Iterative method for the design of a dual-phase-conjugation-mirror resonator with multiple apertures

Apertures have been used to select the low-order transverse modes in resonators. The additional diffraction losses result in a change in the transverse-mode structure, and the presence of apertures inside a resonator generally distorts the mode shape. The optimization of a multiple-aperture resonator demands an approach that differs from the conventional method in which the mode theory is used. We demonstrate an iterative design method to find optimal phase profiles for the reflector surfaces to build a resonator with multiple apertures to produce a lowest-order mode with much smaller diffraction loss and to satisfy the phase-conjugation conditions at the mirrors. The results are compared with conventional stable resonators, and we show that substantial improvement in round-trip loss and beam quality can also be obtained.