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.

Discretization of Maxwell’s Equations for Non-inertial Observers Using Space-Time Algebra

“…We have avoided any extrapolation w.r.t. time as it may be the cause of instabilities as mentioned in [18,Appendix] and confirmed by our numerical examples. In general the decomposition of g = M ξ f according to e, b, d, h would read…”

“…Numerical simulation of electromagnetic field in a rotating medium has been studied in frequencydomain [23, and references therein], as well as in time-domain [19,18]. In all these approaches it is assumed from the beginning that the angular velocity Ω is small, i.e., rΩ c 1 with r the distance from the centre of rotation, and in [23] additionally Ω ω 1 with ω the frequency of the electromagnetic field.…”

Finite-difference time-domain study of modulated and disordered coupled resonator optical waveguide rotation sensors

“…Recently, a few finite-difference-time-domain (FDTD) methods for modeling the Sagnac effect were proposed in the literature [12,13], but their ability to model relatively large optical structures, such as CROW, where the computational widow can have an area of hundreds or more of square microns, was not demonstrated and the issue of numerical stability was not addressed. The development of a stable FDTD scheme, and its successful utilization for modeling such devices was only briefly introduced in our previous work for a CROW consisting of 4 racetrack ring resonators [14].…”

“…We study its performance under periodic modulation of the structure parameters and under structural disorder. We employ the implicit RCN-4 (Rotating Crank-Nicolson) FDTD method developed in [14]. This method is a modification of the Crank-Nicolson scheme holding for rotating frames of reference, having 4 th order accuracy in space and 2 nd order accuracy in time.…”

Rotating Optical Microcavities with Broken Chiral Symmetry

“…Without rotation, both modes are dominated by CCW traveling waves, but one of them (b) transforms into a CW traveling wave mode at high Ω. [4,[27][28][29][30][31][32]. Here we used a finite-difference time-domain algorithm, adapted to the rotating frame [12], to calculate the mode profile and emission pattern.…”