Numerically modeling Brownian thermal noise in amorphous and crystalline thin coatings

Abstract

Thermal noise is expected to be one of the noise sources limiting the astrophysical reach of Advanced LIGO (once commissioning is complete) and third-generation detectors. Adopting crystalline materials for thin, reflecting mirror coatings, rather than the amorphous coatings used in current-generation detectors, could potentially reduce thermal noise. Understanding and reducing thermal noise requires accurate theoretical models, but modeling thermal noise analytically is especially challenging with crystalline materials. Thermal noise models typically rely on the fluctuation-dissipation theorem, which relates the power spectral density of the thermal noise to an auxiliary elastic problem. In this paper, we present results from a new, open-source tool that numerically solves the auxiliary elastic problem to compute the Brownian thermal noise for both amorphous and crystalline coatings. We employ open-source frameworks to solve the auxiliary elastic problem using a finite-element method, adaptive mesh refinement, and parallel processing that enables us to use high resolutions capable of resolving the thin reflective coating. We compare with approximate analytic solutions for amorphous materials, and we verify that our solutions scale as expected. Finally, we model the crystalline coating thermal noise in an experiment reported by Cole and collaborators (2013), comparing our results to a simpler numerical calculation that treats the coating as an "effectively amorphous" material. We find that treating the coating as a cubic crystal instead of as an effectively amorphous material increases the thermal noise by about 3%. Our results are a step toward better understanding and reducing thermal noise to increase the reach of future gravitational-wave detectors. (Abstract abbreviated.)

arXiv comment23 pages, 6 figures, submitted to Classical and Quantum Gravity

References in corpus (30)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• Characterization of the LIGO detectors during their sixth science run
• Interferometer design of the KAGRA gravitational wave detector
• Detector configuration of KAGRA - the Japanese cryogenic gravitational-wave detector
• Internal thermal noise in the LIGO test masses : a direct approach
• Making optical atomic clocks more stable with $10^{-16}$ level laser stabilization
• Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings
• Gravitational Radiation Detection with Laser Interferometry
• Titania-doped tantala/silica coatings for gravitational-wave detection
• Mechanical Loss in Tantala/Silica Dielectric Mirror Coatings
• Thermo-refractive noise in gravitational wave antennae
• Thermoelastic Noise and Homogeneous Thermal Noise in Finite Sized Gravitational-Wave Test Masses
• Thermo-optic noise in coated mirrors for high-precision optical measurements
• Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors
• Thermodynamical fluctuations in optical mirror coatings
• Brownian Thermal Noise in Multilayer Coated Mirrors
• Suspensions Thermal Noise in the LIGO Gravitational Wave Detector
• Coherent Cancellation of Photothermal Noise in GaAs/Al${}_{0.92}$Ga${}_{0.08}$As Bragg Mirrors
• Audio-band Coating Thermal Noise Measurement for Advanced LIGO with a Multi-mode Optical Resonator
• How to reduce the suspension thermal noise in LIGO without improving the Q's of the pendulum and violin modes
• Effect of interference on thermal noise and coating optimization in dielectric mirrors
• Brownian Thermal Noise in Functional Optical Surfaces
• On the mechanical quality factors of cryogenic test masses from fused silica and crystalline quartz
• The dependence of test-mass thermal noises on beam shape in gravitational-wave interferometers
• Coating thermal noise for arbitrary shaped beams

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