Double-sided Feynman diagrams, which trace the evolution of the density operator in time during a nonlinear optical interaction, are used to analyze the processes of four- and three-wave mixing which lead to the production of phase conjugate waves.
Optical phase conjugation by four-wave mixing in a Kerr medium is considered. Two strong counterpropagating lasers pump a nonlinear medium in which they excite the third-order polarization. Mixing with a weak incident field then generates the phase-conjugated image of that field. It is shown how the polarization of the pumps and the tensorial nature of the nonlinear interaction can be accounted for by a geometrical polarization tensor. The electric field is shown to obey two coupled wave equations, which couple a positive- and negative-frequency component of the field. These wave equations allow plane-wave solutions, and we derive the dispersion relation for the wave vectors of these modes. By matching the field of such a mode across the boundaries of the medium to an external incident field, we are able to obtain analytically the Fresnel coefficients for reflection and transmission. Our expressions reduce to earlier results in the appropriate limits.
We have used a diagrammatic approach first developed for nonlinear optical calculations of the density operator to obtain expressions for the transition probability in various laser-switched collision processes. Not only do these diagrams considerably simplify the algebra involved in such calculations, but they also afford a clear visualization of the interaction. In particular, pair absorption, laser-switched Raman scattering, and collisionally enhanced hot luminescence and four-wave mixing processes are considered.
We explore dynamic media, such as plasmas and photorefractive materials, as generators of phase conjugated replicas of transient optical signals via four-wave mixing. The characterizing element of dynamic media is a population of free charge carriers that leads to induced charge density gratings on probe illumination. In steady-state conditions, phase conjugation in such media normally appears with smaller pump intensities than are required in Kerr media but at the expense of potentially slow response times.1