Asymptotic strip boundary condition in the finite difference time domain method

The asymptotic strip boundary condition (ASBC) is proposed to treat finite extent periodic structures of strips loading dielectric materials in the finite-difference time-domain method. The ASBC is an anisotropic averaging type of boundary condition that eliminates the needs for modeling the details of the periodic strips. The ASBC approach has been found to be accurate in its modeling when the number of strips is around ten per wavelength. A new averaging expression is applied on the interface between the dielectric surface loaded with strips and the free space by introducing the information related to the ratio of the spacing between strips to the period (w/p). Such an expression improved the accuracy of the results. Computed results were accurate in its modeling as compared to detailed simulations, which demonstrates the validity of the asymptotic approximations. Lastly, a major improvement in the computation time is achieved when using the ASBC to model structures that have a large number of strips per wavelength. Several examples are presented for scattering, radiations, and internal problem of waveguide.