Model-based parameter estimation (MBPE) for solving non-linear eigenvalue problems

The model-based parameter estimation (MBPE) for the computation of the band structure of photonic crystals (PhCs) is presented. The analysis of the band structure of a periodic structure is a very useful starting point for the PhCs design. PhCs made with metallic wires that have strong dispersion properties in the optical range are currently intensively studied. The calculation of band diagrams of such structures requires the efficient solution of non-linear eigenvalue problems. In this paper, MBPE is combined with two semi-analytic field solvers working in the frequency domain, the multiple multipole program (MMP) and the method of auxiliary sources (MAS). From this combination, two efficient and highly accurate numerical methods for the band structure calculation of PhCs are obtained.