Approximate technique for solution of the problem on second harmonic generation in nonlinear crystals. Part 1
V.V. Kolosov, V.O. Troitskii
V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Keywords: генерация второй гармоники, система нелинейных уравнений, численные схемы, second harmonic generation, system of nonlinear equations, numerical scheme
Abstract
A technique is proposed for approximate solution of the system of equations responsible for second harmonic generation in nonlinear uniaxial crystals. The algorithm of this techniqueis is reduced to numerical calculation of a threefold integrated integral. The study consists of two parts. In the first part, two approximations are considered. These approximations allow the time for computation of twofold integrated integrals with respect to transverse coordinates to be shortened nearly two times in the situations most complicated for computations. The second part discusses an approximate technique for estimation of the power of interacting waves, which also allows the computation time to be decreased by an order of magnitude by means of a decrease in the minimal needed number of steps of the recurrent process. The results of the tests demonstrate that although the use of the approximations proposed decreases the accuracy of solution of the nonlinear problem, but nevertheless keeps the errors at an acceptably low level.
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