W. Kells

Model of thermal wave-front distortion in interferometric gravitational- wave detectors. I. Thermal focusing

We develop a steady-state analytical and numerical model of the optical response of power-recycled Fabry-Perot Michelson laser gravitational-wave detectors to nonlinear thermal focusing in optical substrates. We assume that the thermal distortions are small enough that we can represent all intracavity fields as linear combinations of basis functions derived from the eigenmodes of a Fabry-Perot arm cavity. We have included the effects of power absorption in optical substrates and coatings, mismatches between laser wave-front and mirror surface curvatures, and aperture diffraction. We demonstrate a detailed numerical example of this model using the MATLAB program Melody for the initial Laser Interferometer Gravitational Wave Observatory detector.

Measurement of birefringence of low-loss, high-reflectance coating of m-axis sapphire

The birefringence of a low-loss, high-reflectance coating applied to an 8-cm-diameter sapphire crystal grown in the m-axis direction has been mapped. By monitoring the transmission of a high-finesse Fabry-Perot cavity as a function of the polarization of the input light, we find an upper limit for the magnitude of the birefringence of 2.5 x 10(-4) rad and an upper limit in the variation in direction of the birefringence of 10 deg. These values are sufficiently small to allow consideration of m-axis sapphire as a substrate material for the optics of the advanced detector at the Laser Interferometer Gravitational Wave Observatory.