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

By mapping the signal-recycling (SR) optical configuration to a three-mirror cavity, and then to a single detuned cavity, we express the 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 the 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 the beam splitter. Moreover, so far the quantum-mechanical description of laser-interferometer gravitational-wave detectors, including radiation-pressure effects, has been obtained only at linear order in the transmissivity of arm-cavity internal mirrors. We relax this assumption and discuss how the noise spectral densities change.