**Parametric oscillator** Apr. 21, 2014

General description of parametric amplification:

;
where
mirror and internal losses

For signal & idler
where
and

+
Parametric oscillator:

Condition for oscillation -- loss coef = gain coef; round trip phase
in multiple of .` `

- Assume perfect phase match and round trip phase
in multiple of for
and , i.e. double resonances.` `

- loss coef

- Unidirectional gain owing to phase matching.` `

,

**FWM and nonlinear refraction** Apr. 21, 2014

+
Four-wave mixing (FWM):

E.g. ,
(phase
matching)

+
Optical phase conjugation:

Degenerate FWM, i.e. all beam same freq automatic phase matched

and are strong counterpropagating pump beams;
and 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:

composed of wave mixing, self phase
modulation, cross phase modulation

+
Light induced anisotropy:
describes effect of wave polarization on nonlinear
refractive index.` `

Linear polarized plane wave only phase modulation no change in
polarization

Elliptic or circular polarized waves angular rotation =

_________________________________

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 or 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 , , which
generates
.` `
Find at and
at
with .` `

b) Mixing of 3 beams of , , 0 (DC) which generates
.` `
Find at and
at
with .` `

Last Modified: April 21, 2014

Copyright © < lawc@uwm.edu >