Approximate Technique for Solution of the Problem of Second Harmonic Generation in Nonlinear Crystals: Part 1

Abstract

A technique is suggested for an approximate solution of the set of equations responsible for second harmonic generation in nonlinear uniaxial crystals. The algorithm of this technique is reduced to numerical calculation of a triple integral. The study consists of two parts. In the first part, two approximations are considered, which allow a reduction of nearly two orders of magnitude in the computation time of double integrals over the transverse coordinates. In the second part, we discuss an approximate technique for estimating the power of interacting waves, which also allows a further reduction in the computation time by an order of magnitude by reducing minimum number of required steps in the recurrence process. The test results show that the use of these approximations can decrease the accuracy of the solution of the nonlinear problem but can keep the errors acceptably low.

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Correspondence to V. V. Kolosov or V. O. Troitskii.

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Translated by O. Ponomareva

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Kolosov, V.V., Troitskii, V.O. Approximate Technique for Solution of the Problem of Second Harmonic Generation in Nonlinear Crystals: Part 1. Atmos Ocean Opt 33, 302–311 (2020). https://doi.org/10.1134/S1024856020030069

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Keywords:

  • second harmonic generation
  • set of nonlinear equations
  • numerical scheme