Simulation of whispering gallery modes in the Mie regime using the nonstandard finite-difference time domain algorithm

The nonstandard (NS) finite-difference time domain (FDTD) algorithm has proved be remarkably accurate on a coarse numerical grid, but the well-known resonances called whispering gallery modes (WGMs) in the Mie regime are very sensitive to the scatterer representation on the computational grid, and a very large number of time steps are needed to correctly calculate the modes because the electromagnetic field outside the scatterer is weakly coupled to the inside. Using the NS-FDTD algorithm on a coarse grid, we were able to accurately simulate the WGMs of dielectric cylinders in the Mie regime.

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