We present an accurate numerical description of frequency-conversion processes that are based on the nonlinear interaction between three pulsed electromagnetic fields. Several interesting phenomena arising in these processes are described in detail. The numerical method used is a new modified Runge–Kutta method employing characteristics. This method can be used to solve numerically sets of coupled hyperbolic differential equations in two variables, if the coefficients of the derivatives are constant. In this paper three examples of frequency-conversion processes are presented that are strongly influenced by the combined effects of phase mismatch, group-velocity differences, and depletion of the electromagnetic fields.

© 1989 Optical Society of America

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