Vector versus scalar theory of the double phase conjugate mirror

Abstract

The steady-state vector (TM polarization) and scalar (TE polarization) two-dimensional coupled wave equations for four-wave mixing in a photorefractive medium are derived directly from Maxwell's equations without invoking the slowly varying envelope approximation (SVEA). Without resorting to numerical methods, it is shown that the double phase conjugate mirror operates as an oscillator in the vector case and as an amplifier in the scalar case. It is also shown that this difference in behavior arises from coupling between the different components of the electric and magnetic fields which occurs for TM polarization and not for TE. In addition, it is shown that for TE polarization, the imposition of the full electromagnetic boundary conditions made possible by the inclusion of second derivative terms (which are absent when the SVEA is invoked) is responsible for the difference in these predictions from those of the usual one-dimensional scalar theory. The validity of the SVEA in the theory of photorefractive wave mixing is discussed, as well as some other differences in the operation of the double phase conjugate mirror between the vector and scalar cases.