Title: Thermal distortions of non-Gaussian beams in Fabry-Perot cavities,
Abstract: Thermal effects are already important in currently operating interferometric
gravitational wave detectors. Planned upgrades of these detectors involve
increasing optical power to combat quantum shot noise. We consider the
ramifications of this increased power for one particular class of laser
beams--wide, flat-topped, mesa beams. In particular we model a single mesa beam
Fabry-Perot cavity having thermoelastically deformed mirrors. We calculate the
intensity profile of the fundamental cavity eigenmode in the presence of
thermal perturbations, and the associated changes in thermal noise. We also
outline an idealized method of correcting for such effects. At each stage we
contrast our results with those of a comparable Gaussian beam cavity. Although
we focus on mesa beams the techniques described are applicable to any
azimuthally symmetric system.