Parametric amplification of light waves at low-frequency pumping in aperiodic nonlinear photonic crystals

Abstract

The process of nondegenerate optical parametric amplification in a low-frequency pump field that includes the traditional process of parametric amplification at high-frequency pumping and two up-conversion processes is investigated. Such coupled interactions can be simultaneously realized in an aperiodic nonlinear photonic crystal (ANPC) i.e., in a crystal with an aperiodic change of sign of the nonlinear wave coupling coefficient. ANPCs can be created by the method of superposition of nonlinearity modulations by three functions for each of which the quasi-phase-matching condition is met for one of the processes involved in the interaction. In addition to the results obtained from a direct numerical solution of the original coupled equations with spatially varying wave coupling coefficients, the results of their solution containing effective constant wave coupling coefficients are presented. An approach that allows the calculation of these coefficients to be simplified considerably has been developed. The two methods have been found to yield closely coincident results for the characteristics of the processes studied here. A LiNbO3 ANPC has been used as an example to calculate the tuning characteristics of the process, its dynamics, the frequency bands of parametric amplification, and the effect of a random deviation from the quasi-phase-matching conditions on the wave interaction efficiency.