The Optical Ring Resonator

Expressions are derived for the stability parameter, spot size, and wavefront curvature of a Gaussian beam in a ring resonator containing up to four spherical mirrors unequally spaced. Higher-order transverse modes and aperture effects are not considered. Two methods of analysis are used: (1) replacement of the mirrors by an infinite sequence of equally-spaced identical thick lenses, and (2) transformation of the beam into itself after one circuit of the ring, by means of a ray matrix representation of the equivalent thin lenses. The procedure can readily be extended to ring resonators with any number of spherical mirrors.