Audio-band coating thermal noise measurement for Advanced LIGO with a multimode optical resonator

In modern high precision optical instruments, such as in gravitational wave detectors or frequency references, thermally induced fluctuations in the reflective coatings can be a limiting noise source. This noise, known as coating thermal noise, can be reduced by choosing materials with low mechanical loss. Examination of new materials becomes a necessity in order to further minimize the coating thermal noise and thus improve sensitivity of next generation instruments. We present a novel approach to directly measure coating thermal noise using a high finesse folded cavity in which multiple Hermite-Gaussian modes coresonate. This method is used to probe surface fluctuations on the order ${10}^{\ensuremath{-}17}\text{ }\text{ }\mathrm{m}/\sqrt{\mathrm{Hz}}$ in the frequency range 30--400 Hz. We applied this technique to measure thermal noise and loss angle of the coating used in Advanced LIGO.