**Spatial switching** Mar. 24, 2014

+
Directional coupler (Sect 7.4B in 1st Ed, Sect 8.5B in 2nd Ed):
Two planar waveguides are brought very close to each other
wave in one waveguide can completely escape to another if the propagation
constant of the wave in both waveguides are **phase matched**.` `

Waves --
&

Coupled mode eqn --
,
where & are coupling coef. and is the
phase mismatch.` `

Variation of waves with propagation distance --
where ,
.` `

, phase match complete exchange after a distance of
, i.e. an optical coupler

If distance = , we have a 3dB splitter.` `

+
Spatial switching by phase matching:
Build an optical coupler with an electro-optical material as substrate.` `
Without voltage complete transfer, otherwise reduced transmission.` `

when and when

where
and d is the spacing of the electrodes.` `

+
Spatial light modulator:
2D device makes of photoconductive and electrooptic materials sandwiched
by two electrodes

Writing image from the photoconductive side and causing drop in electric
field drop in and creation of a phase plate according to
the image

Read image by input light to the electrooptic side and the reflected
light is phase modulation by the phase plate.` `

The image retained for a short time.` `

E.g. Pockel readout optical modulator -- BSO which is electrooptic for
red and photoconductive for blue

Setting up image -- apply voltage, write image with intense blue light,
read with uniform red light, erase with uniform blue light and voltage

**Anisotropic EO materials** Mar. 24, 2014

+
Modified index ellipsoid:
where
impermeability
modified to include Kerr and Pockel effects.` `

Expect the orientation and size of the index ellipsoid affected by
orientation (polarization) and strength of the field

Notation on indices -- symmetry

Remap 1,1 1; 2,2 2; 3,3 3; 2,3 4; 3,1 5;
1,2 6 and 18 instead of 27

symmetry

After remapping, 36 instead of 81

+
Determine n when :

1. At , find , , and principal axes.` `

2. Find and from table.` `

3. .` `

4. Write eqn for modified index ellipsoid and see if the principal axes
rotated.` `

5. Find , and and/or new axes
by
rewrite the index ellipsoid eqn into
.` `

6. Use method in Ch. 6 to find n for certain direction of propagation.` `

Expect a) rotation of ellipsoid depending on wave polarization and crystal
structure

b) shape of ellipsoid changed with E

+
Matrix notation for isotropic Kerr media:

where

Notice the cross terms have factor of 2 owing to 2 permutations

+
Modulator design:

Recognize the direction of E-field and propagation direction of light
and choose the appropriate n & r.` `

Use the correct formula for .` `

+
Liquid crystals:

The ellipsoids in LC align with external E-field.` `

twisted nematic LC can be unwinded by E-field, i.e. a switch.` `

nematic LC modulator -- the extension of unwinding angle
depends on strength of
E-field where
for and is a critical voltage.` `

A voltage dependent retarder formed.` `

Applications -- phase modulator, wave retarder and
becomes intensity modulator when put between
cross polarizers.` `

_________________________________

HW #7 due 4/1/14

1. Problem 18.1-1 (page 735 1st Ed.; problem 20.1-2 page 871 2nd Ed.)

2. Exercise 18.2-1 (page 721 1st Ed.; exercise 20.2-1 page 856 2nd Ed.)

3. Problem 18.1-2 (page 735 1st Ed.; problem 20.1-3 page 871 2nd Ed.)

Extra-Credit

4. Problem 18.1-3 (page 735 1st Ed.; problem 20.1-4 page 871 2nd Ed.)

Last Modified: Mar 24, 2014

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