Theoretical Analysis of an Interferometer with Variable Signal Recycling Mirror

Searches for gravitational waves are now conducted with Laser Interferometer Gravitational-wave Observatory (LIGO) which utilizes Michelson interferometers with 4-km arm lengths. To achieve the desired sensitivity the detectors are enhanced with Fabry-Perot resonators in the interferometer arms. Currently, the detectors are undergoing an upgrade to the Advanced LIGO configuration which will involve the Signal Recycling mirror for further increase of their sensitivity. In the present design, the Signal Recycling mirror has fixed reflectivity which leads to fixed detection bandwidth. Future gravitational wave detectors will benefit from variable reflectivity of the Signal Recycling mirror which allows controlled bandwidth. To understand the performance of such a detector we calculate its transfer functions in terms of mirror parameters. We analyze ways to tune its peak sensitivity and its detection bandwidth using the variable signal recycling mirror. The results can be used in future work on prototyping such tunable detectors.