The use of a more accurate scheme is effective in reducing the required memory resources in the explicit time-domain simulation of optical field propagation. A promising technique is the application of the symplectic integrator, which can simulate the long-term evolution of a Hamiltonian system accurately. The stability condition and the numerical dispersion of schemes with fourth-order accuracy in time and space using the symplectic integrator are derived for the transverse electric (TE)-mode in two dimensions. Their stable and accurate performance is qualitatively verified, and is also demonstrated by numerical simulations of wave-converging by a perfect electric conductor wall and propagation along a waveguide whose refractive index difference between the core and cladding is more than 9%.
Takuo Hirono, W. W. Lui, K. Yokoyama, and S. Seki, "Stability and Numerical Dispersion of Symplectic Fourth-Order Time-Domain Schemes for Optical Field Simulation," J. Lightwave Technol. 16, 1915- (1998)