Scaling law in signal recycled laser-interferometer gravitational-wave detectors

Abstract

By mapping the signal-recycling (SR) optical configuration to a three-mirror cavity, and then to a single detuned cavity, we express SR optomechanical dynamics, input--output relation and noise spectral density in terms of only three characteristic parameters: the (free) optical resonant frequency and decay time of the entire interferometer, and the laser power circulating in arm cavities. These parameters, and therefore the properties of the interferometer, are invariant under an appropriate scaling of SR-mirror reflectivity, SR detuning, arm-cavity storage time and input power at beamsplitter. Moreover, so far the quantum-mechanical description of laser-interferometer gravitational-wave detectors, including radiation-pressure effects, was only obtained at linear order in the transmissivity of arm-cavity internal mirrors. We relax this assumption and discuss how the noise spectral densities change.