Double phase conjugation

We model the double phase-conjugate mirror (DPCM) as a function of time, the average direction of propagation of the two beams forming the DPCM, and one transverse coordinate. Calculations show that the conjugation fidelity and reflectivity have different dependencies on the photorefractive coupling coefficient times length; the fidelity turns on abruptly with a threshold, whereas the reflectivity increases smoothly. The DPCM behaves as an oscillator at and above threshold: the time required for the reflectivity to reach the steady state dramatically slows down near threshold (like critical slowing down in lasers); above threshold the DPCM is self-sustaining even if the random noise terms used to start the process are set to zero. A decrease in the noise level improves the fidelity but increases the response time. The use of unbalanced input beam ratios results in asymmetric conjugation such that the fidelity obtained on the side of the weaker input beam is significantly reduced. The slowing down diminishes with increasing noise level or unbalanced input intensities.