Unconditionally stable finite-difference time-domain methods for modeling the Sagnac effect

摘要

We present two unconditionally stable finite-difference time-domain (FDTD) methods for modeling the Sagnacneffect in rotating optical microsensors. The methods are based on the implicit Crank-Nicolson scheme, adaptednto hold in the rotating system reference frame—the rotating Crank-Nicolson (RCN) methods. The first methodn(RCN-2) is second order accurate in space whereas the second method (RCN-4) is fourth order accurate. Bothnmethods are second order accurate in time. We show that the RCN-4 scheme is more accurate and has betterndispersion isotropy. The numerical results show good correspondence with the expression for the classical Sagnacnresonant frequency splitting when using group refractive indices of the resonant modes of a microresonator. Alsonwe show that the numerical results are consistent with the perturbation theory for the rotating degeneratenmicrocavities. We apply our method to simulate the effect of rotation on an entire Coupled Resonator OpticalnWaveguide (CROW) consisting of a set of coupled microresonators. Preliminary results validate the formationnof a rotation-induced gap at the center of a transfer function of a CROW.