Diffractive analysis of unstable optical resonators with super-Gaussian mirrors

Abstract

The azimuthally symmetric diffractive transverse eigenmodes in an unstable optical resonator with a super-Gaussian reflectivity output mirror are computed in the low-Fresnel-number region to quantify the limits of validity of the geometrical-optics solution. It is found that for low cavity magnifications (M ≤ 2) and with mirrors of super-Gaussian orders n ≤ 8, the diffractive eigenvalues deviate significantly from the geometrical-optics value for equivalent Fresnel numbers Neq < 1 and are nearly equal to it for Neq > 2. These new results indicate that for the geometrical-optics approximation to be valid, resonators with M ≤ 2 and n ≤ 8 should be designed with Neq ≥ 2. This will ensure that the cavity exhibits good azimuthally symmetric transverse-mode discrimination and a super-Gaussian fundamental mode.