Parameter Characterization For Coating Thermo-Optic Noise and Coating Brownian Noise in Optical Cavities with Emphasis On Crystalline AIGaAs/GaAs Coatings

Abstract

In this dissertation I describe methods for measuring material properties required for estimating noise in optical cavities from multi-layered optical coatings. This thesis is in two parts: The first part of the thesis describes an enhanced ringdown technique to test for amplitude-dependence of the mechanical loss in optical coatings. Ringdown methods for estimating the coating Brownian noise in a cavity rely on the the assumption that the loss is independent of oscillation amplitude. This allows experiments to artificially excite mechanical modes to amplitudes that are measurable by non-cavity means, such as optical levers and birefringence-based readouts. Here I describe the use of a GeNS system, read out by a low-noise Michelson interferometer to measure the amplitude dependence of loss in GaAs/Al$_{0.92}$Ga$_{0.08}$As multi-layer optical coatings on silica substrates in the range from just above the \textit{rms} thermal noise amplitude up to amplitudes typical of ringdown measurements: $10^{-1}-10^3$~picometers. These measurements set an upper limit on the amplitude dependence. I compare three crystalline coatings with varying levels of damage to determine if delaminated areas or other damage contributes to amplitude dependence. I compare the measured loss to a loss model consisting of coating thermo-elastic loss, coating bulk loss, coating shear loss, surface loss, substrate loss, edge loss and excess loss. I show that these measurements are limited by thermo-elastic and other losses associated primarily with bulk (volume-changing) coating deformations. The second part of this thesis describes methods for characterizing thermo-optic noise in single- and multi-layer coatings. I demonstrate that by measuring the wavelength shift with temperature, $\frac{\mr{d}\lambda}{\mr{d}T}$, of transmission spectra for single-layer coatings, we obtain a linear combination of $\alpha $ and $\beta$, the thermal expansion and thermo-optic coefficients of the coating. If the thermal expansion coefficient, $\alpha$, is already known, then our measurement gives $\beta$. I also demonstrate that by measuring $\frac{\mr{d}\lambda}{\mr{d}T}$ for multi-layer, high-reflectivity mirrors of the same type as in a cavity, we can calculate the cavity thermo-optic noise directly without the intermediate step of finding $\alpha$ and $\beta$ for the high and low index layer types respectively. We still need an estimate of the total coating thermal expansion coefficient $\alpha_c$, but the number of parameters needed is now reduced to 2, from 4 required previously. Finally, I show that by using lasers to measure the transmission changes on the band-edge of a high-reflectivity coating, we can get higher precision measurements but at the cost of reduced systematic accuracy.