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Analytical approximation of the second-harmonic conversion efficiency

Abstract

The second-harmonic generation process of a focused laser beam inside a nonlinear crystal is described by the Boyd–Kleinman theory. Calculating the actual conversion efficiency and upconverted power requires the solution to a double integral that is analytically intractable. We provide an expression that predicts the exact gain coefficient within an error margin of less than 2% over several orders of magnitude of the confocal parameter and as a function of the walk-off parameter. Our result allows for readily tuning the beam parameters to optimize the performance of the upconversion process and improve optical system designs.

© 2020 Optical Society of America

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