Mode matching error signals using radio-frequency beam shape modulation

Precise mode matching is needed to maximize performance in coupled cavity interferometers such as Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO). In this paper, we present a new mode matching sensing scheme, to the best of our knowledge, that uses a single radio-frequency higher-order-mode sideband and single-element photodiodes. It is first-order insensitive to misalignment and can serve as an error signal in a closed loop control system for a set of mode matching actuators. We also discuss how it may be implemented in Advanced LIGO. The proposed mode matching error signal has been successfully demonstrated on a tabletop experiment, where the error signal increased the mode matching of a beam to a cavity to 99.9%.