Losses in rotating degenerate cavities and a coupled-resonator optical-waveguide rotation sensor

We present a rigorous theory of rotating degenerate optical cavities and a coupled-resonator optical waveguide (CROW) including the impact of material losses associated with practical cavities and resonators. The losses are modeled as a perturbation of the material's relative permittivity by adding to it a small imaginary component. The Sagnac frequency shift in a single lossy cavity is shown to be lower than that of a lossless one. For CROWs, the rotation-induced gap formed in the center of the transmission function of a lossy device is reduced compared to that of a lossless one. The inclusion of propagation losses in the analysis of the CROW reveals a relatively insensitive region (a dead zone) in the response of a finite device at low rotation rates. A periodic modulation of the resonators' resonant frequencies is shown to be an effective artificial CROW biasing technique to overcome this problem. This biasing does not require any active control.