Abstract

Using a nonstandard (NS) finite difference model, we derived a high-accuracy finite-difference time domain algorithm to solve the coupled wave equation. The conventional NS-Yee algorithm can greatly reduce the error of the difference approximation and accurately solve the Maxwell’s equations even for sub-wavelength whispering gallery modes, which are very sensitive to the scatterer model on the numerical grid. However, relative to the transverse magnetic mode, the error in the transverse electric mode is large because $\nabla \epsilon$ $\left(\epsilon =\text{permittivity}\right)$ is not accurately represented [J. Opt. Soc. Am. B 27, 631 (2010) ]. In this paper, we derive a nonstandard finite-difference time domain algorithm to solve the coupled wave equation which accurately includes $\nabla \epsilon$, and we demonstrate its higher accuracy and shorter computing time.

© 2010 Optical Society of America

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