Abstract
A numerical formulation based on the precise-integration time-domain (PITD) method for simulating periodic media is extended for overcoming the Courant-Friedrich-Levy (CFL) limit on the time-step size in a finite-difference time-domain (FDTD) simulation. In this new method, the periodic boundary conditions are implemented, permitting the simulation of a wide range of periodic optical media, i.e., gratings, or thin-film filters. Furthermore, the complete tensorial derivation for the permittivity also allows simulating anisotropic periodic media. Numerical results demonstrate that PITD is reliable and even considering anisotropic media can be competitive compared to traditional FDTD solutions. Furthermore, the maximum allowable time-step size has been demonstrated to be much larger than that of the CFL limit of the FDTD method, being a valuable tool in cases in which the steady-state requires a large number of time-steps.
Highlights
Simulation of the electromagnetic wave distribution through periodic media is a popular scenario in diffractive optics and photonics in general
The results show that the precise-integration time-domain (PITD) method is accurate compared to split-field finite-difference time-domain (SF-FDTD) simulations
PITD is tested with time-step resolutions larger than the one established by the CFL condition
Summary
Simulation of the electromagnetic wave distribution through periodic media is a popular scenario in diffractive optics and photonics in general. Limiting the dispersion error implies considering small spatial resolutions compared to the wavelength, setting up very fine meshes In these cases, the CFL condition forces small time-step sizes dramatically, resulting in demanding simulations in terms of running time and memory resources. Even considering all these new approaches, the problems related to the memory requirements remain and, in some cases, limit the PITD method’s applicability It is worth noting the recent contribution of Zhu et al [14] in which a PITD method with a thresholding scheme is shown in order to reduce the computation cost of the matrix exponential involved on PITD. Some analyses are performed related to the computational performance and the capability of using time-step resolution larger than the one established by the CFL condition is corroborated
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