Vol. 19, issue 08, article # 13

Troitskii V.O. Second harmonic generation by focusing a beam into a uniaxial crystal with crossed cylindrical lenses. Approximation of a preset field. // Atmospheric and oceanic optics. 2006. V. 19. No. 08. P. 668-674.
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A method is proposed, which allows the solution of the second-harmonic generation (SHG) problem in a uniaxial nonlinear crystal to be presented as a double integral in the approximation of a preset field at the fundamental frequency. This fact makes the final analytical equation simpler and more convenient for practical use than the known Boyd-Kleinman approximation. Within the frameworks of the method proposed, the problem of SHG by use of a laser beam focused with crossed cylindrical lenses into a crystal is solved. It is shown that, in a certain case of practical interest (ray optics approximation), the equation for the second-harmonic field can be written through elementary functions and is free of quadratures.