Optimal degeneracy for the signal-recycling cavity in advanced LIGO

As currently designed, the signal-recycling cavity (SRC) in the Advanced-LIGO interferometer is degenerate. In such a degenerate cavity, the phase fronts of optical fields become badly distorted when the mirror shapes are slightly deformed due to mirror figure error and/or thermal aberration, and this causes significant loss of the signal power and the signal-to-noise ratio (SNR) of a gravitational wave event. Through a numerical modal simulation of the optical fields in a simplified model of an Advanced-LIGO interferometer, We investigate the loss of the SNR and the behavior of both the carrier and signal optical fields, with the SRC at various levels of degeneracy. We show that the loss of the SNR is severe with a degenerate SRC, and a nondegenerate SRC can be used to solve this problem. We identify the optimal level of degeneracy for the SRC, which is achieved when the cavity Gouy phase is between 0.2 and 1.3 radians. We also discuss possible alternative designs of the SRC to achieve this optimal degeneracy.