Vol. 20, issue 09, article # 10

pdf Troitskii V. O. Scalar approximation for second harmonic generation in a uniaxial crystal. // Atmospheric and oceanic optics. 2007. V. 20. No. 09. P. 741-751.
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The problem of second harmonic generation in a quadratically nonlinear uniaxial crystal is considered. It is shown how a set of differential nonlinear wave equations for scalar fields at the frequencies ω and 2ω can be derived rigorously from the Maxwell equations neglecting the effects of depolarization of interacting waves. The transition to an equivalent set of integral equations is considered in detail. It is shown that for beams with a narrow spatial spectrum the equations derived convert into the well-known contracted equations for slowly varying complex amplitudes of interacting waves. The derivation of a recurrence equation is demonstrated. This equation is proposed to be considered as an approximated (with a known accuracy) analytical solution of the scalar nonlinear problem. At the increased number of steps, it transforms into a well-known algorithm of asymptotically exact numerical solution.