Effects of absorption, pump depletion, and nonlinear refraction on thermal degenerate four-wave mixing

Abstract

Degenerate four-wave mixing, arising from the thermal grating effect or other mechanisms such as the Kerr or photorefractive effect, can be described by a set of four coupled differential equations involving the four fields. Analytical solutions to these equations have been presented for cases where either the pump depletion or the effects of absorption were ignored.1 When both the pump depletion and absorption effects were included, a numerical result involving an iterative solution of the differential equations was presented.2 We present here a solution of the coupled-wave equations in which absorption as well as pump depletion effects are taken into account along with nonlinear refraction. The DFWM reflectivity is reduced to a quadrature using a method proposed by Kessel and Musin.3 For special cases of small absorption and no pump depletion, the solution reduces to the expressions presented earlier.4 The method of solution does not involve finding first integrals of the set of differential equations and can be extended to the description of DFWM using other physical mechanisms.