Degenerate elliptical modes of a confocal cavity

It is shown that among degenerate modes of a confocal cavity there are field distributions which can be described as Gaussian beams of the elliptical type. These modes can be excited in cavities with elliptical or rectangular apertures, and they can be used to increase the efficiency and beam quality of the lasers with rectangular active elements. A numerical simulation is carried out for the Fresnel number N = 1, stability in respect of possible cavity misalignments is demonstrated, and the losses per round trip are calculated for some of the lowest-order modes.