Sensitivity of intracavity filtering schemes for detecting gravitational waves

We consider enhancing the sensitivity of future gravitational-wave detectors by adding optical filters inside the signal-recycling cavity -- an intracavity filtering scheme, which coherently feeds the sideband signal back to the interferometer with a proper frequency-dependent phase. We study three cases of such a scheme with different motivations: (i) the case of backaction noise evasion, trying to cancel radiation-pressure noise with only one filter cavity for a signal-recycled interferometer; (ii) the speed-meter case, similar to the speed-meter scheme proposed by Purdue and Chen [Phys. Rev. D 66, 122004 (2002)] but without the resonant-sideband-extraction mirror, and also relieves the optical requirement on the sloshing mirror; (iii) the broadband detection case with squeezed-light input, numerically optimized for a broadband sensitivity.