Abstract

Using perturbation theory, we examine the fidelity of the photorefractive degenerate four-wave mixing (DFWM) phase conju- gator when the probe wave is spatially and temporally varying. Previous theories are based on linearized undepleted pump approximation and Laplace transform technique. Fully nonlinear solutions assume a single monochromatic plane wave probe. We have considered instead the more general case in which the probe is spatially varying (a beam) and/or temporally varying (a pulse), and the pumps are allowed to deplete. The probe wave is expanded as a sum of monochromatic plane waves of frequencies ω_j = ω_p + Ω_j, wavevectors k_j, and complex amplitudes A_j(Ω_j, k_j), where ω_p is the frequency of the pumps. Using a perturbation approach up to the third order, we found that the components of the probe interact in pairs, so that the component of the conjugate wave at −Ω_l −k_l is H(Ω_l, k_l) is the linearized response, ρ(Ω_l, k_l; Ω_j, k_j) represents crosstalk when j ≠ l, and self-nonlinear effect otherwise. Both functions exhibit resonance behavior. We use Eq. (1) to determine the response of the conjugate to pulsed beams.

© 1989 Optical Society of America