Optical Phase Conjugation As Zakharov-Shabat Problem

Abstract

The generation of an optically phase conjugated signal in four-wave-mixing (FWM) is usually interpreted1–2 as a coherent addition of diffracted waves from the grating structures formed in the nonlinear optical medium by the pump beams. In this paper, optical phase conjugation (OPC) is analyzed from a different point of view, namely, that of potential scattering. The optical medium acts as a "potential” which scatters the incoming probe wave nonlinearly into the conjugate signal, the potential being generated by the counterpropagating pump waves. It is shown that in this picture, transient OPC is described by the Zakharov-Shabat eigenvalue problem3 (ZSP) which is the linear scattering problem for a class of evolution equations such as the nonlinear Schrodinger equation. The methodology of the inverse scattering transform3-4 (1ST) can thus be used to analyze the problem. Many of the well established results of OPC are rederived in this paper using this approach along with some new ones. Moreover, an inverse scattering problem is posed regarding the time evolution of the potential which directly reflects the molecular dynamics involved.