A Technique for In-situ Measurement of Free Spectral Range and Transverse Mode Spacing of Optical Cavities

TL;DR

This paper presents an in-situ technique to measure the free spectral range and transverse mode spacing of optical cavities using dual laser beams and beat note detection, applicable to complex systems like gravitational wave detectors.

Contribution

The paper introduces a novel in-situ measurement method for cavity parameters using laser beat notes, enabling characterization of complex optical systems.

Findings

Successfully applied to a 40-meter gravitational wave interferometer prototype.

Accurately measured free spectral range and transverse mode spacing.

Method is effective for long and coupled optical cavities.

Abstract

Length and g-factor are fundamental parameters that characterize optical cavities. We developed a technique to measure these parameters in-situ by determining the frequency spacing between the resonances of fundamental and spatial modes of an optical cavity. Two laser beams are injected into the cavity, and their relative frequency is scanned by a phase-lock loop, while the cavity is locked to either laser. The measurement of the amplitude of their beat note in transmission reveals the resonances of the longitudinal and the transverse modes of the cavity and their spacing. This method proves particularly useful to characterize complex optical systems, including very long and/or coupled optical cavities, as in gravitational wave interferometers. This technique and the results of its application to the coupled cavities of a 40-meter-long gravitational wave interferometer prototype are here presented.