Method of Auxiliary Sources and Model-Based Parameter Estimation for the Computation of Periodic Structures

The analysis of the band structure is very important for the design of photonic crystals and other periodic structures. Metallic and metallo-dielectric PhCs exhibit strong material loss and dispersion significantly complicating the computation. The calculation of band diagrams of such structures requires the efficient solution of non-linear eigenvalue problems. In this paper, the method of auxiliary sources for the accurate and efficient computation of periodic structures is presented for 2D models. It is based on the Green's function of periodic arrays of monopole sources. Additionally, model-based parameter estimation is applied for speeding up the calculation. Model-based parameter estimation is combined not only with the method of auxiliary sources, but also with the multiple multipole program, another boundary method operating in the frequency domain. This combination represents a highly accurate numerical tool for band structure calculations.