Photorefraction Mar. 31, 2014

Phototrefractive section from 1st edition of the textbook

+ Photorefractive effect: combining photoconductive and electro-optics, e.g. [equation]
Process -- 1. photoionization create electron density with rate [equation] which is proportional to the difference between number of donors [equation] and number of traps [equation] & light intensity [equation].
2. [equation] is a distribution and imprints of electron density distribution which will be equalized by diffusion current [equation]
3. Eventually recombine with at rate [equation] and dynamic equilibrium requires [equation]. Lead to n(x) \(pt I(x).
4. Before reaching equilibrium, photorefractive media has local E-field which causes drift current [equation]. At equilibrium, [equation] assuming [equation] and [equation] are const.
5. Refractive index changed by the local E-field owing to electro-optic effect

+ Applications:
Form gratings on photorefractive media (advantage -- indep of writing intensity)
Dynamic hologram (real time record & playback)
pro -- fast parallel I/O (x10), no moving parts, high capacity (x12)
con -- poor retention, noise of light source, tight physical tolerance
2 wave mixing [equation] form volume hologram; potential problem -- grating scattering leading to cross talk between obj and ref
Phase conjugation -- self correction of image, cross correlation of images and amplification

+ Electroabsorption: The application of electric field cause the bandgap energy of a semiconductor to reduce (Franz-Keldysh effect). The use of heterjunctions to form quantum well further preserve the sharpness of the absorption peak (exciton).

+ Nonlinear optics: modify polarization vector [equation] where [equation] and [equation] to include nonlinearity
Or [equation]
Nonlinear wave equation [equation] where we treat the nonlinear term as a source
Note -- media like liquid and gas have inverse symmetry [equation]
Note: [equation] or [equation] means a time varying field while the textbook uses [equation] to denote the time varying field.
[equation] is a phasor for my notes and textbook.
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HW #8 due 4/8/2014
1. Exercise 18.1-1 (page 709 1st Ed.; exercise 20.1-1 page 846 2nd Ed.)
2. Consider a InAs crystal with a microwave modulating electric field is along y direction, i.e. [equation], a) write down the equation for index ellipsoid under the electric field, b) write down expression for the refractive index seen by a optical beam polarized in x, c) write down expression for the refractive index seen by a optical beam polarized in z.
3. Consider an intensity modulator (see Fig. 6.6-4 for both Ed) with input polarizer in x direction and output polarizer in y direction (i.e. cross polarizer), and electro-optic retarder is made of GaAs with its optic axis along z. Assume n=3.43, [equation] at [equation]. Consider a longitudinal design with both light and modulating E in z direction. Find [equation].
4. Problem 18.2-1 (p. 735 in 1st Ed; problem 20.2-3 on p. 871 in 2nd Ed)
Extra-Credit
Consider the case of a KDP crystal with an applied field along the x axis. Show that in the new principal axes [equation], [equation] coincides with x while [equation] and [equation] are in y-z plane, but rotated from their original position by [equation] where [equation]. The new index ellipsoid equation is [equation]


Last Modified: March 30, 2014
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