Gaussian optics of resonators containing non-Gaussian optical components

A new method for analysis of non-Gaussian optical systems involves their replacement with approximately equivalent Gaussian systems. An algorithm for deriving an equivalent system is proposed. The method is used to analyze the diffraction of a Gaussian beam by an aperture with a partly smoothed edge and the behavior of the fundamental mode of a resonator containing such an aperture. The conditions under which the fundamental mode of a resonator with a finite aperture can be regarded quite accurately as Gaussian are formulated.