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Thermal noise is expected to be one of the noise sources limiting theastrophysical reach of Advanced LIGO (once commissioning is complete) andthird-generation detectors. Adopting crystalline materials for thin, reflectingmirror coatings, rather than the amorphous coatings used in current-generationdetectors, could potentially reduce thermal noise. Understanding and reducingthermal noise requires accurate theoretical models, but modeling thermal noiseanalytically is especially challenging with crystalline materials. Thermalnoise models typically rely on the fluctuation-dissipation theorem, whichrelates the power spectral density of the thermal noise to an auxiliary elasticproblem. In this paper, we present results from a new, open-source tool thatnumerically solves the auxiliary elastic problem to compute the Brownianthermal noise for both amorphous and crystalline coatings. We employopen-source frameworks to solve the auxiliary elastic problem using afinite-element method, adaptive mesh refinement, and parallel processing thatenables us to use high resolutions capable of resolving the thin reflectivecoating. We compare with approximate analytic solutions for amorphousmaterials, and we verify that our solutions scale as expected. Finally, wemodel the crystalline coating thermal noise in an experiment reported by Coleand collaborators (2013), comparing our results to a simpler numericalcalculation that treats the coating as an "effectively amorphous" material. Wefind that treating the coating as a cubic crystal instead of as an effectivelyamorphous material increases the thermal noise by about 3%. Our results are astep toward better understanding and reducing thermal noise to increase thereach of future gravitational-wave detectors. (Abstract abbreviated.)

Numerically modeling Brownian thermal noise in amorphous and crystalline thin coatings