DIFFRACTIVE ANALYSIS OF UNSTABLE OPTICAL RESONATORS WITH SUPER-GAUSSIAN MIRRORS

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 less-than-or-equal-to 2) and with mirrors of super-Gaussian orders n less-than-or-equal-to 8, the diffractive eigenvalues deviate significantly from the geometrical-optics value for equivalent Fresnel numbers N(eq) < 1 and are nearly equal to it for N(eq) > 2. These new results indicate that for the geometrical-optics approximation to be valid, resonators with M less-than-or-equal-to less-than-or-equal-to 2 and n less-than-or-equal-to 8 should be designed with N(eq) greater-than-or-equal-to 2. This will ensure that the cavity exhibits good azimuthally symmetric transverse-mode discrimination and a super-Gaussian fundamental mode.