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Abstract
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Effective permittivities for the two-dimensional Finite-
Difference Time-Domain (FDTD) method are derived using a contour path approach that accounts for the boundary conditions of the electromagnetic field at dielectric interfaces. A phenomenological formula for the effective permittivities is also proposed as an effective and simpler alternative to
the previous result. Our schemes are validated using Mie theory for the
scattering of a dielectric cylinder and they are compared to the usual
staircase and the widely used volume-average approximations. Significant improvements in terms of accuracy and error fluctuations are demonstrated, especially in the calculation of resonances.
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