Degenerate astigmatic cavities

Abstract

At the output of a high-finesse cavity a succession of Lissajous patterns may be observed as the cavity length is finely tuned inside a ``degenerate region'' around a reentrant spherical configuration. This behavior is ascribed to a small parasitic astigmatism of the cavity mirrors. Simple geometrical optics modeling confirms this hypothesis, and then a more realistic analysis using transverse Gaussian modes reveals that the Lissajous patterns correspond to an organization of the astigmatism-split modes into a finer substructure of degenerate modes relative to that of a reentrant spherical cavity. This provides a thorough understanding of the field patterns observed in the degenerate region, including an intriguing spatial symmetry of the patterns corresponding to opposite displacements with respect to a specific central cavity length. This investigation represents a generalization of the theory of reentrant spherical cavities to the astigmatic case.