu(OH)g c r y s t a l s
following
Mroczkowski
These
crystals
Yale
a
needle
3 millimeters
developed
from
crystals
with
and
europium
the
the
crystal.
a diameter
ions
threefold
by
H.E.
Professor
shaped
long
experiments
in
described
hydrothermally
are
and
of
grown
samples
site
axis
the
The
The
needle
were
obtained
m illimeters.
symmetry
in
technique
were
University.
hexagonal
2 or
with
chapters
used
of
these
c axis
S.
M e i s n e r . 4 * ' 49
W. P .
clear,
typical
by
Wol f
of
colorless,
dimensions
approximately
crystals
corresponds
of
0.3
have
to
the
38
Laser
and
general
A Coherent
Newport
apparatus
Radiation
Research
Corporation
pneumatic
vibration
experiments
reported
solid
bar
of
components
Invar
of
the
the
a
cavity.
when
in
This
used
t wo
laser
is
and
intracavity
fold
mirror.
cavity
MHz
effective
Rhodamine
to
range
the
between
which
input
used
in
stability,
40
and
be
with
ofa
control
a
to
30
the
and was
typical
output
the
the
a
focused
on
with
A or
the
20
GHz
The
of
Brewster
the
mounted
length
of
to w ithin. I
GHz ,
I
cm ^ ,
internally,
laser
at
inch
cavity
frequency
controlled
50 m i l l i w a t t s
a 2
filter.
control
connector
the
1/4
the
has
the
for
piezoelectrically
laser
can
of
into
the
with
is
col l i n e a r
elements
The
is
a
all
bench
birefringent
a
of
on
configuration
linewidth
controlling
an
6 G dye was
not
insertion
t wo
linewidth.
through
improve
last
range
a
and
for
optical
basic
is
plate
plate
table
consists
the
the e l e c t r o n i c
thereby
scan
externally
by
optical
t h e . p u mp b e a m
that
by th e
mounted
used
laser
The
has
laser,
was
as
in which
three
These
dye
continuous
$o
tipping
the
laser.
narrowed
e talons
serves
system
a
4 'xlO’
This
direction
with
bandwidth
here.
dye
cavity
CW d y e
isolation,
which
t h r e e —m i r r o r
dye
599-21
control
or
box.
water
cooled
powers
in
the
wavelength
of
interest.
Wavelength
0 ;85
meter,
monochromator
measurements
C z e r n y —T u r n e r
has
t wo 1 8 0 0
were
made
Double
groove/mm
with
a Spex
Monochromator.
holographic
#14018,
This
gratings
and
it
in
will
the
be
referred
following
as
chapter.
measurements
was
chromator
a 1200
with
to
a
simply
Also
used
M c P h e r s o n Model
groove/mm
simple
from
the
monochromators
was
tube
and
a Keithley
picoammeter,
and
fluorescence
stored
channel
analyzer.
to
CRDS M F - 2 1 I
the
the
hole
output
the
In
with
in
was
the
a Northern
stored
( DEC L S I
11)
stored
monitored
and
E u ( OH) g
glass
dewar
reported
was
initially
at
5000
A.
a.
light
photomultiplier
output
of
then
575
be
for
which
by
was
multi­
transferred
analysis.
In
photomultiplier
the
The
identified
crystal
by
Pope
Scientific.
however,
the
dewar
superconducting
solenoid
Magnetics,
a maxi mum
Tesla.
mono­
Scientific
could
experiments
the
with
meter
the
tube
NS—5 7 5
where
averaged.
switch
solenoid
the
d i r e c t Iy
with
superconducting
shift
experiments,
with
the
mo d e
here,
Zeeman
0.3
blazed
computer
a EG+G F N D - 1 0 0 p h o t o d i o d e .
excitation
6.0
data
experiments,
was
phase
in
The
burning
current
data
416
the
#218
excitation
detected
Spex monoch rom ator
in
grating
In
monitored
the
signal
^Fq
For
the
in
all
crystal
field
fluorescence
a
three
the
was
constructed
was
detected
>^Dq t r a n s i t i o n
in
mounted
was
window
experiments
mounted
in
this
in
tab.
constructed
by
rating
kilogauss
of
60
a
Th e
American
or
40
Hole
Burning- Experimental
For
was
a
the
the
hole
computer
laser
burning
generated
would
averaging
digital-to-analog
laser.
is
listed
The
in
controlled
volt
hole.
The
Figure
the
computer
to
each
II
erase
is
erase
a
a
a
be
the
schematic
to
discussed
listing
spectral
before
of
the
hole.
read
signal
to
and
the
laser
program
also
a
I
generating
a
was
portion
a
scanned
generating
laser
arrangement
6.
for
Also
reading
of
the
pulses
of
Chapter
making
computer
dye
used
the
6,
it
the
the
hole
shown a t
representation
Because
in
by
that
the
beam
I = I q s i n^ ( JtV/ 2) . A s c h e m a t i c
drive
burn-read
then
computer
the
for
controlled
burning,
the
Figure
modulator.
hole
in
interfaced
output
cycle
so
was
which
while
wave
a hole
modulator
was
burn-read
read
this
This
equation
in
used
generated
to
volt
light
shown
wave
E u ( OH) g ,
I .
laser
I
of
by
is
acousto-optic
program
experimental
is
6,
triangular
and
amount
measurements
of
0
the
and
and
the
triangular
computer
acousto-optic
determined
of
burn
converter,
while
between
diagram
The
Appendix
voltage
being
modulated
computer
the
output
experiments,
repetitively
purposes.
the
Details
of
the
the
laser,
in
bottom
modulated
and
the
controlling
the
long
was
lived
also
a new m e a s u r e m e n t .
program
burning
w h i c h was
holes
in
necessary
Appendix
used
to
41
Phoronx/lt'OliSr
L aser
Sample
I3*
PDP-11
computer
Figure
6:
S c h e m a t i c d i a g r a m of h o l e b u r n i n g
experiment.
C o m p u t e r g e n e r a t e d , s c a n o f Dye l a s e r , a n d
A c o u s t o - o p t i c m o d u l a t o r p u l s e s shown a t t he
bottom.
The i o d i n e v a p o r c e l l u s e d i n t h e
Zeeman s h i f t m e a s u r e m e n t s i s a l s o shown.
42
P h a s e S w i t c h i n g —E x p e r i m e n t a l
A
schematic
experiment
was
is
drawing
shown
accomplished
lithium
mm.
Gold
a
end
faces
electrodes
width
of
crystal
given
the
microwave
square
wave
through
modulator
length
of
crystal,
and
Therefore
the
The
is
induced
is
as
in
The
crystal,
the
inversely
crystal
phase
lens
^ F q<
> **Dq
was
used
modulator.
lens.
This
It
focus
was
resulted
lower
mm)
was
of
this
rise
the
then
in
laser
recollimated
a waist
in
of
time
thin
as
to
5805
with
is
dc
light
by
this
of
the
the
thickness.
possible.
specifications
through
the
the
of
index
the
out
of
beam
modulator
time
from m a n u f a c t u r e r ' s
wavelength
line,
wavelength,
to
as
so
tantalate
generated
laser
works
height
chosen
lithium
transit
be
of
form
transmission
shift
to
faces
ratio
e l e c t r o —o p t i c
chosen
transition
to
$2
the
the
26 . 2 / X m i l l i r a d i a n s / v o l t w h i c h
the
and
proportional
is
shift
to
a
coated.
matching,
phase
of
antireflection
0.50
the
3126A
mm x 25
constant
as
Model
consists
The
a 50
which
fast
proportional
the
be
switch
mm x 0 . 6 5
line.
impedance
crystal.
is
to
Inc.
0.5
upper
mm t o
switching
phase
device
and
the
(0.65
device
pulse
the
on
dielectric
matched
phase
optical
dimension
polished
appears
correct
The
This
of
crystal
the
velocity
7.
transmission
the
With
are
optical
Laserme t r i e s ,
deposited
that
(e=43).il
a
crystal
parallel-plate
to
the
modulator.
tantalate
The
of
Figure
with
phase/ frequency
a
in
Details
2.57°/volt
at
A.
cm
A 10
the
Li TaOg
another
10
cm
modulator
of
48
43
microns,
beam
of
a
confocal
diameter
the
crystal
of
be
As
and
most
b = Z jtmq^ / X
at
the
a result
to
The
to
alignment
difficult
the
part
the
and
exit
of
the
approximately
microns
modulator
a
a
faces
aperture,
100
doing
mm,
and
angle
within
of
26
small
an
of
of
entrance
of
within
positioned
distortion.
the
microns
aligned
2 milliradians
beam
150
crystal.
must
parameter
to
is
avoid
probably
phase
switched
experiment;
To
provide
the
voltage
modulator
a Tektronix
picosecond
rise
the
initial
time
to
repetition
rate.
to
FE T s
80
fall
have
a push-pull
times.
varied
by
The
the
phase
between
This
experiments,
by
M F-211
( DEC L S I
accomplished
program
by
which
was
and
then
pulser
driving
the
computer
a
drives
dye
the
of
10
this
the
which
delay
lines
in
shot.of
the
in
the
the
pulse
a
power
rise
and
could
be
circuit.
laser
was
hole
burning
laboratory.
during
up
switched
the
wave.
of
be
phase
externally
triangular
laser
the
wa s
could
nanosecond
pulser
in
it
VMOS
laser
generating
control
150
used
enhancement-mode
as
in
was
experiments,
experiments,
averaged
done,
rate
with
pulses
in
switching
pulser
would provide
pulse
length
electro-optic
designed
with
digital
the
relay
later
pulses
was
11)
reed
arrangement,
each
transient.
to
repetition
n-channel
interchanging
In
scanned
This
Hz
In
A pulser
using
109
700
longer
externally.
volts,
in
and
experiments.
necessary
triggered
Model
pulse
with
the
CRDS
The
s c a n wa s
Th e
computer
phase
switch
44
experiment
is
essentially
Appendix
Since
to
A/0
the
be
from
I ,
pulse
through
I
switch,
transient
transfer
except
the
burn
time
of
these
the
the
with
nsec.
was
stored
digitizer
the
averaged
was
pulse
monitored
reverse
transient
and
which
data.
was
with
psec.
enough
constructed
rise
pulser
the
times
and
transmitted
a n EG+G F N D - 1 0 0
and
with
2-10
this
light
is
burning,
fast
was
fast
a rise
signal,
averaged
not
With
The
bias
hole
was
had
program
short,
a pnlser
independently.
was
for
converter
scales,
switch
This
very
m ultivibrators.
90 v o l t
The
III.
program
pulse
D/ A
time
phase
crystal
the
the
mo n o s t a b l e
controlled
photodiode
than
as
and
be
Appendix
s a me
on
74121
in
the
rise
used
could
given
due
a
interfaced
to
time
the
Tektronix
to
the
of
PI N
less
phase
79 12 AD
computer
to
LiTaO 3
A c o u s t o - o p t i c phase
mo d u la to r
mo d u la to r!
Dye
Laser
PIN
diode
= IE E E
Sample I . 3K
v ( t ) T|
L
For
>> T2 t h e homodyne s i g n a l
f o l l o w i n g t h e Phase Swi tch i s :
S ( t ) oc
Tj T2S i n ^ (<J)/2)exp(-2t/T2)
Figure
7:
Pulse
Transient
digitizer
generator
JVK_
I PDP-11
I computer
display I
S c h e m a t i c d i a g r a m of P h a s e
e x p e r i m e n t i n E u ( OH) g
Switched
transient
46
Chapter
6
EXPERIMENTAL RESULTS
Linewidth
The
first
fluorescence
this
mode
excitation
the
containing
H=+ 1 .
to
This
can
When
the
three
site
ways,
there
at
least
symmetry
in
that
indicates
that
i n i t i a l
indicated
or
our
of
than
in
different
case.
The
crystals
all
three
of
of
the
lines
The
the
to
site
the
^Dg t o
three
range.
that
implied
in
disturb
high
g -----> ^ D g
in
there
that
several
indicate
of
this
appear
fact
then
due
symmetry.
w ill
number
were
range
crystal,
E u V O ^ 34
very
In
perturbed,
perturbed
ways
small
were
in
spectrum
observations
30
are
tran sitio n
be
K.
showed
frequency
earth
spectrum.
the
while
from
which
sites
can
1.3
in
a frequency
GHz
rare
the
at
tran sitio n
a 25
one
in
dewar
transition
the
performed
^ F g -----> ^ D g
dislocations
i d e n tif ic a tio n
that
the
local
symmetry
but
glass
through
in
if
observed
different
are
the
excitation
lines
europium
for
lines
more
were
tran sitio n
perturbation
occurs,
a
scanned
known t h a t
fluorescence
were
the
a
Eu(OH) 3
in
m onitored
impurities,
to
this
was
identified
is w ell
lead
mode
excitation
defects,
on
absorption
was
fluorescence
It
laser
the
fluorescence
7
experiments
the
extra
quality.
that
site
lines
This
tra n s itio n
extrem ely
narrow.
47
ranging
between
167
MHz
and
670
MHz
full
width
at
half
m a x i m u m ; FWHM1
Typical
line
widths
in
many
b e t w e e n 1 5 GHz a n d 3 0 GHz w i d e .
rare
F q <-----> 3 D q t r a n s i t i o n
is
rare
earth
Previously,
inhomogeneous
measured
geneous
in
the
state
ground
state
neighbors
is
or
The
nearest
5 2
in
is
of
compared
however
for
3.5
This
first
narrow
order
because
its
to
by
a magnetic
lines,
1 67
t r ansitions
was
inhomo­
affected
these
known
GH z ,
Thus
as
other
narrowest
non-magnetid.
neighbors
narrowest
investigate
taken
to
Bjorklund.
the
Gary
using
normally
an
be
5 3'
the
absorption
other.
Roger
several
MacfarTane*
capable
laser
same
the
the
J=O
nearest
ion
would
MHz w i d e ,
in
other
the
one
but
sideband
detection
of
a
is
rare
the
crystals
experiments
called
weak a b s o r p t i o n .
is
frequency
frequencies
as
in
and Gary
technique
beam
band
intensity,
for
very
laser
side
different
Bob S h e l b y ,
developed
measuring
beam
profile,
Heterodyne
has
of
technique
The
of
further,
Bjorklund
th is
m odulated.
this
I BM R e s e a r c h L a b o r a t o r y
with
FM s p e c t r o s c o p y
the
understood
level
the
than
transition,
m agnetically
narrow
collaboration
into
this
narrower
are
m aterials.
To
In
be
not
next
exceptionally
were
can
electronic
affected.
earth
for
usually
E uP ^ O ^ q c o m p o u n d .
profile
ground
be
width
compounds
In Eu^+ compounds
the
transitions.
earth
the
laser
w ill
scans
becomes
weaker
than
beats
between
the
48
modulated
the
and u n m o d u l a t e d
d e te c tio n
experiment
of
did
very
not
show
F q ---- > j D 0 t r a n s i t i o n
in
one
this
on
thousand
experiment
this
that
the
Isotope
did
not
add
of
MHz
as
is
be
these
in
it
was
new
did
in
167
less
laser
anything
to
the
the
singlet
of
several
be
allows
lin es.
This
that
than
the
part
Although
information
reconfirm
the
the
one
beam.
to
the
fact
neighborhood,
and
MHz FWHM.
the
discussed
in
of
section
determine
that
the
in tr in s ic
site
in
with
the
states,
the
it
this
a nuclear
and
The
strength
the
the
of
. T his
two
the
narrow
can
which
state
be
f irs t
or
observed
on t h e
an
different
The
sites
167
w ith
^D q e x c i t e d
section,
of
chapter,
line,
splitting
structure
splitting
this
structure
perturbed
follow ing
for
shows
perturbations.
la ttic e .
absorption
narrowest
crystal.
apparent
w o u l d be
oscillator
of
superposition
state
the
a sso c ia te d
Eu(OH) g
different
the
lin e
because
^Fq ground
explanation
is
dependence
next
c r y s ta llin e
possibility
in
considered
of
unlikely
quadratic
interesting
Since
dependence
as
the
beam,
w hich means
the
associated
each
result
three
the
axial
most
lines.
are
in
transitions
the
to
was
unperturbed
could
ab so rp tio n
Eu(OH)g,
discussed
possible
F WH M,
line
laser
Shift
strength,
was
in
the
the
E u ( OH) g a b s o r b s
light
By m e a s u r i n g
it
in
three
of
any a b s o r p t i o n ,
the
were
narrowest
weak
of
tran sitio n
there
portions
the
of
strains
quadratic
magnetic
makes
however.
electronic
field,
this
an
Another
ground
state.
last
On t h e
section
the
cause
Finally,
shift
basis
of
of
the
isotopes,
47.82%
this
the
structure
spectral
1 5 3 Eu
have
because
may
s h ifts
linewidth
the
transition
the
> Dg
f irs t
isotope
to
time
shift.
measure
estimates
this
that
fluorescence
Eu(OH)3 .
the
with
the
shift
to ta l
accounting
8,
stable
is
compare
52.18%
with
transitions.
in
Eu(OH)g,
the
it
with
Because
it
clear
the
way
the
ma y
be
of
an
evidence
firs t
and
state
resolved
compared
clear
provide
europium
so lid
clearly
narrow
there
in
isotope
chance
theoretical
the
experim ental
line
shape
in
excitation
for
the
tran sitio n
in
this
of
line
the
is
two
167
and
46%
peak
the
left
high
energy
the
total
area.
th is
it
is
not
does
a
the
peaks
is
best
shown
fit
in
e a c h h a v e FWHM o f 9 6 MHz
the
of
abundances,
on
MHz a n d
gaussian
two g a u s s i a n l i n e s
energy
Although
isotope
a
p ro file .
an
of
as
shows
area
for
in
the
e x i s t . 54
These
low
two
in
eliminated
with
s h ifts
optical
so
also
be
abundances
sm all
the
is
and
superposition
the
of
may
T h e FWHM o f
F i g u r e 9.
seen
which
It
Figure
for
in
are
with
are
also
associated
There
been
measurements
inhomogeneous
Isotope
inhomogeneous
Fq
be
1 5 1 Eu,
never
these
can
the
line.
and
burning
this
in
re s p e c tiv e ly .
m aterials
hole
chapter
s tru c tu re
the
of
of
accounting
peak
54% o f
the
rig h t
.
p e rfe c t
provide
on
for
some
m atch
with
the
m otivation
for
50
further
experiments
to
results
with
m e a s u r e m e n t s 55 a n d
current
measure
this
shift
and
compare
t h e o r i e s . 54
the
51
Figure
8:
E x p e r im e n t a l l i n e shape
fluorescence excitatio n
FWHM = 1 6 7 MHz .
o f t h e ^ F q ------- ^ D q
l i n e i n E u ( OH) 3 .
52
Figure
9:
B e s t f i t s u p e r p o s i t i o n o f t wo g a u s s i a n p e a k s .
Peak
on t h e l e f t ,
high energy sid e,
54% o f
total
area.
P e a k o n t h e r i g h t 46% o f
total
area.
Isotope abundances,
^ Eu
52. 2%,
1 5 1 Eu 4 7 . 8 % .
53
Quadratic
Optical
crystal
i o„n.
a
transitions
field
defect
defect
different
levels
of
A
will
field
the
distortion
potential.
in
forced
the
For
the
Eu5
crystal
symmetry. * 7
allowed
i n ma n y
to
the
optically
the
The
are
active
small
a
in
field
due
with
the
of
terms
rare
and
a
of
earth
thereby
change
change
expansion.
optical
are
that
intensity
i n ma n y
crystals.
This
to
in
distortion
associated
appears
cases
dipole
identify
a local
S y m m e t r i e s , * 6 an
shown
vicinity
interpreted
crystalline
field
often
immediate
in
the
the
energy
site.
levels
magnetic
difficult
be
leads
dipole
have
ion
transitions
of
s o me
field
measurements
can
field.
then
Dependence
the
create
symmet r y
electric
crystal
to
perturbed
affect
exist
sites
crystal
crystalline
the
adjacent
Field
in
transition
sites
Th e
Magnetic
the
odd
If
when
these
transitions
defect
crystalline
term
terms
can
exist,
between
the
Experimental
^ F q <-----> ^ D q t r a n s i t i o n
it
of
the
a
harmonic
possible.
the
to
is
allowed
forced
s a me
transitions.
intrinsic
the
electric
order
This
crystal
by
of
of
site
dipole
magnitude
makes
field
it
as
very
transition
54
Enhancement
It
of
wa s
these
applied
magnetic
states
the
of J=I
vary
as
through
into
strength
square
Eu(OH)g
magnet
60
crystal
dewar
magnetic
with
field
microns
the
fluorescence
magnetic
the
effect
it
when
was
at
inserted
keep
the
in
signal
50
kiIogaus s
by
almost
d e n s ity
zero
c-axis
was
the
the
three
photomultiplier
scale
an
magnetic
of
s
F q- D
field
was
to
a
wa s
adjusted
for
to
along
there
a n u m b e r /2 n e u t r a l
used
which
strength.
to
a
function
field
the
of
line
of
was
a
a
the
very
changed.
With
full
scale
density
filter
monochromator
of m a g n i tu d e
result
By m o n i t o r i n g
magnetic
excitation
then
a diameter
sample
that
Spex
This
parallel
obvious
the
I).
identified.
“N
superconducting
the
as
nearby
easily
crystal.
signal
dipole
transition
q
focused
the
the
would
fluorescence
tube.
transition,
state
a.magnetic
was
one
Figure
with
orders
f i l t e r
of
if
crystal
the
that
(see
in
the
in
of
the
magnetic
of
voltage
field,
front
on
7
the
mounted
placed
photomultiplier
deflection
J =O
the
excitation
field,
dramatic
the
The b e a m w a s
was
to
state
c-axis
Cone,
admixture
enhancement
was
the
axis.
and
perpendicular
the
this
Dr .
enhance
for
of
of
intrinsic
the
states
E x p e r i m e n t a l Iy
On e
would
ground
the
help
the
^Fq
oscillator
should
the
was
field
strength
into
admixture
an
with
transitions
transition
in
realized,
field
signal
in
of
20
had
order
to
kG.
At
changed
and a number 3 n e u t r a l
avoid
s a t u r a t i n g
the
55
This
implied
phenomenal
that
detected.
This
transmitted
photodiode.
the
change
detected
There
of
50
would
in
wa s
no
as
the
' F q ---- > D q
was
easily
done
the
crystal
through
The
that
result,
detectable
function
absorption
by
with
in
The
45% o f
the
magnetic
could
an
Figure
at
at
300
laser
the
10,
zero
zero
be
field
d i r e c t Iy
laser
light
EG + G F N D - 1 00 PI N
transition
absorption
this
of
monitoring
excitation
however,
almost
a
shown
occurred.
fluorescence
kilogauss,
absorb
change
demonstrates
could
magnetic
field.
micron
only
In
thick
be
field.
a field
crystal
light.
5 0 0 MHz/div.
Figure
10:
^ F q -----> ^ D q a b s o r p t i o n p r o f i l e
of E u ( OH) g
c r y s t a l a t 1 . 3 K i n a 50 k g a u s s m a g n e t i c f i e l d .
56
Al t h o u g h
further
did
demonstrate
measurements
change
The
this
was
qua d r a t i c a l Iy
absorption
magnetic
were
field
p ro file
intensity
using
law
Beer's
in
dependent
was
strength.
transmitted
made
a
raw
physical
order
on
data
to
the
recorded
The
into
large
sure
field
as
was
absorption
be
a
change,
this
strength.
function
transformed
of
from
coefficient,
a ( m) ,
I(a>)=I0 e_a((o)L
which
i mp l i e s
a( a>) =
where
a ( m)
is
the
cen tim eters,
transmitted
I
laser
thickness.
absorption
then
log
2.0.
the
and
This
As
absorption
to
the
square
with
a(t o)
at
for
as
a
11.
function
shown
through
in
or
I ( to)
is
the
is
the
crystal
5 kG i n c r e m e n t s
Plotting
of
the
magnetic
12.
This
data
points
has
quadratic
is
a
dependence
o sc illa to r
from
t he maximum
Figure
the
the
c m,
inverse
field
a log-
slope
of
of
the
on
the
measuring
the
strength,
strength.
check,
coefficient
the
result
establishes
further
c —a x i s
of
line
L= 0 . 0 3
Figure
in
in te n s ity ,
and
in
coefficient,
field
a
result
c o e ffic ie n t
laser
the
given
the
then
absorption
magnetic
of
coefficient
gives
plot
the
intensity,
A plot
1 0 kG t o 5 0 kG i s
ab so rp tio n
is
q
)/L
ln(lQ/I(ti))
of
with
the
magnetic
each
field
this
was
the
magnetic
crystal.
field
plotted
repeated
This
as
in
by
field
also
illu strate d
Figure
14.
perpendicular
varies
in
as
Figure
the
13
CM ' 1
IOO MHz/dlv.
Figure
11:
Absorption
Magnetic
between
to
coefficient,
field
1.0
c - ax i s ,
T
B
changed
and
I Ic .
5.0
a(w),
in
T .
0.5
in
inverse
Tesla
Magnetic
centimeters.
increments
field
parallel
5 8
o
5
£* .a
O -6
J
.4 a .6.7431
2
3
MAGNETIC FIELD (TESLA)
Figure
12:
Ma x i m u m a b s o r p t i o n c o e f f i c i e n t , a (a>) m a
with
magnetic
field parallel
to c - a x i s ,
B I I c.
Slope= 2 .0 .
ABSORPTI ON
coefficient
59
■ ■■I
.3
.4
J
.a .7 4 J I
2
3
4
3 6 7 • SIO
MAGNETIC FIELD (TESLA)
Figure
13:
Ma x i m u m a b s o r p t i o n c o e f f i c i e n t ,
magnetic
fie ld
p erp en d icu lar
B
c.
Slope = 2 . 0 .
to
max* w i t h
c- xi s,
CM-'
30.0 r
25.0
20.0
5 0 0 MHzAtIv
Figure
14:
Absorption
c o e f f i c i e n t , a ( to) , i n i n v e r s e
c e n t i m e t e r s . Magnetic f i e l d changed in 0.5 Tesla
increments
b e t w e e n 1 . 0 T and 5 . 0 T .
Magnetic
f i e l d p e r p e n d i c u l a r to
c- ax i s .
61
T wo
From
things
Figure
should
12
and
be
noted
Figure
13
in
the
coefficient
at
50
kG
is
17.0
cm-1
and
^
for
B
J_ c
in
Figure
2 8.6
cm
theory,
the
one
would
inverse
energy
the
level
^Fg
[i = 0
absorption
Ji = I
of
the
at
339
energy
at
level.
4 4 0.5
cm- * ,
it
the
function
of
field
can
perturbation
theory
also,
Zeeman
Oscillator
From
number
would
the
axis.
be
section
of
I I c
be
the
will
this
the
to
^ F q (i = l
state
than
sense
that
the
admixture
with
the
notice
profile
be
12
perturbation
ground
makes
t o'
Figure
proportional
the
This
in
Since
is
is
from
that
plotted
frequency
calculated
and
can
absorption
also
be
because
by
Dr .
indicate
this
magnetic
field
states
For
thing
absorption
From
to
figures.
discussed
with
shift
second
in
in
as
a
order
detail
in
chapter.
Strength
important
computer
horizontal
shift
for
absorption
on t h e
the
larger
other
frequency
B
difference.
to
The
and 14,
change
four
maximum
13.
closer
is
last
for
is
coefficient
11
the
cm ^
state
energy
Figures
expect
the
the
operator
transformed
in
this
the
and
the
into
oscillator
J=O
had
of
the
c a lc u la tio n
been
calculated
of
the
two
interpretation
admixture
of
the
or
f
is
on
a
numbers
concerning
J=I
crystal
magnetic
moment
state.
calculation,
R u s s e l l —S a u n d e r s
the
strength
This
a comparison
dependent
computer
the
number
accuracy
field
the
c a lc u la te d .
Cone,
into
data,
intermediate
the
coupling
coupling
case,
was
representation
62
using
the
free
Crosswhite.5*
moment
the
ion
wave
functions
gave
the
intermediate
between
the
This
operator
oscillator
strength
and
could
be
^ Dq
of
Carnall
coupling
states.
calculated
and
magnetic
From
using
this
standard
t e c h n i q u e s 59
f Md -
( Sn^mc/ 3 h e ^ )
f MD =
( 4 .028xl0-1 1 )
k is
where
and
n
is
result
the
the
for
the
k
I ( - e / 2 m c ) < F ^ q | L + 2 S I Dq q > I ^ n
k n
transition
index
of
I <F1 0 IL + 2 S | D0 0 > I 2
energy
in wavenumbers,
refraction,
7
transition
for
results
the
factor
the
in
D q— ' F ^
of
an
^ D q--- > 7 F
q
o scillato r
transition
(0.0032)2,
the
transition
The
computer
and
15
(0.201)2
strength
by
resulting
at
= 1.5.
5
F ^ ---- > D q , wa s
I <F1 0 I L + 2 S | D 0 0 > I 2 =
This
n
k = l 67 85 cm ^
of
f j j D = 4 . 0 9 x I O- **
including
oscillator
the
admixture
strength
for
kG i s
^MD = 4 . 1 x 10
The
experimental
calculated
by
standard
f Md -
o scillator
the
number
lattice
density
of
( 2 m c 8 q / n e ^ h ) ( I / n ) ( I / Nq )
4 . 0 0 x 1 0 ^ / Nq
constants
the
europium
integration
of
also
be
ions
can
the
( m ) dm
a (d)) da)
a = 6.32
Nq = 7 . 9 6 5 x l o 2 1
and
can,
techniques*
f Md From
strength
A and
be
c = 3.63
A
6X
the
calculated,
ions/cm^
absorption
coefficient
over
the
63
experimental
profile
gives
J a ( M) d to = 0 . 7 05
This
implies
an e x p e r i m e n t a l
oscillator
fMD = 3 . 5 4
The
computer
dependent
which
result
dipole
the
in
measured
and
confirm ation
of
matrix
L + 2 S.
This
strength
calculated
with
of
the
the
th is
this,
.
strength
of
.
o scillato r
admixture
Considering
agreement,
x 10-13
nonzero
oscillator
magnitude.
This
small
operator,
calculated
of
on
calculation
cm ^ GHz
coefficients
elements
means
can
quadratic
adm ixture
the
easily
the
oscillator
strength
of
of
the
states
magnetic
magnitude
vary
by
agreement
strengths
dependence,
process
of
an
in
the
order
between
is
is
the
excellent.
is
another
E u (OH)g .
64
Electronic
As
mentioned
theory
predicts
function
in
the
and
This
field
width
so
is
calculated
From
correction
Because
an
ideal
mechanics
energy
is
AE = <f 0 0 I h 1 I f 0 0 > +
where
and
F qq
p=0,
and
and
E qq
are
wave f u n c t i o n
of
Fj
energy
and
diagonal
the
the
matrix
energy
H1
is
or
text
shift
the
square
of
the
line
demonstrates
to
measure
the
element.
6 2
the
second
order
by
state
wave
respectively,
J ,p crystal
Ej
Zeeman
a Zeeman
I <f 0 0 I h 1 I f 1 0 > I 2 / ( E 0 0 - E 1 0 )
E q q =O,
by
wave
calculation
ground
elements,
shift,
AE =
where
the
state
inhomogeneous
matrix
given
the
energy,
to
as
opportunity
any
quantum
perturbation
ground
the
following
coupling
the
the
appears
intermediate
to
chapter,
proportional
the
E u ( OH) g p r e s e n t s
to
change
strength.
narrow,
Shift
previous
correction
which
magnetic
that
a
the
energy.
energy
is
in
Zeeman
field
The
so
function,
and
level
where
is
perturbation
is
the
denoted
by
H1
no
<Fq q |H1 I F qq> e q u a l s
shift
J =O
has
zero
and
then
I <f 0 q I h 1 I f 1 0 ) 12 Z ( E 0 0 - E 1 0 )
the
Zeeman
term
in
the
Hamiltonian
which
c a n be
written
H1 =
and
pg
=
e hZ 2 m c
^
^
( e Z 2mc ) B ' ( L+2 S)
is
the
Bohr
= | i gB ( L z + 2 S z )
magneton.
B
is the
applied
65
magnetic
field,
operator.
In
matrix
B — Bz ,
LS
element
The
state
is
^ n=0
^F q , and
k-ilogauss,
so
or
and
( L Z+ 2 S Z )
is
the
R u s s e l l —S a u n d e r s
magnetic
coupling
mome nt
the
<F o 0 *L z + S s S z *F 1 0 > = 2 . 0 0 2 3 2 . $9
energy
the
level
Bohr
the
is
440.5
magneton
change
in
is
energy
c m- *
above
the
ground
Hg = ( l / 2 1 . 4 2 ) c m ~ ^ "
per
is
AE = - ( 2j i gB) ^ / 4 4 0 . 5 cm- *
= - ( 2 / 2 1 . 4 2 ) 2 ( c m - 1 ) 2 / ( k G ) 2 ( I / 4 4 0 . 5 cm- 1 ) B2
= - ( l . 9 7 9 x l 0 " 5 c m' ' 1 / ( k G) 2 ) B2
AE = - ( 0 . 5 9 3 7 4
This
implies
field
of
energy,
for
50
and
this
would
be
narrow
check
a
total
Zeeman
kilogauss.
This
if
not
it
were
shift
is
for
an
in
Eu(OH)g
impossible
to
measure.
means
interpretation
that
and
of
1484
that
so
small,
This
lucky
has
an
ideal
understanding
of
MHz
small
fact
is
one
only
extremely
the
tran sitio n
linewidth,
the
MHz Z( k G ) 2 ) B2
the
for
change
a
in
line width
167
MHz ,
it
coincidence,
opportunity
this
to
admixture
process.
Measurements
described
1265
MHz
num ber,
in
transformed
and
this
detail
+. 3 0
the
of
this
presently,
MHz .
To
the
calculation
gave
compare
elem ents
into
Zeeman
for
the
the
which
will
be
total
energy
shift
of
calculations
LS
intermediate
resulted
a
shift,
coupling
coupling
i n a new v a l u e
eIement,
< F 0 0 1 ( L Z+ 2 S Z ) I F 1 0 > = 1 . 9 6 5 .
with
case
this
were
representation
of
the
matrix
66
On e
must
causes
an
5
state,
gives
also
realize
that
admixture
Dq .
of
A sim ilar
a matrix
an
external
J =I
states
calculation
magnetic
into
for
the
the
field
J =0
also
excited
excited- s ta t e s
element,
<d 0 0 I ( l z + 2 S z ) I d i o > = 1 . 2 8 0 ,
for
the
the
excited
because
energy
excited
state
state
the
than
^ D^
the
admixture.
is. in
fi = 0
the
s a me
excited
Dq e x c i t e d
So
the
energy
direction
state-
is
but
1771
cm
shift
mu c h
^
for
smaller
higher
i n
state.
A E = ( I . 2 8 0 / 2 1 . 4 2 ) 2 B2 ( 3 0 , 0 0 0 M H z / c m - 1 ) / ( - 1 7 7 1 c m _ 1 )
AE = - 1 5 1
Since
each
field
strength
the
of
the
difference
energy
increases,
given
MHz
levels
the
1265
compares
MHz + 3 0
very
MHz .
is
50kG
depressed
measured
as
Zeeman
the
shift
magnetic
will
be
shift
of
by
AE = ( 1 4 3 3 - 1 5 1 )
which
at
well
MHz = 1 2 8 2
with
.
the
.
MHz
measured
.
Zeeman
67
Magnetic
Field
Parallel
To m e a s u r e
required;
narrow
one
the
This
is
only
measurement
of
magnetic
recording
minute.
shift
To
the
sample
100
was
and
shown
at
50
kG
spectrum
in
of
in
15,
as
function
and
of
an
the
iodine
6,
recorded
the
is
shown
absolute
field.
The
about
the
in
a
pressure
t wo
the
cm,
diagram
the
An
example
and
the
of
of
this
inputs
from
of
the
this
spectrum
absorption
15(b).
shown
and
glass
different
spectrum
calibration
result
Zeeman
at
Figure
one
recording
Eu( OH) g a b s o r p t i o n
15(a)
because
10
where
a
change
Eu( OH) g s a m p l e ,
schematic
a
in
a
simultaneously.
where
scans,
for
and
to
takes
in
CW- d y e
from
vapor
The
very
completed
simultaneously
signal
Figure
599-21
necessary
field
are
calibration
be
between
from
in 'F ig u re
I 2 vapor
a relative
by
the
increments,
each
drift
analyzer
shown
both
at
is
MHz / h o u r
only
is
things
transition
the
+.1 0 0
k ilo gauss
signal
cell
Figure
is
5
millitorr.
iodine
because
time
made
with
frequency
The
excitation
shown
F q <-----> D q
can
shift
excitation
multi-channel
is
a
in
were
f i l l e d
the
shift
period.
two
mentioned,
w ith in
frequency
fluorescence
experiment
to
small,
been
absolute
Zeeman
time
of
this
necessary
stable
avoid
approximately
of
is
measurements
cylinder
an
frequency
fluorescence
the
width
field
the
shift
already
is
the
one t o two h o u r
the
has
other
laser.
laser
that
The
c —a x i s
an e n e r g y
inhomogeneous
Eu( OH) ^•
to
This
of
the
in
Figure
gives
frequency
16
is
68
the Zeeman s h i f t
increments
plotted
of
t h e ^ F q to ^Dq a b s o r p t i o n a t 5 k i l o g a u s s
between
on
dependence
a
50
k i logauss
log-log
on
graph,
t he. m a g n e t i c
measurements
can
be
in
that
field.
measurement
+ 30
MHz
c —a x i s
of
record
was
the
17,
the
from
quoted,
crystal.
signal
for
the
which
for.the
the
strength.
because
to
Figure
field
showing
monitoring
sensitivity
in
again
kilogauss.
by
signal
shown
10
made
excitation
The
and
case
right
fluorescence
the
Zeeman
magnetic
is
adequate
zero
magnetic
excitation
shift
field
accurate
fluorescence
there
down t o
is
quadratic
Mor e
the
This
of
1265
parallel
to
is
MHz
the
Absorption
c
30
5 0 0 MHz/dIv.
Figure
15:
S i m u l t a n e o u s a b s o r p t i o n s p e c t r a of E u ( OH) g and
I2 vapor.
(a)
Abs o r p t i o n s p e c t r u m of
transition
i n E u ( OH) ^ i n a m a g n e t i c f i e l d o f 50 k G .
(b)
Abs o r p t i o n s p e c t r u m of I 2 v a p o r
ZEEMAN
SHIFT (MHz)
70
.3
.4
J
^ .7 3 . 9 I
MAGNETIC FIELD
Figure
16:
5
6 7 » 9 10
(TESLA)
E l e c t r o n i c Z e e m a n s h i f t o f t h e ^ F q ---- > ^ D q
a b s o r p t i o n spectrum in Eu(OH)^.
Dat a p o i n t s
e ve r y 0.5 T e s l a between 1.0 T and 5. 0 T .
Bile.
71
ZEEMAN
SHIFT (MHz)
3000
.3
.4
J
MAGNETIC FIELD
Figure
17:
4
.8 .7 .8 .9 I
9 6 7 8 9 (0
(TESLA)
E l e c t r o n i c Zeeman s h i f t
of f l u o r e s c e n c e
e x c i t a t i o n signal corresponding to
q---- ^ Dq
t r a n s i t i o n . B i l e , t o t a l s h i f t 1 2 6 5 MHz.
72
Magnetic
Field
A check
can
he
shift
P e r p e n d i c u l ar
of
the
by
crystal.
the
a dmixt ur e is
from
In
the
closer
to
give
larger
a
closer
19
to
the
In
matrix
with
case
the
th 6 ?F1
5 D1
to
the
is
i t
is
Zeeman
c-axis
which
H= I
33 9 cm.
101.5
state
state
Zeeman
intermediate
of
except
=O s t a t e
D^ n = 0
calculated
the
same,
P
measured
elements
the
Since
the
total
is
state
The
than
the
I
than
shift.
Dq s t a t e
each
perpendicular
state.
state
matrix
measuring
everything
ground
so
and
t h e . ^,F ^ p =
Zeeman
closer,
larger.
field
case,
ground
the
c m~
this
^Fq
coupling
calculating
magnetic
the
away
c - axis
the.intermediate
obtained
with
to
cm
-I
*— I
i t
will
i s
also
but
shift
only
is
coupling
elements,
<F 0 0 | L z + 2 Sz l F l l >
= 1.965,
< d 0 q I L z + 2 S z 1d h > = I . 2 8 0 ,
are
the
s a me ,
and
AE=
the
Zeeman
shift
the
The
change
^Fq ground
in
50
kilogauss
is
( I . 9 6 5 ) 2 ( 50) 2 Z ( 21 . 4 2 ) 2 ( 3 3 9 )
AE = 1 8 6 3
for
at
MHz
state.
energy
for
the
^ Dq e x c i t e d
state
is
A E = ( 1 . 2 8 0 3 ) 2 ( 5 0 ) 2 Z ( 21 . 4 2 ) 2 ( 1'7 5 2 )
AE = 1 5 3
Thus,
the
total
Zeeman
AE =
Again
this
coupling
is
a
matrix
shift
(1863
-
MH z .
is
153)
MHz = 1 7 1 0
confirmation
of
elements
the
and
the
MHz.
calculated
interpretation
intermediate
as
a whole.
73
because, the m easured value
i s 1 7 3 4 MHz + 3 0 MHz .
was
18,
determined
shift
in
taken
Figure
which
only
be
is
from
from
19
not
is
as
monitored
Figure
fluorescence
the
Zeeman
accurate
between
which
the
excitation
shift
because
10
is
kG a n d
of
the
50
the
m e a s u r e d Zeeman
data.
Al s o
absorption
change
kG.
This value
in
s hown
line,
energy
can
9 P
9
8 3 888
ZEEMAN
SHIFT (MHz)
74
.3
.4
J
.4 .7 4 .9 I
MAGNETIC FIELD
Figure
18:
2
3
4
3 6 7 9 910
(TESLA)
E l e c t r o n i c Z e e m a n s h i f t of f l u o r e s c e n c e
e x c i t a t i o n c o r r e s p o n d i n g t o ^ F 0 ---- > 5 d O
t o t a l s h i f t 1 7 3 4 MHz.
t r a n s i t i o n . B J_
ZEEMAN
SHIFT (MHi)
3000
.3
.4
J
.6 .7 .8.9 I
MAGNETIC FIELD
Figure
19:
Electronic
absorption
2
3
4
3 6 7 8 9 0
(TESLA)
Z e e m a n s h i f t o f ^ F q — > **D
s p e c t r u m i n Eu ( OH) ^ . B
c
Measurement
The
phase
of
switch
time
were
characterize
the
response
against
Dephasing
measurements
relaxation
results
Optical
first
done
time
measurements
of
already
of
on
the
T i me
the
transient
iodine
system
ma d e
by
vapor
and
to
check
Genack
et
the
aI .
4 7
6 3
and measurements
response
t i me
F N D - 1 00
the
Tektronix
by
pulse
model
monitored
162
a
70
of
Type
This
picoseconds
s hown
measured
less
representation
sake
of
20,
consists
of
reference.
of
20.
the
The
with
from
163
has
timing
rise
EG+G
time
to
pulse
generated
to
by
a
150
picosecond
long,
determined
amplitude
the
Applied
of
the
photodiode
wa s
Research
Processor
Head
averager
with
a rise
Mo d e l
Mo d u l e
50
H
time
using
input
limited
to
uncertainties.
type
of
This
figure
measurement
e l e c t r o —o p t i c
experimental
the
the
The
an
Th e
wa s
nanoseconds
a Mo d e l
using
sample.
pulser
signal
t wo p a r t s ,
by
modulator
Sampling
thi.s
techniques.
nanosecond
cable,and
internal
of
I
the
relay
32
other
a Princeton
with
boxcar
Figure
phase
The
with
than
from
wa s
S—2
by
example
in
wa s
charging
Averager
resistance.
is
time
reed
volts.
Tektronix
An
of
signal
pulse
directly
Boxcar
100
use
with
109
This
length
wa s
the
electro-optic
time.
the
by
rise
homodyne
Li Ta Og
rise
or
photodiode
monitor
the
ma d e
also
in
s hows
modulator
result,
initial
iodine
a
schematic
pulse
shown
change
vapor
in
in
for
the
Figure
signal.
77
marked
by
related
Tg,
to
is
the
transition.
the
linear
!averse
The
of
rise
the
is
approximately
rise
of
this
probably
the
is
diode.
Th e
response
limit
and
the
15
the
slope
measurement
nanoseconds,
time
is
able
the
response
to
of
measure
this
mor e
system
into
a
slope
the
is
linewidth
and
the
o n T^
just
the
the
it
microsecond
which
photo­
nonlinear
plot
In
of
is
the
,
just
a relaxation
t i me
establishes
that
picoseconds,
relaxation
the
measured
a function
gives
is
phase
a n d T2 .
s e m i —l o g
500
of
FND- 1 0 0
, T2 » i s
importantly
transient
subnanosecond
on
is
which
picoseconds,
of
by
sample
e l e c t r o —o p t i c
500
depends
response
of
the
is
marked
plotted
but
the
response
which
this
the
picoseconds,
portion
part,
sample
inverse
A
the
from
second
of
300
intrinsic
% ^ T ^ T 2 < <1 ,
Tg / 2 .
of
of
linear
of
inhomogeneous
t i me
modulator
time
response
times
range.
and
it
accurately
78
Elecco-opcic
modulacor
pulse
(b)
Figure
20:
(a)
(b )
T r a n s i e n t s i g n a l f o l l o w i n g a phase s h i f t
of n r a d i a n s i n i o d i n e v a p o r .
Schematic
representation
of
70
volt
e l e c t r o - o p t i c m o d u l a t o r p u l s e , 32 n s e c
long.
Dephasing
The
manner,
The
first
with
with
measurements
the
Tektronix
Mo d e l
it
exposure
time,
a
the
bandwidth
preparation
in
a
burn
time
long
also
each
mo r e
than
in
the
one
T2 .
times
population
of
a
long
a measurement
of
be
triggered
externally,
the
over
phase
switch.
a
variable
It
population
saturation
generate
laser
hole
to
corrected
the
wa s
hole
be
delay
between
the
the
in
and
possible
because
200
beginning
of
results
to
than
the
Tj
can
inhomogeneous
hole
will
a pulser
which
profile
between
eliminate,
but
it
By
A/ 0
or
allowed
computer
w h i c h wa s
the
Th e
computer
the
msec.
with
the
to
profile,
pulse
states
T2 .
by b u i l d i n g
the
relaxation
population
wrong
the
resonant
then
greater
run
continuous
related
and p r o g r a m i n g
then
light
2 0 0 . nsec
not
inhomogeneous
burnt
an A/ 0 m o d u l a t o r
between
the
is
in
lived
with
linewidth.
packet
7.
basis
free
to
prepare
mu c h
holes
wa s
scan
which
this
long
s a me
run
diagonal
ma y
the
Figure
light
in
homogeneous
Exposure
decay
of
homogeneous
time
in
exposed
the
jitte r
situation
erase,
t i me
than
is
in
a free
the
resulted
than
This
could
to
wider
Th e
result
longer
relaxation
gate
sample
frequency
lived
profile.
the
on
Because
to
This
laser
of
Hz .
done
s hown
operates
possible
Wh e n
a time
measured
dephasing
not
E n ( OH) g
arrangement
700
modulator.
for
T^,
of
in
E u ( OH) g wer e
pulser
rate
times.
radiation
109
wa s
acousto-optic
in
experimental
a repetition
operation,
Ti me
a
could
continuously
changing
pulse
and
the
the
80
phase
was
switch
easy
delaying
pulse.
500
a
pulse,
to
nsec
phase
time
to
up
to
for
64
E u ( OH ) 3
inverse
163
time,
is
of
time
kHz,
of
974
the
variation
the
of
in
other
the
in stru m e n ta l
measurement
psec,
This
the
by
had
same
material,
a 1.95
of
such
as
experiment
where
the
at
as
200
the
are
To
confirm
its
upper
dephasing
sim ilar
at
to
shot
the
same
results
location
within
in d ic a tio n
the
that
nsec.
s ame
an
of
fact
that
instrumental
lim it
repeated
dephasing
in
time,
an
linewidth
shot
gave
the
diagonal
as
the
shots
with
off
averages
profile
mu c h
was
an
using
22,
scale
magnitude
that
the
16
microsecond
But
in
average
Figure
A homogeneous
p r o file
reached
of
psec.
measurements
lim it.
In
compounds.
was
could
average
21.
A/0
averaged
which
to
the
was
implies
to
Eu^+
into
This
inhomogeneous
inhomogeneous
were
it
advantage
o n a s e m i —l o g
order
unsystematically
shots
Figure
nsec.
signal
psec
digitizer
plotted
same
Inconsistent
the
is
10
A typical
corresponding
in
varied
in
no
strength
Eu( OH) g s a m p l e
and
transient
signal
was
than
the
o f ' T2 = 1 . 9 5
measurements
position
of
range
shown
the
there
more
internally.
slope
is
response
response
relaxation
of
switch
7 9 1 2 AD
shots
nonlinear
that
microsecond
Tektronix
monitoring
determine
the
The
and
0.05% Pr
T2 ,
is
an
the
at
2
:LaFg.
5.6
psec,
6 4
has
been
result
of
the
subject
that
of
mu c h
experiment
Eu( OH) 3 e x p e r i m e n t ,
implying
study
in
recent
years.
was
the
same
as
that
that
the
laser
frequency
The
for
the
jitter
ONAL ClLANG K
(Arbitrary Units )
81
100 nsec/div
Figure
21:
Phase Switch t r a n s i e n t sig n a l
A v e r a g e of 16 s h o t s . M a g n e t i c
i n Eu(OH)g.
f i e l d 15 kG.
100 n s e c / d i v
Figure
22:
S e m i - l o g p l o t of n o n l i n e a r r e s p o n s e
i n F i g u r e 4 . 1 4 . I n v e r s e s l o p e = 974
s hown
nsec.
82
wa s
contributing
stand
tion
the
If
this
of
the
the
a very
phase
switch
polarization
a single
homogeneous
the
the
mor e
■t h e
phase
one
decay
mor e
time
than
one
shot
basis
be
time,
shot.
systems,
Eu ( OH) g
and
5
would
have
the
down
on
Several
the
be
correct
laboratory
lifetim e,
but
to
the
width
573
Hz,
in
set
must
on
be
the
and
the
is
in
of
2
the
not
third
or
Eu^+
time
microseconds
it
using
dye
an
laser
present
This
to
decay
other
599-21
than
it
on a s h o t
shorter
measure
range.
time
excited
relaxation
between
to
more
but
But
linewidth
every
transient
E u (OH) g .
by
the
results
range
k Hz
reasonable
mechanisms
with
technique,
10
phase,
interference
observe
o r der
stabilized
lin ew id th ,
is
in
burn
2 / T2 .
be
signal
j itte r ,
the
phase.
the
will
of
a new
laser
the
switch
real
equipment,
any
homogeneous
o p tical
in
switching
to
linewidth,
the
by
mixing
a rate
the
genera­
simultaneously.
could
laser
that
probably
phase
than
can under­
the
at
in
at
packet
phase
together
microseconds,
optical
less
one
the
This,
is
the
beam
decay
decaying
that
by
indicates
for
with
such
generated
fourth
of
One
homo d y n e
excited
determined
i so chrom a t
was
is
will
is
the
laser
homogeneous
will
The v a r i a t i o n
by
the
packet
it
time.
way by c o n s i d e r i n g
with
width
single
decay
signal
switch,
homogeneous
than
measured
simple
sample
after
if
in
to
I
MHz
could
be
done
possible
in
this
scale.
considered
The
ultimate
o p tical
corresponding
to
to
a
account
limit
ex cited
lifetim e
to
for
the
state
of
278
83
fisec.
This
linewidth
expected
states
not
of
to
are
support
kG
6 0 k Hz
be
this,
as
and
also
support
does
not
k G.
dephasing
likely
a result
caused
optical
10
of
it
1.3
weak
flip-flops.
nearby
in
as
would
contributions
to
the
and
be
simple
and
ions
the
that
technique
can
by
An
for
Phonon
of
the
I
studies
of
the
an
nuclear
to
of
Th e
nucleus
local
effect
spin
to
field
on
the
decoupling
stabilized
do
kHz
linewidth
europium
determine
both
laser,
of
these
specifically
the
linewidth.
optical
for
dephasing
than
residual
have
one
section,
s ome
more
did
the
contribution.
actively
allow
homogeneous
noted
induced
to
between
into
next
dependent
this
of
varied
the
be
The.f lu c tu a tio n
P r ^ + : L a F g „6 4
Eu(OH)g
to
remaining
demonstrated
bandwidth,
should
the
hydrogen
in
accurate
determine
excited
linewidth.
Temperature
coupling
the
in
also
evidence
burned
account
unlikely
of
experiments
It
is
K.
would
holes
is
apparently
was
hyperfine
could
of
linewidth
k Hz
but
field
homogeneous
explanation
the
measurements
the
time
discussed
that
and
experimental
lived
be
transfer
time
spin
by
to
homogeneous
ground
relaxation
long
to
wa s
a
dephasing
the
magnetic
conclusion
linewidth
hydrogen
of
the
a temperature
most
is
profile,
both
There
The
energy
residual
because
external
to
Hyperfine
measured
contribute
assisted
the
the
compared
more.
states.
the
50
or
small
as
inhomogeneous
at
insignificant
J = O
change
10
is
the
ph a s e s w i t c h i n g
measurement
of
is
an
optical
84
transient
to
relaxation
measure
switching
very
a
measurement
and
gas
It
fast
very
of
The
sim plicity
transient
attractiv e
dephasing
phase
has
times.
signals
method
times
in
and
make
to
solids
the
ability
optical
be
used
as
well
phase
for
as
the
liquid
m aterials.
been
shown
that
the
homogeneous
FWHM f o r
the
o
^Fq
<----- > ^ D q
This
tran sitio n
c o rr e s p onds
m icroseconds.
basis
of
signal
6 0 kHz.
the
implies
to
An
shot
a
a
in
Eu(OH)g
dephasing
estim ate
to
shot
of
is
time,
the
T2 ,
than
linewidth
of
the
163
greater
dephasing
variation
homogeneous
less
time
phase
between
150
kHz.
than
on
2
the
switch
kHz
and
85
Hole
The
is
experimental
shown
cycle
in
Figure
for
the
of
between
5 0 0 [isec
read
time
could
controlled
optic
bundle
1.5
the
from
into
a
used
the
times
as
read
and
was
noise
for
the
to
and
'F2
Scientific
burn
the
state
was
using
575
at
the
just
available,
increment's,
and
and
second,
computer.
A fiber­
fluorescence
emission
located
The
states
separated
tube
fed
averager
to
from
from
2.61
was
s o me
fluorescence
excited
a Corning
signal
the
filter.
directly
which
was
as
it
began
to
burn
holes
in
Eu(OH) 3 w i t h
exposure
by
both
the
it
wa s
milliseconds,
cycle,
as
deepest
hole
burn
shown
generate
the
sweep.
milliseconds
longer
lying
photomultiplier
20
read
I
cryostat.
low
by
computer,
as
that
and
En(OH)^
and
are
jisec
the
in
burn
a photomultiplier
excited
possible
the
100
' F^
frequency
small
500
transmit
magnet
the
Northern
determined
about
to
radiation
from
'read'
It
of
the
by
in
times
the
laser
triggered
laser
seconds
burn
through
optically
signal
and A/0 m o d u l a t o r
independently
the
exciting
driven
64 m s e c
to
^Dq
computer
burning
between
was
be
hole
varied
emission
The
30
E u ( OH) 3
for
Variable
Eu(OH)g c r y s t a l
meters
the
laser
6.
and
in
schematic
with
Figure
each
from
6
C W- d y e
bottom
the
Burning
with
times.
but
shown
in
would
no
For
recording
Figure
burn
on
23,
a
time
improvement
of
this
the
reason
scale
signal
burn
to
time
86
was
always
are
between
necessary
dependent
scan.
In
MHz/msec,
that
of
the
and
because
interactions
sensitivity.
MHz
100
level
The
scan
this
way
the
read
300
milliseconds.
broadening
of
Fast
the
hole
loss
of
results
in
a
time
456
milliseconds
the
wa s
tuning
cycle
ma d e
rate
wa s
only
a
fast
small
scan
times
by
time
detection
for
a 400
enough,
perturbation
populations.
5 0 m s e c /d iv
READ
Figure
23:
~1
•BURN
Read and Burn c y c l e f o r h o l e b u r n i n g n e a r
t h e c e n t e r of t h e i n h o m o g e n e o u s p r o f i l e .
F l u o r e s c e n c e i n t e n s i t y i n c r e a s e s toward the
b o t to m of the f i g u r e .
87
QuadrupoIe
S p l i t t ings
Much
can
be
learned
effective
use
of
this
splittings
hidden
These
hyperfine
inhomogeneous
the
energy
and
read
the
with
scans
which
Figure
,2 5
in
Figure
24.
hole
across
are
with
very
laser
25
was
The
a
new
resolution
to
the
Comparing
into
weak,
the
or
MHz
Figures
to
I
describes
This
can
be
of
16
average
by
the
computer
excitation
burn-read
the
signal
signal
laser
shown
back
5 or 10 m i n u t e s
burnt
into
which
the
side
sp littin g s
24
and
be
cycle.
for
and 25,
inhomogeneous
resolution
measuring
the
by
and
the
line
was
averaging
16
wide.
see
energy
absent,
Appendix
recorded
technique
to
than
of 16 b u r n
scanning
been
less
an a v e r a g e
simple
the
by
line.
aritiholes.
fluorescence
then
400
a
and
controlled
line
much
of
the
24.
is
after
was
each
introduce
enough
which
most
broadened
usually
read-burn
previously
scans,
burnt
25,
the
determ ination
holes
Figure
of
but
determined
side
inhomogeneous
had
corresponding
hole
c a n be
By r e p e t i t i v e l y
experimental
levels.
in
II.
are
output with
obtained
Figure
successive
We
was
the
which
erased.
the
Appendix
in
forth
Figure
the
inhomogeneously
the
shown
control
compared
in
of
burning
is
which
spectral
is
computer
program
the
broadening,
the
cycles
in
within
separations
of
hole
technique
splittings,
the
An e x a m p l e
from
only
it
line,
one
gives
the
necessary
holes
and
antiholes
of
the
is
easy
but
the
q u a d r up o l e
antihole
distinguishable.
to
see
side
the
holes
shows
up
88
500 MHz/div.
Figure
24:
A v e r a g e o f 16
Burn time 100
read scans
msec.
of
400
MHz.
5 0 0 M H z/div.
Figure
25:
Average
No B u r n
o f 16
time.
r e a d s c a n s o f 4 0 0 MHz.
Fluorescence e x citatio n
signal
89
By t a k i n g
into
that
the
in
resolving
Figure
power
corresponding
levels.
new
is
of
side
one
of
the
taking
energy
Figure
data
in F igure
the
of
26.
By
map
out
the
sp littin g s,
as
a
25
experim ental
frequencies
the
q u a d r up o l e
resolution
and
can
the
sp littin g s
files
one
data
measure
improved
in
two
the
obtains
to
energy
shown
holes,
quadrupole
24,
the
An e x a m p l e
procedure,
or d i v i d i n g
necessary
to
technique
the
ratio,
using
using
this
dividing
hole
to
this
new
resolve
frequencies,
function,
of
magnetic
field.
In
zero
magnetic
field,
H = PEIz2 describes
isotope.
of
the
the
1 ( 1 + 1) / 3
sp littin g
Measurements
quadrupole
in
zero
the
the
+1/2,
zero
+3/2,
should
+5/2.
the
red istrib u tio n
would
Thus
not
hole
result
of
be
of
levels
allow
transitions
Furthermore,
for
each
the
determination
P,
for
each
are
too
in
the
isotope.
weak fo r
axial
small
K I
lim it
hole
the
+ I) /3]
nuclear
eigenstates
are
Optical
transitions
between
selection
rule
population
expected,
burning,
a
quadrupole
field
Hamiltonian,
is
field
satisfy
spin
I y2) /3] ,
parameters,
H = P t I z2 “
and
effective
+ ti ( I x 2 -
the
zero
coupling
field.
spin Hamiltonian
of
at
I n E u ( OH) g , h o w e v e r ,
burning
the
if
and
it
among
hole
is
admixture
Amj=O,
the
which
the
these
would
is
not
that
levels
occur.
presum ably
nuclear
+mj =
levels
implies
quadrupole
burning
observed,
of
I+mj > w h e r e
the
eigenstates.
|mj>.
On e
possible
so
that
field
An
attrib u te
effects;
T} ^
where
graphic
can
0,
one,
or
the
field
analysis
of
former,
is
what
was
zero
the
it
is
from
burning
true
axial
application
not
so
process
the
magnetic
is
parallel
burning
the
This
and
is
c-axis
This
observed.
hole
responsible
eigenstates.
direction.
burning
in
which
crystal
field
axis
the
hole
to
to
two
symmetry
of
a magnetic
the
crystallo­
c-axis.
that
the
observed
departure
secondly,
E u ( OH)g p r o v e s
nuclear
a
the
lead
Also,
field.
for
done
was
last
la tte r
it
deeper
was
not
the
admixture
of
the
intentionally
would
holes,
not
in
and
parallel
procedure
to
effect,
the
by
not
ch aracteristics
to
the
enhance
which
possible
to
was
aligning
applied
the
hole
exactly
burn
holes
H------ 1------ 1-------1------- 1------ 1-------1-------1------ 1------- 1------ 1-------1-------1------ 1---- —*-------1------ 1------ •-------1 1
*
IO MHz/dlv.
Figure
26:
D a t a shown
F ig u re 25.
top of the
toward the
i n F i g u r e 24 d i v i d e d b y d a t a s h o w n i n
Hole i n t e n s i t y i n c r e a s e s toward the
figure. Antihole in te n s ity increases
b o t t o m of t h e f i g u r e .
92
Magnetic
Field
The
Effect s
spin
Hamiltonian
in
H = P tIz2 To o b t a i n
the
parameters
coupling
parameters,
P,
magnetic
field
where
the
6P f o r
each
4P,
and
burn
holes
nuclear
spin
in
an
of
primary
one
would
holes
isotope.
effect
Hamiltonian.
Since
it
is
easy
to
interaction
levels.
side
of
the
laser
7 for
burn
y pN B z / I ,
nuclear
level
im portant
expected
energy
2 P,
field,
the
to
the
effective
( Yli N/ I ) f - B ,
energy
level
spectrum
isotope,
can
each
other
as
the
the
nuclear
into
appear
Zeeman
a pair
significantly
A further
large
of
of
because
on e a c h
complication
side
is
the
the m agnetic f i e l d
before
the
q u a d r up o l e
Zeeman
coupling
P.
moment,
experim ental
field
as
zero
as,
each
through
gets
in
of
frequency.
in
possible
a magnetic
included
-
holes
only
effect
the
is
q u a d r np o I e
splitting
the
each
crossing
parameter,
the
sp lit
is
t h e h o l e s move as a f u n c t i o n of
strength,
The
to
that
complicates
holes,
that
term,
is
This
14
fact
discern
is
a
Hamiltonian
H = P [ I Z2 - I ( I + 1 ) / 3 ]
it
rj = 0 ,
the
burn
show
be
the
to
would
also
. Writing
where
interest,
like
there
must
limit,
+ I) /3] .
K I
E u ( OH) g w h e n
Zeeman
axial
data
depends
involved.
role
to
level
YHn * t h a t
The
s h o u l d be
on
reduced
in
the
ground
affect
the
<r
3 Dq n u c l e a r
is
much
further
the
away
in f i t t i n g
p articu lar
nuclear
state,
used
Fq,
moment
moment
but
it
because
( ~1 7 5 3 c m - ^).
crystal
plays
is
the
One
an
not
5
D^
can.
93
assume
and
the
bare
nuclear
magnetic
moments
f or
^ Eu,
v alid ity
of
the
different
In
the
Fuller
= 0 .466
ME z / k G
= 1 .055
ME z / k G
1 5 1 Eu.
comparing
two
by
and
y| iN =( 3 . 4 6 / ( 5 / 2 ) ) ( 0 . 7 6 2 M H z / k G )
The
given
Cohen,
7 Hn = ( ( I - 5 3 ) / ( 5 / 2 ) ) ( 0 . 7 6 2 M H z / k G )
for
as
one
a function
with
is
the
field
it
fie ld
p erp en d icu lar
given
by
moments
and
then
the
easier
to
sp littin g s
2P,
4P,
are
used
the
other
magnetic
it
is
also
splitting
155 Eu,
quadrupole
the
c-axis,
effective
of
data
can
be
checked
by
constants
in
perpendicular
to
fitted
cases.
case,
the
assum ption
experimental
crystalline
Because
this
and
in
to
also
6 P.
possible
does
strength,
make
field
not
at
vary
least
measurements
the
to
as
for
with
c ry s ta llin e
show
In
the
this
f it ti n g
same
case
the
burn
holes.
rapidly
the
the
isotope
magnetic
c-ax is.
zero
the
field
bare
quadrupole
as
The
lim it
nuclear
coupling
constants.
In
parallel
to
the
coupling
to
first
the
with
crystalline
quadrupole
fit
case,
constants
case.
the
c —a x i s ,
and
the
magnetic
one
field
can
nuclear
check
moments
axis
the
used
94
Magnetic
Field
To
Pernendicnlar
measure
coefficients,
function
dicular
a
of
to
P,
field
the
nuclear
is
equation
can
dividing
by
value
one
can
f or
field
be
by
the
each
5/2
in
t/5
the
hole
m atrix
the
1/2
/ 4yB
0
This
manner
parameter
P,
m atrix
by
first
and
then
-5/2
0
0
I
I
I
VTyB
-(2/3) P
0
- ( 8/3 ) P
3 / 2yB
0
3 / 2yB
-(8/3)P
V^yB
I
0
0
0
V^yB
I
0
0
0
0
■0
0
0
0
I
0
I
I
VTyB
- ( 2/3 ) P
j
The
function
Figure
parallel
resulting
of
27.
to
the
eig ehvalues
dim ensionless
Just
the
as
sp littin g
m onitoring
the
of
the
in
the
crystalline
quadrupole
function
to
this
I
I ]/5 / 4yB
I
0
I
H = I
0
I
a
yB/P.
-3/2
0
leads
describing
constant
- 1/2
as
p erp e n-
also
below.
coupling
of
c-axis
This
clearest
coupling
locations
Hamiltonian
the
value
3/2
I (10/3) P
I
the
quadrupole
for
qua d r u p o le
direction.
the
solved
the
crystal lographic
splitting;
given
diagonalizing
of
measure
the
applied
Zeeman
sp littin g
the
t o c —a x i s
can
magnetic
then
case
with
c-axis.
the
P
can
I
I
(10/ 3 ) P I
as
be
shows
as
shown
magnetic
27
of
y571yB
plotted
yB/P
Figure
frequencies
field.
be
param eter
parameter
relativ e
l /5/ 4-yB
I
J
field
that
the
determined
by
the
holes
as
a
VO
Ul
Figure
27:
E i g e n v a l u e s of qua dr u p o I e H a m i l t o n i a n p l o t t e d as
a f u n c t i o n of t he d i m e n s i o n l e s s p a r a m e t e r y B/ P.
96
F ig u re
28
measurements
to
the
are
2
made w i t h
the
wide,
the
Figure
in
IP I = 11.6
the
MHz
and
2.4 5
the
isotope
is
smaller
barns.
isotope
In
increases,
pN,
the
was
hole
the
the
way
get
from
provide
value
for
the
151
for
lines
s p littin g s
Hamiltonian
with
moment
an
solid
IP I = 4.5
isotope
the
q u a d r up o l e
for
of
a value
0.466
of
M H z / kG
lines
MHz
of
the
The
coupling
and
so
reading
k G.
in
so
153
for
is
1.53
3.464
of
magnetic
of
to
the
rapidly,
it
the
field
faster.
P for
close
Eu ,
nuclear
levels
admix
the
The
151
central
is
more
of
hole
position
data
does
convincingly
constant
Figure
29
a bare
moment
europium.
Q. = 0 . 9 5
Eu
is
measurement
are
*^
energy
as
place
accurate
moment
it
eigenstates
the
10
the
moment
for
^^^Eu
rapidly
takes
to
moment
holes
quadrupole
The
the
the
2 kG u p
the
however.
for
admixture
to
Th e s o l i d
obtained
field ,
more
used
but- b e c a u s e
d iffic u lt
which
holes
energy
q ua d r up o l e
and
nuclear
isotope,
and
bars,
side
k G.
a
magnetic
change
and
geometry
has
a magnetic
^ Eu
perpendicular
diagonalized
nuclear
than
The
magnetons,
magnetons.
bare
is
of
the
the
f it
axis
of
J Eu.
^ * Eu
which
This
10
are
of
r e s u l ts
The v e r t i c a l
2 kG a n d
p o sitio n s
27.
field
lo c a tio n
eigenvalues
isotope
The
nuclear
between
hole
shown
the
mark
fields
by
same
magnetic
MHz
described
Q =
the
e x p e rim e n ta l
c-axis.
through
barns
the
c ry s ta llographic
different
for
shows
are
IP I
4.5
MHz ,
calculated
with
of
=
all
1 .055
MH z / kG
MHz
VO
-J
kG
Figure
28:
N u c l e a r Zeeman q u a d r u p o t e s p l i t t i n g s in a m a g n e t i c
f i e l d p e r p e n d i c u l a r to the c r y s t a l l i n e c - a x i s ,
B lc
I s o t o p e I 53E u ;
I p I = 1 1 . 6 MHz
MHz
80 —
Figure
29:
C
a x is .
Isotope
l 5 l Eu;
|p|
= 4.5
MHz.
99
Magnetic
side
the
Field
Shown
in, F i g u r e
holes
relative
magnetic
data
zero
the
= 4.5
MHz f o r
now
be
with
the
IP I = 1 1 . 6
32
of
the
with
qua drup o le
bare
nuclear
The
symmetry.
and
a
to
YAlOgrEu^ +31 b u t
the
no
MHz
the
magnetic
in
for
This
in
burn
axis.
and
Figure
level
in
IP I
of
30
and
field
Figure
31,
^**^Eu.
parallel
the
to
^*Eu
IP I = 4.5
as
a
the
c
isotope
MHz ,
and a
MH z / k G .
chapter
the
represent
^Dq e x c i t e d
are
on
are
ions
en tirely
M acfarlane
P values
153
position
field
co efficient,
1.055
left
a function
for
with
do n o t
hyperfine
lines
the
different
the
shown
hole
is
laser
four
on
of
c-axis.
isotope
as
measured
measurement
by
for
solid
plot
the
holes
data
splits
by
sp littin g s
made
Since
Yf1N = 0 . 4 6 6 MH z / k G
this
a
at
the h o les
level
coupling
in
made
20kG.
is
of
crystalline
particu lar
the
of
frequencies
frequency
the
all
This
sp littin g s
The
to
the
for
moment
m easurements
smaller
to
crystal.
correspond
to
151,
shows
resu lts
qua drup ole
burn
shown
MHz
measured
IP I = 11.6
is
field
of
the
there
quadrupole
axis
They
field,
splitting
function
the
SkG
attached
Figure
are
measurements
isotope
Each
c - axis
parallel
two v a l u e s ,
isotope.
and
to
from
magnetic
to
30
to
fields
With
can
field
corresponds
magnetic
in
Parallel
et
more
aI,
than
the
state
in
measured
of
E u ( OH ) 3 .
complete
axial
consistent
with
in
EuP^
a factor
4
of
and
four
MHz
100
Figure
30:
Side h ole f r e q u e n c i e s r e l a t i v e to l a s e r burn
frequency at four d iff e re n t magnetic f ie ld s .
Magnetic f i e l d p a r a l l e l to c- a x i s , B I I c .
MHz
101
20 kG
Figure
31:
N u c l e a r Z e e m a n q u a d r up o I e s p l i t t i n g o f * ^ Eu
a m ag n etic f i e l d p a r a l l e l to the c r y s t a l l i n e
B i l e . | P | = 1 1 . 6 MHz, YMn = 0 . 4 6 6 MI I z / k G.
in
c-axis.
MHz
102
Figure
32:
Nuclear
Zeeman
a magnetic
Bi I c . | P |
q u a d r up o I e
field parallel
=
4.5
MHz.
YHn =
splitting
in
to
c- axi s ,
the
1.05 5
o f * ^ * Eu
crystalline
MIIz/kG.
103
A way
to
check
the
the
ratio
of
the
quadrupole
known r a t i o
of
the
qua dr upo I e m o m e n t s 3 *
comparing
with
the
v alid ity
Q1 5 3 ZQ1 5 1
This
c a n be
compared
to
= 2.5812
the
1 5 3p / 1 5 I p =
again
confirming
Although
to
measure
the
ground s ta te
as
shown
with
that
these
optical
rf
this
do
ground
state,
3,
of
exist,
7F q ,
measurement
coupling
that
no
in
= 2.58
the
and
d o u b l e —r e s o n a n c e
param eters
be
this
work,
+ 0.5,
it
should
hyperfine
attempt
best
by
measurements.
was
technique.
could
is
+ 0 .0010 .
s e e m t o be so s m a l l ,
experim ental
measurements
laboratories.
. 6/4.5
h
antiholes
Chapter
the
measurements
accuracy
sp littin g s
in
them
the
of
less
is
carried
t e c h n i q u e 22
possible
splittings,
made
It
be
the
t h a n 4 MEz
to
measure
most
out
available
likely
using
in
an
other
104
Ho I e
Lifetimes
and
Linewidths
A complete
versus
time
MHz w e r e
already
laser
was
measured,
known
into
the
the
time
pursued
was
not
dramatic
greater
than
position
and
deeper
the
read
would
These
long
im portant,
in
the
side
than
at
the
burn
enough
t o make
an
the
also
hour
the
of
it
the
on
tran sitio n
on t h e
was
30
minutes
imply
the
that
wider
read
and
transient
as
was
than
the
the
hole
a function
cycle
in
but
hole
this
width
measurement,
exist
at
and
this
the
hole
lifetim e
was
the
burn
time
and
the
on
the
profile.
would
burn
side.
that
these
possibly
hyperfine
scale
it
spectral
not
energy
determ ined
on a t i m e
of
low
got
does
inhomogeneous
holes
least
depending
the
as 1 - 2
data,
less
that
accurate
widths
as. s m a l l
was
change
that
hole
switching
and
dynamics
observed
least
chapter.
profile
and
widths
width
observed
between
explanation
previous
phase
homogeneous
was
holes
lived
at
the
the
1/2
cycle,
last
It
Hole
because
was
energy
from
the
of
w ithin
lifetim es
further
explanation
It
hole
inhomogeneous
not
high
but
delay
tim e .66
of
attempted.
that
was
an
not
I inewidth.
burnt
of
study
on t h e
Holes
much
By d e l a y i n g
deep
much
dephasing
order
relaxation
easier
holes
longer.
is
not
of m i n u t e s ,
time
in
the
105
Chapter
7
CONCLUSI ONS
We
of
the
have
Eu^+ ion
variety
of
measure
and
the
studied
in
will
also
rare
time
measure
Narrow
earth
crystal
field
Cg^
in
F
other
To
of
E u ( OH) g .
in
hole
E u ( O H ) g.
were
used
this
Eu(OH)g.
of
an
ion
that
has
been
ion
in
novel
this
is
the
used
an
to
has
contain
this
A
with
study
These
knowledge,
burning
splitting
in
This
m aterials
our
Dq t r a n s i t i o n
symmetry
interaction
in
5
<----->
q
techniques
effects
optical
to
axially
potential.
Linewidth
An e x c e p t i o n a l l y
MHz
FWHM
---- >
^Dq
has
ever
Isotope
narrow
inhomogeneous
been measured
transition
stoichiometric
width
the
ion.
qua d r u p o I e
of
nonlinear
novel
occur
that
the
symmetric
sites
environment
several
trivalent
first
and
7
intrinsic
characterize
crystalline
effects
axial
linear
identified
the
in
solids,
measured
for
for
the
Eu(OH)g.
this
is
linewidth
first
time
for
Compared w i t h
the
an o p t i c a l
narrowest
of
167
the
all
F
q
other
inhomogeneous
transition.
Shift
Line
shape
provided
an
measured
isotope
fitting
indication
shift
of
of
an
of
~85
the
isotope
MHz
^ F q <-----> **Dq
shift.
is
about
transition
The
1.5x10
apparent
—3
—I
cm
106
per
unit
mass.
magnitude
that
it
is
This
is
apparently
in
including
ODNMR,
Resonance,
and
are
to
planned
Electronic
expected
the
resolvable
the
exactly
with
clarify
the
c —a x i s ,
the
with
the
a check
it
ma y
Further
Detected
of
order
of
m a t e r i a l s , 11
which
state.
be
but
clearly
measurements
Nuclear
iso t o p i c a l l y
Magnetic
pure
samples
further.
the
electronic
line
in
With
MHz.
provides
of
second
1282
in
earth
the
Shift
the
of
case
this
measured
tion
rare
acquisition
explained
The
agrees
first
excitation
theory.
approximately
Optically
Measurements
completely
is
for
solid
the
Ze e ma n
fluorescence
shift
second
shift
of
1265
order
perturbation
the
magnetic
shift
of
change
calculated
order
field
the
line
are
MHz
theory
agrees
calcula­
perpendicular
MHz + 3 0
1710
of
perturbation
MEz + 30
1734
of
shifts
absorption
of
predicted
the
the
terms
Zeeman
of
and
Zeeman
MHz.
electronic
to
MHz
also
This
also
Zeeman
matrix
e I erne n t s ,
<F0 0 | L + 2 S | F 1 0 > = I .965 ,
<D0 0 I L + 2 S | D 1 0 > = I . 2 8 0 ,
for
each
of
the
is
the
highest
in
any
rare
The
the
s a me
J=I
resolution
earth
admixture
oscillator
excited
states
with
electronic
the
Zeeman
J=O
states.
effect
This
measured
solid.
matrix
which
strength.
elements
results
The
in
three
lead
to
the
dramatically
order
of
an
understanding
magnitude
of
increased
quadratic
107
variation
of
transition
strength
can
be
m aterials
and
lasers.
Quadra t i c
Enhancement
The
tion,
very
quadratic
w h i c h we
probability
useful
has
t wo m a t e r i a l s ,
EuVO^
to
(unperturbed)
dislocation
This
sites
effect
is
of
already
commonly
applicable
divalent
played
role
in
in
Samarium
in
the
gated
a
sites
compounds
hole
Shelby.
The
quadratic
useful
a practical
way
for
others
sensitive
from
t r ivalent
and
by
defect
and
and has.
experiments
ma y
switching
and
samples.
presently
enhancement
in
detector
Europium
burning
optical
earth
transi­
spectroscopic
both
Macfarlane
in
as
used
field
rare
intrinsic
been
intrinsic
found
magnetic
work w i t h
the
a n d E u A s O ^ , 67
isoelectronic
a major
future
enhancement
pioneered,
distinguish
in
with
also
and
of
be
energy
transfer .
Dephas i n s
Ti me
While
of
the
that
off
it
it
is
very
between
phase
to
and
in
fast
memory.
the
the
range
in
which
The
lead
to
make
time,
between
that
dephasing
an e x a c t
T2 .
2
it
and
5
stoichiometric
times
because
of
the
transfer
residual
width,
not
nuclear
fluctuation
of
local
of
determined
This
the
ground
fields
which
is
usually
interactions
and
a
accounted
I / Z jtT^ = 57 3 H z ,
moment
was
materials
energy
rate,
measurement
psec.
to
relaxation
reduced
possible
dephasing
the
long
ions
population
not
diagonal
surprisingly
have
was
is
loss
by
the
probably
due
state
for
of
Eu^+
modulates
ion
the
108
local
environment
and
causes
depha s i n g .
Quadrnpole S p littin g s
Excited
reported
hole
state
for
nuclear
europium
burning
as
ions
a
in
an
axial
sensitive
overcoming
inhomogeneous
qua d r u p o I e
splittings
trivalent
qua d r u p o I e
field.
detection
broadening,
of
each
measurements
of
Using
optical
technique
we h a v e
the
are
for
measured
stable
the
isotopes
of
europium.
1 5 1 Eu
|P|
= 4.5
MHz + 0 . 5
MHz
Tl = 0 . 0
1 5 3 Eu
Ip I = 1 1 . 6
MHz + 0 . 5
MHz
q = 0 .0
These
measurements
contribution
distortion
to
caused
proportional
Considering
the
the
to
agree
qua d r u p o I e
by
the
Erickson's
measured
ratio
with
of
the
the
predicted
coupling
crystalline
nuclear
parameter.
electric
electric
nuclear
electric
1 5 3 q/1 5 1
q
quad ru p ole
second
order
This
is
field
q u a d r up o l e
qua d r u p o I e
a
and
moment.
ratio
of
= 2.58
coupling
parameters
in
this
study,
1 5 3 p /1 5 1 p
is
in
state
caused
exact
agreement.
only,
by
dominates
the
This
distortion
admixtures
the
= 2 .5 8 + 0 .5 ,
nuclear
of
J
implies
of
= 2
the
that
the
electronic
states
qua d r u p o I e
in
into
the
interaction
5 Dq e x c i t e d
charge
cloud
J =
state
0
parameter
P.
109
Chapter
8
FOUR-WAVE MI XI NG AND HYP E RF I NE S P L I T T I N G S
IN L i T b F 4
AND Tb ( O H ) g
I NTRODUCTI ON
F o u r —wa v e
recently
mental
because
of
technique
F o u r —w a v e
free
mixing
has
also
evident
in
w a v e 70
to
overcome
our
their
means
Four-wave
important
the
been
used
as
of
and
in
has
Mixing
new p r o p e r t i e s
An
has
also
in
the
will
in
Interest
is
of
in
an
filter.
of
of
i mage
inhomogeneous
a potential
7 I
has
Doubly
shown
Tb^+ compounds
these
be
four-wave
conjugate
particular
explanation
importance
use
mixing
useful
demonstrated
study
Doppler-
f o u r —w a v e
a phase
optical
in
of
been
the
experi­
applications.
properties.
distortion
n a r r o w —b a n d
Four-Wave
potential
solids
interest
an
in measurements
generating
phase
as
practical
concerning
mixing
a
laboratory.
considerable
usefulness
possible
proposals
a
Resonant
general
e x c i t o n —t r a n s p o r t
as
usefulness
of
sp e ctro sc o p y 6'
mixing
medium.
been
spectra,**
transient-grating
characterizing
its
and
mixing
t w o —p h o t o n
has
ne w
results
discussed
in
s o me
in
and
what
follows.
Studies
were
of
undertaken
hyperfine
splittings
fortuitously
in
trying
in
to
L i T b F 4 and
understand
T b ( OH) 3
results
HO
obtained
from
by D.
Doubly
Th e
understand
the
line
signal.
the
wave
observed
mixing
This
new,
including
the
its
on
effect
index
the
phase
F o u r —Wa v e
Mixing
dispersion
(I)2 .
and
been
has
these
dependence
be
three
a
four-wave
possible
eliminated
of
the
four-
developed
by
to
of
refraction
and
the
index
conditions.
in
in
coherent
in
treatments
Nonresonant
all
the
anoma I o u s
at
beam
mixing
occur.
experiment
beams,
Resonant
f o u r —w a v e
resonances
fourth
anomalous
a Doubly
and
wave m i x i n g
input
The
other
considered,
double
The
to
is
considered
four
was
explanation
the
or
these
33.
ignored
is
the
c a n be
following,
in
in
several
But
a
generate
in
contribution
single
34(a).
M3 ,
due
process
Schematically,
Figure
Figure
O t t e s o n , 73
t h i s . work
negligible
must
where
of
S.
experiments
observed
angle
matching
has
is
Mixing.
in
in
dispersion
there
experiments
matching
additional
Four-Wave
index
one
a n d M.
in
narrowing
but
shown
dispersion
because
line
all
phase
signal
Cone,
emphasis
narrowing
This
and
L.
F o u r —Wa ve M i x i n g
original
e x p l a n a t i o n s , 74
by
E n d e r , 7 2 R.
Resonant
m aterials.
mixing
A.
is
shown
frequencies
at
frequency
,
M4 ,
where
h>4 = toI
The
beam
mixing,
other
at
both
three.
frequency
M4
spatially
The
sample
is,
and
+ toZ ~ tdS *
unlike
degenerate
spectrally
polarization
distinct
P( M4 )
is
four-wave
from
related
the
to
Ill
I
0 = 3.0
0
=
1.4
INHOMOGENEOUS Fwhm
Figure
33:
F o u r-w a v e m ix in g s i g n a l in LiTbF^.
Signal
shown is
a t f r e q u e n c y w^ = 2 w ^ - w ^ f o r
different crossing angles, 9 .
Uig=I 7 4 2 2 cm ^ .
112
SAMPLE
CJ4 = CU, + U 2 - U 3
P(CJ4 ) a x ^ ( - u 4 .u ,.CJ2--U 3) E(U1) E(U2) E(U3)
K4 = Zkl - K 3
Figure
34:
(a)
S c h e m a t i c d i a g r a m of
four-wave
mixing
experiment.
(b ) General
three
beam
phase
matching
diagram.
( c ) Two
beam p h a s e m a t c h i n g
diagram
with
beam c r o s s i n g a n g l e 6 ^ g .
113
the
input
third
laser
order
electric
P (u 4 )«
The
and
resonances,
of
a major
existing
induced
this
photon
whenever
phase
role
which
and E3 ( U2 ) ,
X ^ ^ (-
in
occur
resonances,
there
matching
theories
frequency
study.
E2 ( U2 ) >
susceptibility
resonances
double
experiments,
plays
E1 ( U1 ) ,
by
u ^ , W1 , U 2 , - U
3)
X ( ^ N - U 4 , W1 , u 2 , - W3 ) E 1 (W1 ) E 2 (W2 ) E 3 (W3 ) .
possible
single
fields
the
in
are
in
but
single
induced
Xv
in
or
can
double
frequency
The
accounting
phase
selectivity
was
the
the
original
*
both
mixing
photon
selectivity
i n t e r p r e t a t i o n . 74
for
. 7
6.1
be
nonlinear
the
inadequacy
matching
reason
for
114
Theory
In
the
resonances
experiments
and E x p e rim en ts
terbium
compounds,
occur,
but
here
the
sufficient
inhomogeneously.broadened
resonance.
assumed,
In
this
choice
the
with
simplest
k^=!^
geometry,
of
Wg a n d
and
the
the
phase
the
phase
to
as
analyzing
consider
7x3
Also
to
in
each
is
loss
of
can
be
other.
set
Figure
the
single
condition
condition
shown
a
without
parallel
matching
,
of
matching
beams
angle
a n d T b ( OH) g , m u l t i p l e
purpose
is
generality,
it
for
LiTbF^
by
34(c) .
a>4 = 2 u ) j - u ) g
The more
general
Two p h o t o n
Freidmann,
Gg
of
of
~6 8 cm- '*" ,
but
enough
over
5
or
In
is
any
4 f°
away
the
excitation
the
electronic
^ F g ---- > ^®4
yield
to
Figure
located
34(b) .
studies
excited
show no
by
Cone . a n d
^Kg,
,
configuration,
energy.
multiresonant
f o u r —w a v e m i x i n g
factor
6.3
to
the
which
generated
path.
individual
equation
the
in
6.2
structure
^ Kg
in
is
and
the
close
enhancement
to
when
scanned
is
10 w a v e n u m b e r s .
c o h e r e n t Iy
optical
have
to
proportional
matching
shown
35,
twice
enough,
far
is
fluorescence
Figure
manifolds
vicinity
case
the
wave
A
product
takes
waves
to
of
account
at
different
the
change
the
I X^ \ l ^
into
in
change
v e c t or
experiment,
the
observed
and
the
. phase
interference
points
frequency
in
a
signal
manner
along
of
th e
causes
an
shown
in
115
=G6
3G6 B 5K
a =K 5
2 u ,—
38,800cm-'
-39,900 cm*'
5^
4 f7 54
and (?)
charge
transfer
4 f7 5d
[Nof to scale,
Spacing -6 8 cm * 1 between
twice 3D4 (Zu1) and 3Ka ]
20,568.8 cm*1
3D4 T1
OJ1(TT)
O J1(T T )
Ocm-'
7F6J 1 = - S
20,538.3 cm*'
5 D4 /*=3 - j
Ocm-'
7F6 J1 =-S-
4 f8
LiTbF4
(a)
Figure
35 :
T b ( O H )3
(W
Excited
states
identified
fluorescence ex citatio n .
(a) L i T b F 4 ; (b) Tb(OH) 3
by
t wo
photon
116
Aki Zki
Over
the
narrow
FWHM
for
LiTbF4 ,
negligible
The
jsT
I inewidths
0.8
changes
Ak = 2 n Z L w h i c h
in
is
terms
= n i Wi Z c ,
it
will
be
term,
( Wi Z c ) A n i ,
these
and
is
easy
the
to
term
for
for
can
0.35
Tb(OH)3 ,
in
phase
6.4
6.3
m aterials,
changes
an
intensity.
see
( P i Zc)Awi
that
be
wave
Am1
H1 m u s t
matching
be
cm- 1
gives
provide
the
selectivity.
rewritten,
using
the
+
( Wi Z c ) A h i
dominant
But
on
approximation,
one
term
6.4
off
resonance
resonance
the
other
dominant.
can
expression
This
order
=
( n i Zc)Awi .
experiments,
third
So
equation
will
plane
obtain
the
these
FWHM
necessary
in
+ Ani Zni
as
where
the
in
cm- 1
kj^ .
Aki
In
= Aui Zui
integrate
for
intensity
which
the
is
along
and
a phase
applicable
the
four-wave
proportional
susceptibility
is
path
mixing
to
the
in
length
signal
square
matching
of
factor
G(Ak).
I t i 4 (U )1 )
A
the
general
form
following
the
phase
=I
I 2 G( Ak)
matching
factor
6.5
c a n be
written
in
way.
T + e x p [ - ( 2 a 1+Og-o4 ) L ] - 2 e x p [ - ( 2 a 1+ a 3- a 4 )LZ2][cosAkL]
G( Ak )
[ A k ] 2 + ( 2 a 1 + a 3 _ a 4 ) 2 Z4
In
any
the
experiments
electronic
or
described
r am a n
here,
resonances
W3 wa s
such
tuned
that
Ct3
away
=
(Z 4
from
=
0,
117
and w i t h
= a2 = a ,
l + e z p [ - 2 a ( ( i ) 1 ) L ] - 2 e x p [ - a ( ( o 1 ) L ] c o s (AkL)
G ( A k ) = ------------------------------------------------— -------------------------- .
[ A k ] 2 + Ea(O)1 ) ] 2
Two
things
reduces
zero,
One
should
to
and
the
a
condition
Now f o r
fam iliar
this
is
in
and
the
phase
depends
the
line
by
the
law
One,
it
as
goes
to
a(o>)
t wo
parameters.
line
shape,
expressing
the
k|
= 4k2 + k2 at
only
G(Ak).
one
shape .
To
must
determine
phase
matching
W1 .
of
matching
on
other
on
done
factor
s i n c 2 ( A k L / 2)
frequency
easily
terms
this
form
dependence
on
in
G( Ak)
( Oi1 ) " L
h ow Ak d e p e n d s
This
noted
secondly,
being
understand
be
6. 6
of
the
cosines.
4k1kgcos01g
W1 Q , Ak = 0 ,
within
6.7
the
resonance
line.
k 4Q =
where
kg,
resonance
3 » ^lO'
~5
= 0
for
cm
a n ^ ^40
-
4 k 10
are
k g c o s O ^ g ) 1^ 2
constants
fixed
6 .9
for
+ A k 4 = k 4Q + ( “ 4 0 / c ) An 4 +
the
and
small
from
scan
range
equation
used
6.2,
( U4 0 Z c ) A w 4
in
these
experiments,
Aw4 = 2 Aw1 f o r
fixed
Then
k 4
and
in
a given
profile.
k 4 = k 40
An 4
( 4k20 + k |
equation
6.7
=
k
with
4Q
+
( 2 n 4 0 / c ) A w i»
k 1 = k 10
+ Ak1 ,
k 4
-
k40
+
2 ( 2 k 1 0 - k g c o s © 1 g ) Z k 40 A k 1 + ( ^ ( A k 2 )
k 4
~
k 40
+
2A ki
-
k
4Q
+
2
w i q
Z
c
A nj
+
Z n i 0 Zc
Aw^
Wg.
118
Ak =
The
-
final
k^
result
= ( 2 u 1 q / c ) An 1 + ( ZAm 1 / c ) ( U1 Q - n ^ Q ) .
is
1
Ak ~
This
result
implies
intermediate
resonance,
characteristic
change
in
of
phase
matching
the
Figure
value
of
smaller,
line
center.
to
matching
more,
the
the
index
To
33.
As
for
signal
change
is
signal
and
absorption
coefficient
To
phase
that
more
and
the
matching
the
very
four
the
matching
increases
matching
condition
it
away
moves
to
from
3.0° the
signal
where
phase
the
center,
gets
on
dispersion
angles
angle
line
angle,
thin
experimental
increasing
signal
a
wave m i x i n g .
line,
toward
dependence
and
end,
By
driven
this
times
angle
index.
homogeneous
a thousand
as
the
This
to
phase
of
width
leads
phase
the
an
also
matching
the
a
index.
the
again
broadens
side
steeper
dispersion
transition.
phase
increasing
again
to
nonresonant
different
the
smaller
understand
the
at
the
This
over
consider
energy
is
is
satisfies
the
high
of
this,
signals
Then by
occurs
which
cases.
through
display
in
related
s o me
case
of
and
the
the
in
scans
will
change
is
6.10
laser
signal
dispersive
k1 which
gets
moves
in
the
the
condition
mixing
in
as
dn1/dw1 ,
example
four-wave
the
the
transition
than
As a n
shown
of
index,
width
selective
that
( Zto1 Q / c ) A n 1 .
angle
where
narrower.
the
anomalous
one
must
know
for
the
resonant
samples
of
LiTbF ^
the
and
119
T b ( OH) 3
With
of
were
patience,
26
of
The
scanned
experiment
intensity
for
into
are
later.
a LiTbF^
profiles
with
I
LiTbF^
have
asymmetric
diamond
was
polishing
polished
crystal
was
to
techniques.
a
thickness
polished
to
a
78 m i c r o n s .
laser
techniques
profile
and
absorption
dye
using
a T b ( OH) g s a m p l e
microns,
thickness
that
polished
is
been
absorption
shape
and
GHz
were
bandwidth.
shown
in
used
to
Figure
but
the
36,
using
structure
using
The
convert
coefficient
apparent
important,
obtained
a pressure
result
where
the
of
this
standard
transmitted
Beer's,
law.
Th e
in
this
absorption
discussion
will
r e t u r n . to
120
(cm-1 J
,
t
I
-1.0
Figure
I
I
I
I
-0.5
36:
I
I
I
I________ I
0
.
a .A,= 3 5 5 cm"'
I
0.5
1.0
WAVE NUMBERS
Experimental absorption co e ffic ien t
c r y s t a l 78 m i c r o n s t h i c k .
-I
FWHM = 0 . 3 5
LiTbF4
121
Simulation
Using
the
plasma
this
experimental
line
shape,
by
using
obtained
one
in
the
was
the
37.
fitted
It
does
the
This
observed
angle.
it
a FWHM o f
calculate
Figure
shows
the
show
experimentally,
It
profile.
hidden
was
If
one
the
on
individual
hyperfine
asymmetric
shape
was
taken
at
components
the
Boltzman
with
wa s
1.3
would
The
36,
of
original
fit
inhomogeneous
s a me
dispersion
function,
type
line
which
is
shown
of. b e h a v i o r
of
phase
narrowing
that
GHz,
as
matching
also,
was
which
reconsider
there
of
was
line,
but
observed
was
the
would
K,
where
higher
the
a reduced
structure
is
forced
levels,
inhomogeneous
This
absorption
really
hyperfine
the
the
one
line,
width
also
because
energy
population
to
with
for
a
each
explain
this
the
data
hyperfine
proportional
to
exp(-E/kT).
experimental
a
Then
profiles
absorption
with
GHz .
index
the
distribution
then
to
component.
have
10.5
LiTbF^.
that
of
gaussian
signal
1.68
necessary
order
approximate
a function
inhomogeneous
splitting
profile,
narrowing
in
possibility
the
the
c m- * ,
believes
the
mixing
as
line
detected
then
within
consider
shows
Voigt
and
plasma
characteristic
the
an
coefficient
four-wave
fit
to
or
wavenumbers,
complex
0.056
signal
function,
fit
0.35
e x p e rim e n ta l Iy
not
narrowest
was
absorption
from
can
dispersion
profile
with
Studies
absorption
superposition
widths
of
0.08
of
cm- * ,
4
profile.
Figure
gaussian
lines
2.4
GHz ,
• and
122
hype r f i n e
which
splittings
took
into
hyperfine
level
of
account
of
ground
absorption
data
almost
The
from
complex
this
the
of
was
the
inhomogeneous
to
each
curve
mixing
of
of
the
is
the
inhomogeneous
fit
between
shows,
signal
33
This
to
also
the
the
38.
This
the
the
experimental
factor
duplicate
shown
the
resulted
the
model
An e x a m p l e
in
narrowing
displays
of
Figure
39.
observed
in
correct
position
the
for
the
curve
four
hyperfine
each
of
4
the
shown
inverse
factor
the
is
The
of
a
FWHM o f
cases
components
is
which
generate
is
line
matching
t wo
of
width
splitting
needed
of
within
signal.
signal
the
plotted
plotted
to.
mixing
inverse
(a),
profile.
case.
levels
fit
behavior
within
the
'
the
absorption
for
it
phase
marked
signal
the
Figure
reproduces
used
mixing
profile.
Comparison
the
This
dependence
in
energy
GHz .
dispersion, function
f o u r —w a v e
and
respect
for
shown
profile
reproduces
experiments,
signal
is
then
four-wave
simulation
with
temperature
hyperfine
plasma
fit
simulated
This
3.18
exactly.
simulations
the
four
cm- * ,
the
populations
superposition
state
0.106
f o u r —w a v e m i x i n g
in
Figure
FWHM o f
the
gaussian
(b)
is
is
2.4
is
3.18
GHz .
of
four
narrower
narrowing
experimental
fit
the
is
As
exactly
results
For
four-wave
to
s a me
components,
component
40.
the
and
the
this
the
the
shown
thing
where
GHz
in
the
in
figure
latter
amount
Figure
123
INTENSITY
0.5
IX
WAVE NUMBERS
Figure
37:
Model s i m u l a t i o n of f o u r - w a v e m i x i n g
signal
as
a f u n c t i o n of p h a s e m a t c h i n g a n g l e f o r
a
g a u s s i a n f i t to the complex plasma d i s p e r s i o n
function.
124
[cm"']
WAVE NUMBERS
Figure
38:
S u p e r p o s i t i o n of f o u r g a u s s i a n l i n e s , each
with
an
i n h o m o g e n e o u s w i d t h of
0.08
cm
w i t h h y p e r f i n e s p l i t t i n g o f 0 . 1 0 6 cm ^ .
,
125
INTENSITY
0.5
1.0
WAVE NUMBERS
Figure
39:
Model s i m u l a t i o n o f f o u r - w a v e m i x i n g s i g n a l
as
a
function
of
phase
matching
angle
Complex
plasma d i s p e r s i o n f u n c t i o n f i t to
s u p e r p o s i t i o n of f o u r g a u s s i a n l i n e s .
126
17.0
[wave
numbers]
0.5
LO
WAVE NUMBERS
Figure
40:
Comparison
of i n v e r s e F u l l W i d t h a t
Half
Ma x i mu m o f f o u r - w a v e m i x i n g s i g n a l .
(a) S i n g l e g a u s s i a n .
(b) S u p e r p o s i t i o n of f o u r g a u s s i a n l i n e s .
127
The
important
studies,
is
simulated,
is
the
that
the
depends
on
absorption
duplicate
is
point
the
the
only
shape,
duplicate
the
structure
absorption
profile.
great
signal
Thus
gives
of
in
narrowing.
For
hy p e r f i n e
of
in
by
its
the
was
with
are
familiar
One
a range
the
free
form
the
that
the
of
of
one
other
which
values
the
can
to
and
signal
obtain
four-wave
the
a
mixing
dependence
parameter
no
to
inhomogeneous
writing
with
fit
parameters
matching
GHz ,
was
and
simulation
fitted
3.18
parameters.
parameter,
of
analyzing
the
wa s
which
in
implies
phase
which
profile,
no
simulation
signal,
last
accurate
example,
splitting
Hamiltonian
fit
This
information
terms
This
there
an
these
a( ) >
and w i d t h
experimentally.
deal
mixing
absorption
was
in
experimental
profile.
line
fit
made
coefficient,
dispersion
observed
t wo
experimental
resulting
be
f o u r —w a v e
determines
the
to
and
for
the
hy p e r f i n e
external
magnetic
f i e l d . 7<
H = Aj(J-t) .
The
splitting
between
hyperfirie
levels
for
Tb 3 + i s
then
AE = 6 Aj ,
where
and
J =6
In
LiTbF4 .
electron
7 7
in
spin
This
checking
that
discovered
Bleaney,
1=3/2.
this
is
the
in
a value
Aj = 5 3 0
measurements,
previous
measurements
resonance
i mp I i e s
exact
rare
techniques.
value
earth
MHz
it
was
obtained
salts,
in
by
using
128
Conclusions
The m o s t
wave
mixing
interesting
ma y b e
I inewidth.
These
restrictions
will
the
homogeneous
I inewidth
could
experiment
. and
signal
as
this,
one must
the
But
the
strength
is
a ( a)) * L .
the
s a me
be
a
a
a role,
signal
fit
strength
thick
crystals
extreme
scale
with
very
linewidth
oscillator
strengths
many
are
ma y
9xl0- ^
rare
larger
be
for
earth
by
prime
2 or
in
the
is
reach
^Fg
m aterials
3 orders
candidates
the
3+
<----->
have
of
for
f-f
enough
in
to
the
LiTbF^
of
oscillator
41
crystal
the
limited
the
thick,
and
the
dimension,
so
produce
only
transitions
transition
this
is
discussed
by
m aterial.
magnitude.
is
signal
will
oscillator
limit.
centimeter
thickness
testing
produce
parameter
Figure
one
particular
Tb
narrowest
fundamental
absorptions
signals
the
for
the
mixing
To r e a l i z e
important
shown
by
homogeneous
changed.
a crystal
as
imposed
the
because
four-
matching
f o u r —w a v e
big
the
phase
the
of
this
of
homogeneous
limit
a
was
that
with
narrow
homogeneous
angle
narrowing
strong
the
linewidth
signal
parameters
both
doing
since
from
the
holds,
restriction,
simulated
signal
small,
the
to
of
that
that
by
sample
severe
The
and
measured
have
application
fundamental
If
matching
plays
previously.
strong
the
necessary
The
indicate
linewidth.
f o u r —w a v e m i x i n g
with
approach
useful
measurement
studies
phase
not
also
the
measuring
narrowing
this
in
and
the
Although
are
in
quite
LiTbF^,
strengths
These
very
which
materials
hypothesis
and
129
reaching
the
homogeneous
Further
detail,
simulations,
have
homogeneous
limit
demonstrated
linewidth.
simulation
and
varying
expected,
homogeneous
Doubly
have
to
far
wait
reaching
future
Resonant
for
which
that
the
f o u r —w a v e m i x i n g
the
is
the
mixing.
been
crystal
if
length
in
the
it
of
is
it
the
that,
as
limit
prediction
practical
experiments,
the
fundamental
but
in
is
predict
This
done
limit
width
verification,
a n d many
transition.
fundamental
simulations
Four-Wave
implications
not
homogeneous
width
experimental
material
have
the
the
profile,
this
the
By v a r y i n g
inhomogeneous
the
of
will
will
have
applications
confirmed.
in
in
130
INTENSITY
WAVE NUMBERS
Figure
41:
Model s i m u l a t i o n
as a f u n c t i o n of
L = 1 .0 cm.
of f o u r - w a v e m i x i n g
signal
phase matching angle.
AP P ENDI CES
132
APPENDI X I
/*
# i n c l u de
# i nolude
^include
HOLE BURNI NG PROGRAM TO R E P E T I T I V E L Y
SCAN LASER I N BURN- READ CYCLE
*/
< s t d. h >
< r t 1 I . h>
"da.c"
main ()
i nt
i nt
scan, r d l y , v o lt , hbtime ;
i , j , k, I , m, s , t ;
/ * SET HOLE BURN TIME * /
p u t f m t ( "Ho l e b u r n i n g t i m e , i n t e g e r \ n " ) ;
g e t f m t( " g i\ n » , &hbtime);
/ * SET SCAN SPEED * /
p u t f m t ( " s c a n s p e e d , ramp i n c r e m e n t \ n " ) ; {
g e t f m t ( "%i \ n ", & s c a n ) ;
p u t f m t ( "ramp d e l a y \n
.
g e t f m t ( "%i \ n ", & r d l y ) ;
/ * SET ACOUSTO-OPTIC MODULATOR VOLTAGE # /
p u t f m t ( " v o l t a g e , A / 0 m o d u l a t o r , I 84 3 < = v o l t a g e < = 2 0 4 7 \ n " ) ;
g e t f mt( "% i\n», & v o lt) ;
/ « NUMBER OF SCANS TO AVERAGE * /
p u t f m t ( "How many s c a n s do. y o u w a n t ? \ n " ) ;
g e t f m t ( "%i \ n " , &j ) ;
/ * SET START POSI TI ON * /
p u t f m t ( " 0 => m i d f r e q . , I => l o w f r e q . X n " ) ;
g e t f m t ( " % i \ n " , &m) ;
■ i f ( m == I ) {
fo r(s= 3 0 7 1 ;s> = 2 0 4 7 ; s-=16)
.
{
p u t v o l t ( 2 , 2 0 47 ) ;
p u t v o l t (0, s );
}
}
Z 8 START SCAN 8 Z
putfm t( "hit return
ge t f m t ( " \ n " );
key
to
s t a r t X n ");
133
f o r ( k = I ; k <= j ; k + = I )
{
f o r ( s = 1 ; 3 < = h b t i m e ; s + =1 )
p u t v o l t ( 0 , 2 O4 7 )
/ » SET A / 0 MODULATOR VOLTAGE TO 1 VOLT TO BURN HOLE * /
p u t v o l t ( 2 , I 844);
f o r ( 1 = 2 0 4 7 ; I < =3 07 I ; i + = l 6 )
{
pu tv o l t (2,2047) ;
put v o l t ( 0 , I ) ;
}
p u t v o l t ( I , I 024) ;
f o r ( 1 = 0 ; 1 < = 2 5 ; 1 + = 1 ){}
. / $ TRIGGER PULSE * /
p u t v o l t ( I , 20 47 ) ;
' / * LASER SCAN VOLTAGE * /
f o r ( s = 3 07 I ; s > = 10 2 3 ; S- = S c a n )
{
putvolt(0,s );
p u t v o l t ( 2, v o l t ) ;
f o r ( 1 = 0 ; K =r d l y ; ! + = I ) H
>
.
f o r ( s = 1 0 2 3 ; s < = 2 0 4 7 ; s +=16)
{
p u t v o l t ( 2 , 2047);
p u t v o l t ( 0 , s );
}
•
.
}
f o r ( s = 20 47 J s <=3 07 I ; 1 + = 1 6 )
{
putvolt(2,2047);
p u t v o l t ( 0 , s );
}
p u tv o l t( 0 ,3071);
p u tfm t( "done\ n ");
}
134
AP PENDI X I I
/9
PROGRAM TO ERASE HOLE IN THE INHOMOGENEOUS L I N E
#in e l u d e
#include
#in e l u d e
*/
<std.h>
<r tlI . h>
"da.c"
main()
{
i nt
i nt
scan, r d ly , vol t ;
j , k, I , m, n, s ;
/ * I N I T I A L I Z E ALL D/ A OUTPUTS TO ZERO * /
p u t f m t ( nSho u l d s c a n b e i n i t i a l i z e d ? O => y e s \ n n ) ;
g e t f m t C rt% i \ n n, &n ) ;
i f ( n == 0 ) {
p u t i n i t () ;
}
/ * NUMBER OF SCANS TO ERASE HOLE * /
p u t f m t ( nHow many s c a n s do y o u w a n t ? \ n n ) ;
g e t f m t ( n ^ i N n " , &j ) ;
/ * SET SCAN SPEED * /
p u t f m t ( ns c a n s p e e d , r amp i n c r e m e n t \ n " ) ; {
ge t f m t ( n%i \ n ”, &s c a n ) ;
p u t f m t ( rtr amp d e l ay \ n " ) ;
g e t f m t ( n$ i \ n ”, &r d I y ) ;
/ » SET ACOUSTO-OPTIC MODULATOR VOLTAGE » /
p u t f m t ( " v o l t a g e , A / 0 m o d u l a t o r , I 8 4 3 < = v o l t a g e < =20 4 7 \ n " ) ;
g e t f mt ( " % i \ n " , &vdl t ) ;
.
/ 9 SET START POSITION * /
p u t f mt ( " O => m i d f r e q . ,
g e t f m t ( " % i \ n " , &m);
i f ( m = = O) {
I => l o w
f r e q . \ n " );
f o f ( s = 2 0 47 ; s <=307 I ; s + = 1 6)
.
• { ;
putvol t(2 ,2 0 4 7 ) ;
■p u t v o l t ( 0 , s );
}
}
/ 9 START SCAN * /
putfm t( "hit return
ge t f m t ( " \ n " );
key
to
s t a r t \ n ");
135
f o r( k = 1;k<=j;k+=I ) .
{
p u t v o l t ( I , I 024) ;
f o r ( 1 = 0 ; 1 < = 2 5 ; 1 + = 1 ){}
p u t v o l t ( I ,2047);
Z 8 LASER SCAN VOLTAGE * /
f o r ( s = 3 0 7 1 ; 3>=1 0 2 3 ; s - = s c a n )
{
putvolt(0, s ) ;
putvolt(2,v o lt) ;
f o r ( 1=0 ; K = r d l y ; I + = I ){}
}
for(s=1023;s<=2047;s+=l6)
{
p u tv o lt( 2 ,2047);
p u t v o l t ( 0 , s );
}
p u t v o l t ( 0 , 2 0 47) ;
p u t v o l t ( 3 , 1 53 5 ) ;
p u t v o l t ( 3 , 2 0 47 ) ;
f or(s=2047;s<=3071;1+=16)
{
p Ut V o l t ( 2 , 2 0 47 ) ;
putv ol t ( 0 , s ) ;
}
}
putvolt(0,3071);
p u t v o l t ( 2 , 2 0 47 ) ;
p u t v o l t (3>2047);
P u t f m t ( nUoneXnn );
}
■
/#
TRI GGER
PULSE
»/
136
APPENDIX I I I
/^PROGRAM
TO SCAN LASER AND ACCEPT PHASE SWITCH DATA
TEKTRONIX 7912AD TRANSIENT DI GI TI Z ER * /
# i nclude
^include
# i nclude
< s t d . h>
< r 11 I . h >
"da. c "
main( )
{
i nt
IBUPO ;
int
w r i t e = 0;
int
read = I ;
i nt
r e m o t e = 4;
i nt
l o c a l = 5;
int
digitizer = I ;
char
s COmdI ;
char
s Comd2 ;
char
s comd3;
int
len stl;
int
lenst2;
' int
lenstg;
char
stripC g];
u n s ig n e d char a r r ay[ 1024]
long
s u m a r a y [ 51 2]
int
three = g;
int
s i z e = 1024;
i nt
two = 2;
int
one = I ;
int
b it9 = 256;
int
ji
I, s ;
int
s can, r d l y , v o l t ;
int
sh o t = I ;
char
f ilnam [20];
FIO
fio ;
int
sh o ts, save ;
p u t f mt ( nWh a t i s t h e name o f
g e t f m t ( n% p \ n n, f i l n a m ) ;
i f ( I f c r e a t e ( & f i o , f i l n a m , I ))
the
data
f i l e ? \ n " );
{
p u t f mt ( wE r r o r : c a n ' t
return;
}
o p e n %p \ n n, f i l nam) ;
FROM
137
/ » NUMBER OF SHOTS TO AVERAGE * /
P u t f mf c CnHow many s h o t s do y o u w a n t ? \ n u ) ;
g e t f m t ( u % i \ n ", A s h o t s ) ;
c o md I = uDIG S A , \ 0 U;
i = i t o b ( G o md l + 7 , s h o t , I O) ;
c o m d I [ 7 + i ] = 1XO*;
comd2 = uREAD SA \ 0 U;
comd3 = uMOD TVXOu ;
l e n s t l = I e n s t r C comdI);
I e n s t E = l e n s t r ( comdE);
I e n s t S = l e n s t r ( comd3);
f c a l l ( I B U P , 2 , Ar e m o t e , Adi g i ' t i z e r ) ;
f c a l l ( IBU P, 4, A w r i t e , A d i g i t i z e r , comd I , A l e n s t l ) ;
/ * SET SCAN SPEED * /
p u t f mt ( us c a n s p e e d , r a m p i n c r e m e n t Xnu ) ; {
g e t f m t ( u % i Xn ” , As c a n ) ;
p u t f m t ( ur a m p d e l a y \ n u ) ;
g e t f m t ( u% i \ n u, A r d l y ) ;
/ * SET ACOUSTO-OPTIC MODULATOR VOLTAGE * /
p u t f m t ( " v o l t a g e , A / 0 m o d u l a t o r , 1843< =v o l t a g e < = 2 0 4 7 \ n u );
g e t f m t ( u % i \ n u, Avol t ) ;
/ * START SCAN « / '
p u t f m t ( " h i t r e t u r n key t o s t a r t \ n u );
ge t f m t ( u Xnu ) ; .
f o r ( k =I ; k <=sh o t s ; k + = I )
{ ■
p Ut Vo l t ( I , I 0 2 4 ) ;
f o r ( 1 =0 ;1<=2 5 ; 1 + = I ) {}
/ » TRIGGER PULSE * /
p u.tv o l t ( 1 , 2 0 4 7 ) ;
/ * LASER SCAN VOLTAGE * /
f o r ( s = 3 07 I ; s > = I 0 2 3 ; s - = s c a n )
{
p u t v o l t ( 0 , s );
p u t v o l t ( 2 , v o l t );
f o r ( 1 = 0 ; K = r d l y ; 1 + = I ){}
}
f o r ( s = I 023 ; s < = 2 0 4 7 ; s + = l 6 )
{
p u t v o l t ( 2 , 2 0 47 ) ;
p u t v o l t ( 0 , s );
}
p u t v o l t ( 0 , 2 0 47) 5
p u t v o l t ( 3 , 1 53 5 ) ;
p u t v o l t ( 3 , 2 0 47) ;
f or(s=2047;s<=3071;s+=l6)
{
P u t v o l t ( 2 , 2 0 47) ;
p u t v o l t ( 0 , s );
138
}
shots
f
f
f
f
= shots + I ;
c a l l ( IBUP, 4 ,
c a l l ( IBU P, 4 ,
c a l l ( I B UP, 4 ,
c a l l ( IBUP, 4,
putfmtC'SAVE?
ge t f m t ( " % i \ n ",
i f ( s a v e == 0)
&wri t e , & d i g i t i z e r , c om<32 , & l e n s t 2 ) ;
&r e a d, &d i g i t i z e r , s t r i p , & t h r e e ) ;
&r e a d , &di g i t i z e r , a r r a y , & s i z e ) ;
&r e a d, & d i g i t i z e r , s t r i p , &two ) ;
0 => Y E S X n " ) ;
&s a v e ) ;
{
shots = shots- I ;
for(i= 1;i< 7;i+ =1)
'{
:
. a r r a y [ I 5 9 + i ] = ( a r r a y [ I 57 + i ] + a r r a y [ 1 6 3 + i ] ) / 2 ;
a r r a y [ 2 5 1 + i ] = ( a r r a y [ 2 4 7 + i ] + a r r a y [ 24 9 + i ] +
array[257+i] + a r r ay[259+i])/4 ;
-}
f o r ( j= 0 ; j< 5 1 2 ; j++)
{
s u m a r ay [ j ] = s u m a r a y [ j ] + a r r a y [ 2 s j ] s b i t 9
a r r a y [ 2®j + 1 ] $o n e ;
}
+
}
f c a l l ( IBUP, 4 , &wri t e , &di g i t i z e r , com d I , &1 e n s t I ) ;
}
p u t f ( &f i o , " % \ n " ) ;
f o r ( i = 0 ; i < 6 4 ; i++)
{
p u t f ( &f i o , "55+ X06041 2 + X 0 6 0 6 1 % + \ 0 6 0 6 I % + \ 0 6 0 6 I
% + \ 0 6 0 6 I %+\0606I 2 + X0 6 0 6 1
% + \ 0 6 0 6 I %+ \ 0 6 06 I X n "
( l o n g ) ( S8I ) , s u m a r a y [ 8 c i ] , s u m a r a y [ 8 8 i + 1 ] , s u m a r a y [ 8 8 i + 2 ] ,
s u ma r a y [ 8 # i + 3 ] , s u m a r a y [ 8 5 i + 4 ] , s u m a r a y [ 8 s i + 5 ] ,
s u m a r a y E8 s i + 6 ] , s u m a r a y [ 8 * i + 7 ] ) ;
}
f close(& fio);
p u t v o l t ( 3 , 1 53 5 ) ;
p u tv o l t( 3,2047 ) ;
f c a l l ( IB UP, 4 , &wri t e , & d i g i t i z e r , comd3 , &1 e n s t 3 ) ;
p u t v o l t ( 0 ,307 1 );
p u t v o l t ( 2 , 2047);
p u tv o lt (3,2047);
f c a l l . ( IB UP, 2 , &1 o c a l , &di g i t i z e r ) ;
p u t f m t ( "done \ n " );
}
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DATE
O t t e s o n , M. S.
O n tic a l c o h e r e n t
tra n s ie n ts an d ...
ISSUED TO
D378
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