Parametric Oscillation Thresholds in Symmetric and Half-Symmetric Configurations in the Absence of Double Refraction

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Abstract
We have computed the parametric oscillation threshold in the case of no double refraction for a resonator geometry in which the beam waists are located at a crystal face (half‐symmetric). The result is a simple approximate analytic expression for the threshold which is given in terms of the functions derived by Boyd and Kleinman for the geometry in which the beam waists are at the center of the crystal (symmetric). The approximation is valid throughout the range of experimentally significant focusing parameters. Our work complements the recent work of Ammann and Montgomery who have given computer produced curves for the half‐symmetric geometry and arbitrary double refraction.