Virtual-source theory of unstable resonator modes.

A new method for understanding and calculating unstable resonator modes has been developed. It consists of propagating an initial uniform plane wave N round trips through the resonator, as in the Fox and Li [Bell Syst. Tech. J. 40, 453 (1961)] approach. The propagation, however, is performed entirely in collimated space that results from unfolding the resonator into its virtual images of the feedback mirror. In this unfolded space, the field after N round trips consists of a single plane-wave propagation plus the sum of diffracted waves from N pairs of virtual sources (for the strip-resonator case). The edge-diffraction function is determined from an asymptotic solution to the Huygens-Fresnel integral for an incident plane wave. The advantages of the method are that it is conceptually simple and numerically accurate and requires only minimal computer time.