title: Unconditionally stable finite-difference time-domain methods for modeling the Sagnac effect.
abstract: We present two unconditionally stable finite-difference time-domain (FDTD) methods for modeling the Sagnac effect in rotating optical microsensors. The methods are based on the implicit Crank-Nicolson scheme, adapted to hold in the rotating system reference frame-the rotating Crank-Nicolson (RCN) methods. The first method (RCN-2) is second order accurate in space whereas the second method (RCN-4) is fourth order accurate. Both methods are second order accurate in time. We show that the RCN-4 scheme is more accurate and has better dispersion isotropy. The numerical results show good correspondence with the expression for the classical Sagnac resonant frequency splitting when using group refractive indices of the resonant modes of a microresonator. Also we show that the numerical results are consistent with the perturbation theory for the rotating degenerate microcavities. We apply our method to simulate the effect of rotation on an entire Coupled Resonator Optical Waveguide (CROW) consisting of a set of coupled microresonators. Preliminary results validate the formation of a rotation-induced gap at the center of a transfer function of a CROW.
authors.affiliation: School of Electrical Engineering, Tel-Aviv University, Ramat Aviv, Tel-Aviv 69978, Israel.
authors.forename: Roman
authors.initials: R
authors.lastname: Novitski
authors.forename: Jacob
authors.initials: J
authors.lastname: Scheuer
authors.forename: Ben Z
authors.initials: BZ
authors.lastname: Steinberg
mesh_terms: D003198:Computer Simulation; D017076:Computer-Aided Design; D019544:Equipment Failure Analysis; D008962:Models, Theoretical; D020349:Surface Plasmon Resonance / Q000295:instrumentation*; D014159:Transducers