A stable fourth-order FDTD method for modeling electrically long dielectric waveguides

Accurate time-domain modeling of electrically long structures such as dielectric waveguides in integrated optics often demands prohibitive computational cost. In this paper, an efficient fourth-order finite-difference time-domain (FDTD) method is investigated in a two-dimensional (2-D) transverse electric (TE) case. The method is a combination of fourth-order staggered backward-differentiation time integrator and fourth-order staggered spatial discretization. A rigorous stability and dispersion analysis is conducted to show its useful numerical characteristics. Fourth-order convergence of the numerical scheme is demonstrated by monitoring numerical errors in the L₂ norm in 2-D cavities. Numerical efficiency of the fourth-order method is validated through its applications for full-wave time-domain simulations of long 2-D optical waveguide structures.