RESEARCH ARTICLE | OCTOBER 21 2003
OPTICAL PARAMETRIC OSCILLATION IN LITHIUM IODATE
Lawrence S. Goldberg
Appl. Phys. Lett. 17, 489–491 (1970)
https://doi.org/10.1063/1.1653280
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VOLUME 17, NUMBER 11
1 DECEMBER 1970
APPLIED PHYSICS LETTERS
OPTICAL PARAMETRIC OSCILLATION IN LITHIUM IODATE
Lawrence S. Goldberg
Naval Research Laboratory, Washington, D. C. 20390
(Received 4 September 1970)
Optical parametric oscillation has been achieved in Lil0 3 pumped by a pulsed ruby laser.
with tunable output to 411. Operation of the singly resonant oscillator is described and threshold measurements are compared with theory.
deft =d31 sin (6 M +p),
where only type I birefringent phase matching
(w; =w~ + w~) is allowed. In the oscillator experi-
ments an extraordinary-polarized pump wave at
O. 6943jJ. interacted collinearly with ordinary signal and idler waves. The crystal was 8 mm long
and cut for phase matching at 21 ° from the optic
axis. Its faces were polished flat and parallel and
were Ar coated for the resonant signal wavelength
by a single quarter-wave layer of cryolite centered at O. 86jJ.. Measured single-pass transmission loss at the signal wavelength was 2%. Wavelength tuning of the interaction was by crystal
rotation at room temperature, as Lil03 has reportedly no temperature tunability.
The oscillator cavity was formed by a pair of
flat dielectric-coated mirrors, highly reflecting
(R >99%) only for the resonant short-wavelength
signal while transmitting 85% of the pump. The
nonresonant infrared idler was strongly coupled
out of the cavity (T >85%) through a BaFz output
mirror coated by multiple layers of ZnS and cryolite. The cavity mirrors were spaced 1. 5 cm apart
and located 1 m from the laser; a slight misalignment between the cavity and pump axes prevented
feedback that would distort development of the
laser pulse. The pump source was an unfocused
2-mm-diam beam from a passively Q-switched
ruby oscillator-amplifier operating in TEMooq
single mode with pulse width at half-peak power of
25 nsec.
Figure 1 gives the collinear wavelength tuning
curve measured from spontaneous parametriC
scattering, without the cavity mirrors in place.
Signal radiation was detected from 0.77 to 1. 05jJ.
by an S -1 photomultiplier in combination with a
monochromator of 32-A. pass band, polarizer, and
Schott RG-series filters. In order to conSistently
determine crystal orientation, the direction of
crystal face normal was measured relative to the
phase-matching direction for second harmonic
generation from a Nd : YAG laser operating at
1. 064jJ., for which an internal phase-match angle
of 29.5° was assumed from extrapolated data of
Nash et al. 2 The ordinary index of refraction was
then calculated for the idler wave between 2 and 7
jJ. using the tuning curve of Fig. 1 and the refractive-index data of Nath and Haussiihl 1 for the pump
and signal waves. Our calculated index values
differ in some degree with those of Campillo and
Tang3 obtained from parametriC scattering measurements with an Ar laser. We find a mean refractive index approximately 0.01 smaller at 2,
4, and 5jJ. and 0.02 smaller at 3 jJ.. Possible
errors of 0.003 to 0.006 in the calculated idler
SIGNAL WAVELENGTH (MICRONS)
5.02.0
§UJ
23
UJ
22
1.0
0.90
~
0.85
0.80
0.78
0.77
Li 10,
0.69431"
g
I
g
21
..it:
20
~
UJ
<J)
...J
~
'"~19
z
L-~_ _~~~-,~~~~~~~~~~~~~
1.0
2.0
3.0
4.0
IDLER WAVELENGTH
5.0
6.0
7.0
(MICRONS)
FIG. 1. Collinear tuning curve measured from spontaneous parametric scattering. The dashed portion of
the curve near degeneracy is calculated from interpolated
refractive-index data.
489
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In this letter experiments on optical parametric
oscillation in a lithium iodate (Lil0 3) crystal are
reported. Lil03 has been shown in recent studies 1 •2
to have considerable potential as a nonlinear material. It has nonlinear coefficients comparable to
LiNbOa, but with much better resistance to optical damage and a greater transparency range in
the infrared. Parametric scattering studies indicate 3 that oscillation could be sustained in Lil03
to wavelengths of about 5. 4jJ. before attenuation
occurs, whereas LiNb03 , which has been employed
extensively in parametric oscillator experiments, 4
appears limited to about 4. 2jJ.. 5 In the present
experiments using a singly resonant cavity design
and a pulsed ruby laser pump, we obtained tunable
infrared output in Lil03 to 4 jJ.. The operating char
acteristics of the oscillator were studied and its
observed threshold power was compared with theory.
Lil03 is a negative uniaxial crystal of hexagonal
point symmetry C s . Its effective nonlinear coefficient is given bys.7
VOLUME 17, NUMBER 11
-<I
20ns
1-
,....
V
V
'-1/
~
I\..
'l'.-
1---
FIG. 2. Parametric oscillator waveforms. Left to
right: laser pump pulse incident on the cavity, pump
showing depletion after passing through the cavity, signal radiation emitted at 0.9011 .
wavelengths and the tuning curve again becomes
single-valued.
Because of the short duration of its pumping
pulse the oscillator operates in a highly transient
condition. Accordingly, higher pump powers than
calculated under steady-state conditions are required to reach oscillation threshold during the
brief build-up time available. A lower bound on
threshold power density can be evaluated after
Kreuzer9 for a single resonant oscillator in the
steady state. Expressed in its explicit wavelengthdependent terms for LiIOa pumped at 0.6943 /.l
""3 7
P
T
•
AS(/.l) Ai(/J.) MW/c 2
Z2(cm) sin2(8 M +p)
m,
_ €-
(1)
where € is the equivalent round-trip loss at the
resonant wavelength, Z is the crystal length, da1
'" 1. 8 x 10- 8 esu, a and the double-refraction angle
p '" 3°. For an idler at 3 /.l, Eq. (1) reduces to
P T ""65(€/Z2) MW/cm2 ; at 4/J. and 5/J., P T is higher
by factors 1. 3 and 1. 6. The present experiment
has Z'" O. 8 cm and € '" O. 05, taking only the measured transmission and coupling losses. This gives
a calculated steady-state threshold at 3/J. of 5 MW/
cm2 • The experimental threshold, in comparison,
is approximately 12 times higher; at this pumping
level a round-trip gain9 ,lO of 1. 8 dB is calculated
which is consistent with the observed build-Up
time of about 10 nsec or 70 round trips.
Steady-state thresholds calculated from Eq. (1)
for the ruby pumped LiIOa oscillator compare
favorably with those for an equivalent oscillator
employing LiNbO a. If we assume equal (E/Z2) terms,
an idler at 3 J.l, and take for LiNb03 11 liM'" 50° ,
and appropriate deff , then we find PTLII03/PT LINbOa
""3.6. The need for somewhat greater pump power
density with LiIOa is compensated in part by its
very high resistance to optical damage. LiIOa cannot be phase matched at liM'" 90°, for which optimum focusing 7 in the absence of double refraction
affords a considerable reduction in total pump
power requirement. It does, however, offer particular advantage in high peak power applications
due to its optical damage resistance as well as in
high average power applications due to insensitivity
of its phase-matching conditions to crystal temperature changes. In addition, the use of LiI03 offers
the potential of obtaining tunable output over a
wider wavelength range in the infrared.
The author is indebted to F. von Batchelder of
the NRL Central Materials Research Activity for
growth of the LiIOa crystal and to 0. Laing and A.
Pratt for polishing and dielectric coatings.
lG. Nath and S. Haussiihl, Appl. Phys. Letters 14,
Downloaded from http://pubs.aip.org/aip/apl/article-pdf/17/11/489/7728837/489_1_online.pdf
index can result from uncertainties of only 0.001
in the index at the pump or Signal wavelengths or
0.5° in measured phase-match angle.
Operation of the parametric oscillator is shown
in the oscilloscope trace of Fig. 2. The waveforms
depict, from left to right, the laser pump incident
on the cavity, the pump showing depletion after
passing through the cavity, and the signal radiation emitted at O. 90 /.l (idler 3. 0 /.l). Detection was
by separate PIN photodiodes delayed by cable and
displayed on a single oscilloscope trace with combined risetime of 2.5 nsec. The amplitudes of the
waveforms in Fig. 2 are not directly comparable.
At this wavelength oscillation threshold occurred
at a measured in-crystal peak power density of
approximately 60 MW/cm2 • In Fig. 2, pumping
is 1. 3 times this threshold and the signal power
measured approximately 2 kW, or about 0.1%
conversion of pump power. Signal conversion efficiencies approaching 1% and pump depletion of
about 15% have been observed. Higher conversion
efficiencies can be expected for the nonresonant
idler since it is strongly coupled out of the cavity. 8
Tuning of the oscillator covered a range of signal wavelengths from 0.84 to 0.96 /.l, corresponding to idler radiation from 4.0 to 2.5 /.l. Idler
output beyond 4 /.l was not obtained in these initial
experiments since damage was incurred in the
BaF2 mirror coating at the higher power densities
needed to reach threshold. The Ar-coated LiIOa
crystal withstood damage to above 125 MW/cm2 ,
at which point some surface pitting occurred. Inspection of the tuning curve in Fig. 1 shows it to
be double-valued about the wavelength at 4. 6/.l,
and hence a significant reduction in parametric
gain for wavelengths in this vicinity could be expected. This feature arises from a rapid decrease
of refractive index at the idler due to anomalous
disper sion of the absorption band2 at - 6 /.l. For
pump wavelengths shorter than 0.6943 /.l, however,
the extremum at 4.6 /.l shifts toward longer idler
490
1 DECEMBER 1970
APPLIED PHYSICS LETTERS
1 DECEMBER 1970
APPLIED PHYSICS LETTERS
VOLUME 17, NUMBER 11
154 (1969).
2F.R. Nash, J.G. Bergman, G.D. Boyd, and E.H.
Turner. J. Appl. Phys. 40, 5201 (1969).
3A . J : Campillo and C.L. Tang, Appl. Phys. Letters
16,242 (1970); 16,537 (1970).
4 For a review, see S. E. Harris, Proc. IEEE 57,
2096 (1969).
sT. G. Giallorenzi and C. L. Tang, Phys. Rev. 184,
353 (1969).
6J .E. Midwinter and J. Warner, Brit. J. Appl. Phys.
16, 1135 (1965).
D. Boyd and D. A. Kleinman, J. Appl. Phys. 39,
3597 (1968).
BJ . E . Bjorkholm, Appl. Phys. Letters 13,399 (1968).
9 L. B. Kreuzer, Proceedings of the Joint Conference
on Lasers and Optoelectronics, IERE, London, 1969,
p. 53 (unpublished).
IOL.B. Kreuzer, Appl. Phys. Letters 15.263 (1969).
l1J. E. Bjorkholm. Appl. Phys. Letters 13, 53 (1968).
- 7 G.
ON THE COUPLING OF AN HIGH-CURRENT RELATIVISTIC ELECTRON BEAM
TO A SLOW WAVE STRUCTURE
John A. Nation
Annular relativistic electron beams carrying currents of 30-40 kA at energies
of 200-500 keV have been propagated through a cylindrically symmetric, annular,
ridged waveguide. An interaction between the electron beam and a backward wave
in the guide has been observed. This leads to oscillations in the range 7. 8-9. 7
GHz at power levels of about 10 MW in a 30-nsec pulse.
A Blumlein hansmission line1 has been used to
produce an annular electron beam of 60 nsec duration and 200-500 keV energy, carrying electron
currents of 30-40 kA. The beam was propagated
through an evacuated drift region (-10-4 to 10-1
Torr) and held together by an axial magnetic field
of 3.0 -12 kG. 2 The beam was produced in an
evacuated planar diode with an annular cathode and
entered the drift region through a I-mil aluminum
foil. Approximate values of the beam parameters
are listed in Table I.
In the experiments described in this letter the
electron beam was propagated through the structure shown in Fig. 1. Similar structures have
been used in low-power travelling-wave tubes. 3
The wave properties of this ridged waveguide have
been examined numerically and are based on the
existence of a transverse magnetic wave in the
annular region and standing transverse electromagnetic waves in the radial stubs. In these calculations the effect of the dielectric tensor of the
electron beam on the wave propagation has been
ignored, i. e., the solution gives the vacuum
properties of the waveguide. The dispersion relation describing the wave propagation is readily
shown to be
1
c
15 (K (r,p)I (r"p) + Io(r nb)Kl(r"p) )
O
rn
d)/Z) 2
k n(l-d)/2
'
and
k~=w2/c2+r~.
In the above equations, J, N, I, and K are the
Bessel functions and wand k represent the angu-
lar frequency and wave number, respectively. A
similar dispersion relation has been derived elsewhere. 3,4
Numerical solutions for the lowest-order azimuthally symmetric modes are shown in Fig. 2.
The high k section of the curve shown represents
a backward wave and hence provides a feedback
mechanism within the beamguide system. An
electron beam travelling with velocity Vb can
support, in the absence of the structure, spacecharge waves with phase velocities
V
-
(2)
Vb
1 ± (wi wy3/2)'
ph -
where w is the angular frequency of the wave, wp
(ne 2/E om o)l/2 is the beam plasma frequency, and
'Y =(1 - vU c 2rl/2. The conventional analysis of
travelling-wave tubes (see, for example, GouldS)
indicates that when the phase velocity of the slow
space-charge wave is approximately equal to the
phase velocity of a mode of the unloaded circuit,
coupling between the two waves occurs and ampli=
Injection
energy
(kA)
Major
radius
of beam
(cm)
30-40
3.4
Beam
current
1
n=-~ Ko(rnb)Io(rna) -Io(rnb)Ko(rna )
x....!. (Sinkn(l -
kn=ko+2rrn/l
TABLE 1. Electron beam parameters.
J 1 (Wa/C)No(Wg /c) - N 1(Wa/C)Jo(wg /C»)
( Jo(wa/c)No(wg/c) - No(wa/c)Jo(wg/c)
=~(l-d)
where
(ke\!)
(1)
200 - 500
Minor
radius
of beam
(cm)
0.4
Beam
plasma
frequency
(rad/sec)
x 10- 10
~4
491
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Laboratory of Plasma Studies and School of Electrical Engineering, Cornell University, Ithaca, New York 14850
(Received 18 August 1970)