Analytical Approximation of the Second-Harmonic Conversion Efficiency

TL;DR

This paper derives an analytical expression for second-harmonic conversion efficiency in focused laser beams within nonlinear crystals, enabling easier optimization of optical systems by accurately predicting gain coefficients.

Contribution

It provides a nearly exact analytical approximation for the Boyd-Kleinman gain coefficient, reducing computational complexity in designing nonlinear optical systems.

Findings

Predicts gain coefficient with less than 2% error

Applicable over a wide range of confocal parameters

Facilitates optimization of beam parameters for better 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 of 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.