A Novel High-Order Symplectic Compact FDTD Schemes for Optical Waveguide Simulation

Abstract

As a 2-D full-wave numerical algorithm in the time domain, the compact Finite Difference Time Domain ( FDTD ) is an efficient algorithm for eigenvalue analysis of optical waveguide system. However, the numerical dispersion accuracy and stability of fast algorithm need to be improved while simulating at high frequency. A novel high-order symplectic compact FDTD scheme is developed and validated for optical waveguide modal analysis. The stability condition and the numerical dispersion of schemes with fourth-order accuracy in temporal and spatial using the symplectic integrator and compact scheme are analyzed. By comparisons with other time-domain schemes, their stable and accurate performance is qualitatively verified. The proposed high-order SC-FDTD method can be used for efficiently simulating electrically large and longitudinally invariant optical devices since the reduction of simulation dimensionality and the novel high-order symplectic algorithm can greatly reduce the memory cost and the numerical dispersive errors.

A Nonstandard Path Integral Model for Curved Surface Analysis

“…Therefore, to model the tiny-scale features of curved-shaped surfaces, such as those of an aircraft, the cell size selected should be adequately small, enforcing an upper threshold on the time-step that, in turn, leads to thousands of time iterations for the steady-state. To overcome this shortcoming, the alternating-direction implicit (ADI) [44][45][46][47][48][49][50][51] and the locally one-dimensional (LOD) [52][53][54][55][56][57] time marching concepts have been introduced in the update mechanism of most FDTDoriented schemes. The resulting approach is a semi-explicit technique which surpasses the CFL limit and can conduct unconditionally stable simulations, on the condition that the numerical dispersion and dissipation errors are carefully taken into account.…”