Absolute-length determination of a long-baseline Fabry–Perot cavity by means of resonating modulation sidebands

Abstract

A new method has been demonstrated for absolute-length measurements of a long-baseline Fabry–Perot cavity by use of phase-modulated light. This method is based on determination of a free spectral range (FSR) of the cavity from the frequency difference between a carrier and phase-modulation sidebands, both of which resonate in the cavity. Sensitive response of the Fabry–Perot cavity near resonant frequencies ensures accurate determination of the FSR and thus of the absolute length of the cavity. This method was applied to a 300-m Fabry–Perot cavity of the TAMA gravitational wave detector that is being developed at the National Astronomical Observatory, Tokyo. With a modulation frequency of ∼12 MHz, we successfully determined the absolute cavity length with resolution of 1 µm (3 × 10^-9 in strain) and observed local ground strain variations of 6 × 10^-8.