Diagonalization of the length sensing matrix of a dual recycled laser interferometer gravitational wave antenna

Next generation gravitational wave antennas employ resonant sideband extraction (RSE) interferometers with Fabry-Perot cavities in the arms as an optical configuration. In order to realize stable, robust control of the detector system, it is a key issue to extract appropriate control signals for longitudinal degrees of freedom of the complex coupled-cavity system. In this paper, a novel length sensing and control scheme is proposed for the tuned RSE interferometer that is both simple and efficient. The sensing matrix can be well diagonalized, owing to a simple allocation of two rf modulations and to a macroscopic displacement of the cavity mirrors, which cause a detuning of the rf modulation sidebands.