LIGO Document T1700196-v3

Laser Mode Spectroscopy for Mirror Metrology

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T - Technical notes
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The LIGO gravitational wave detectors are specialized Michelson interferometers each with two arms that are four kilometers in length. Each arm of the interferometers forms an optical cavity capped by semi-transparent mirrors by which laser light is transmitted and reflected. Imperfections on the surfaces of these mirrors cause optical power losses in the cavities that must be minimized for optimal performance. In a cavity with perfectly spherical mirrors, the modes of a Gaussian beam will resonate at equally spaced frequencies. In reality, surface perturbations cause the resonance peaks of several higher-order (Hermite-Gaussian) modes to shift in the cavity transmission spectrum. The aim of this project is to use cavity scan techniques to measure deviations in the spacing of these higher-order modes. By comparing these experimental deviations with theoretical mode spacings, we can learn about the physical properties of the cavity mirrors. Our ultimate goal is to use Bayesian inference techniques to recreate the surface perturbation map of a mirror from its cavity transmission spectrum.
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