Stability and numerical dispersion of symplectic fourth-order time-domain schemes for optical field simulation

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%.