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This paper describes a numerical formulation for calculating wave propagationwith high precision in a three-dimensional system. Yee's discretization schemeis used to formulate a frequency domain method that is compatible with thefinite-difference time-domain (FDTD) procedure. When the S-matrix satisfies aunitarity (power flow conservation) condition, the method enables arbitraryS-matrix elements to be obtained within a numerical error of less than$10^{-8}$ ($2 \times 10^{-13}$) for double precision format.

Numerical formulation of three-dimensional scattering problems for optical structures