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