kjn
c
EE
kk
B
Through the Looking Glass and What We Found There
Reduced phase velocity: nAbsorption:
external reflection: n = 1.5
TM
TE
-1
-0.5
0
0.5
1
0 20 40 60 80
r
Angle of Incidence
internal reflection: n = 0.667
TM
TE
-1
-0.5
0
0.5
1
0 20 40 60 80
r
Angle of Incidence
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80
R
Angle of Incidence
TM
TE
external reflection: n = 1.5 internal reflection: n = 0.667
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80
R
Angle of Incidence
TMTE
variable phase
j
j
ee
r
xerEE tkzjir ˆ
xeEee
E tkzjij
j
r ˆ
xeEeE tkzji
jr ˆ2
xeEE tkzjir ˆ2
write r in this form:
Why? Because:
phase shift = 2
sincossincos
jj
sincossincos
jj
j
j
ee
r
Great, but what is ?
i coscos 22sinsin ni
i
i
n
n
cos
sintan 2
22
TE:
Phase shift upon total internal reflection:
i
i
n
n
cos
sin
2tan 2
22
TM
i
i n
cos
sin
2tan
22
TE
0
40
80
120
160
0 20 40 60 80
Pha
se S
hift
(de
g)
Angle of incidence (deg)
TM
TE
TM-TE
Tunable phase lag based only on dielectric reflections!
The Fresnel Rhomb:
linear
circular
glass
Phase Retarder
“birefringence”
A dependence of the index of refraction on polarization (anisotropy in n).
y
x
j
j
e
e
0
0 oeo
nnd 2
Jones:
linear
circular or elliptical
Phase shift between H and V.
Jones matrix:
y
x
j
j
e
e
0
0
SA
Phase Retarder
polarizer
TA
QWP
FA
SA
1/8 WP
0
1
10
0
10
0
21
21
21
2124 jj ee
21
2124
10
0
10
0 jj ee
21
2214
10
0 jj ee
21
4221 jje
Phase Retarder
linear
Jones Matrix:
cossin
sincos
rotate by
Rotator
“optical activity”
Rotation of linearly polarized light as it travels through a material.
“optical activity”
RCP + LCP = linear
= Specific rotation:10’s – 100’s degree/mm(depends on wavelength)
Optical activity can be thought of as the result of circular birefringence!
nL > nR
BirefringenceDichroism
Circular
Linear
Manipulating Polarization:
2
2
sincossin
cossincos
y
x
j
j
e
e
0
0
cossin
sincos
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