Parametric oscillator Apr. 21, 2014
General description of parametric amplification:
[equation]; [equation] where [equation] mirror and internal losses
For signal [equation] & idler [equation] [equation] where [equation] and [equation]

+ Parametric oscillator:
Condition for oscillation -- loss coef = gain coef; round trip phase in multiple of [equation].
- Assume perfect phase match [equation] and round trip phase in multiple of [equation] for [equation] and [equation], i.e. double resonances.
- loss coef [equation]
- Unidirectional gain owing to phase matching.
[equation]
[equation], [equation] [equation] [equation]

FWM and nonlinear refraction Apr. 21, 2014

+ Four-wave mixing (FWM):
E.g. [equation], [equation] (phase matching)

+ Optical phase conjugation:
Degenerate FWM, i.e. all beam same freq [equation] automatic phase matched
[equation] and [equation] are strong counterpropagating pump beams; [equation] and [equation] are probe and conjugate beams.
Conjugate beam retraces the path of probe.
Conjugate beam is the time reversal of probe.
Real-time holography
Wave restoration

+ FWM and nonlinear refraction:
[equation] composed of wave mixing, self phase modulation, cross phase modulation

+ Light induced anisotropy: [equation] describes effect of wave polarization on nonlinear refractive index.
Linear polarized plane wave [equation] only phase modulation no change in polarization
Elliptic or circular polarized waves [equation] angular rotation = [equation]
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HW #11 due 4/29/14
1. Problem 19.4-3 (p. 797; problem 21.4-9 2nd Ed, p. 935)
2. Find the threshold intensity or field for a single resonant parametric oscillator for the example on page 40 of the notes. Single resonant means only [equation] or [equation] reflected by the mirrors.

3. a. Find the r matrix for electro-optics effect and d-matrix for 2nd order nonlinearity in Quartz crystal
b. Ex 19.3-1 (page 751; Ex. 21.3-1 2nd Ed, p. 895)
4. Ex 19.3-2 (page 754; Ex. 21.3-2 2nd Ed, p. 897)
Extra-Credit
5. a) Mixing of 3 beams of [equation], [equation], [equation] which generates [equation]. Find [equation] at [equation] and [equation] at [equation] with [equation].
b) Mixing of 3 beams of [equation], [equation], 0 (DC) which generates [equation]. Find [equation] at [equation] and [equation] at [equation] with [equation].


Last Modified: April 21, 2014
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