Optical rigidity in signal-recycling configurations of laser gravitational-wave detectors with lossy mirrors

We analyze the signal-recycled laser gravitational-wave interferometers with optical losses in arms for the Advanced LIGO topologies. We show that usage of the optical rigidity allows to obtain better than Standard Quantum Limit (SQL) sensitivity without increasing laser pumping. The gain in sensitivity is inversely proportional to the bandwidth inside which this gain is achieved. Varying the position of signal recycled mirror and optical power, which circulates in arms one can modify the sensitivity dependence on frequency from a single minimum to a double minimum dependence. We show that optical losses degrade sensitivity of measurements with usage of optical rigidity by relatively small value in contrast with other measurements beating SQL which degradation due to losses is considerable. It is also important that "narrow band" regimes provides the gain in signal to noise ratio even for signals with wide spectrum and the presence of losses also decreases this gain by relatively small numerical factor