Uniaxial crystal
“ordinary index”
no  nx  n y
“extraordinary index” ne  nz
Call the unique direction z: “optic axis”
Ordinary wave or ray:
Any wave with polarization E  to the optic axis (OA).
The wave travels with index no.
Extraordinary wave or ray:
Any wave with E component along OA! (polarization in the k-OA plane)
The wave travels with index between no and ne,
which we call the function ne(q). Angle q between k and OA
General case: 2k’s, 2S’s
OA

2
x
u y2
u z2
1
 2 2  2 2  2
2
2
n
n  no
n  no
n  ne
u
 
 

becomes
ne (q ) 
no ne
no2 sin 2 q  ne2 cos 2 q
Crystals may be cut at
any angle vs. the optic
axis!
k
q
Optic axis
ne>no
no>ne
Don’t confuse s,p polarization with o,e polarization!
No direct connection
For this cut of crystal and k
vector shown, an e-wave is
the ____
a) s-polarization
b) p-polarization
c) both s,p are e-waves
d) neither s,p are e-waves
OA
For this cut of crystal and k
vector shown, an e-wave is
the ____
a) s-polarization
b) p-polarization
c) both s,p are e-waves
d) neither s,p are e-waves
OA
Finding E, S directions for the
extraordinary wave
Text gives equations for
directions of S, E for ONLY
the case in this picture:
OA  the interface….
so these equations aren’t
very important…
OA
Finding E, B,
S directions
for the
extraordinary
wave
x
z
 Px 
 x
 

P


y
o
 
0
P 
0
 z

k   o E  P   0
0
y
0
0  Ex 
 
0  E y 

 z 
 Ez 
Gives ratios of E components
Bo 
k  Eo

S  E
B
o
What is  to what?
E EE
 E  P 
o
OA
S
k
Polarizing prisms
Good for high
powered lasers.
(no heating from
absorption)
Cut and rejoin,
with OA perhaps
oriented
differently.
Polarizing prisms from uniaxial crystals
In prism d, which
exiting beam was
the e-ray in the
material it left?
a) top
b) bottom
Polarizing prisms
In prism a, the
the beams are
separated by TIR
___
So in this
material which
index is greater?
a) n-e
b) n-o
Polarizing prisms
In prism b, the
beams (k’s) are
separated by
Snell’s law.
Imagine the k-vectors
are shown.
So in this
material which
index is greater?
a) n-e
b) n-o