Abstract
Abstract. An algorithm to perform a higher-order sensitivity analysis for electromagnetic eigenvalue problems is presented. By computing the eigenvalue and eigenvector derivatives, the Brillouin Diagram for periodic structures can be calculated. The discrete model is described using the Finite Integration Technique (FIT) with periodic boundaries, and the sensitivity analysis is performed with respect to the phase shift φ between the periodic boundaries. For validation, a reference solution is calculated by solving multiple eigenvalue problems (EVP). Furthermore, the eigenvalue derivatives are compared to reference values using finite difference (FD) formulas.
Highlights
Numerical algorithms for the solution of eigenvalue problems (EVP) have been known for many years
A reference solution is calculated by solving multiple eigenvalue problems (EVP)
Different numerical methods can be applied to find a discrete formulation of this problem, including the Finite Integration Technique (FIT) or the Finite Element method (FE) to only name two of them (Weiland, 1996; Schuhmann and Weiland, 2006)
Summary
Numerical algorithms for the solution of eigenvalue problems (EVP) have been known for many years. In Bandlow (2011) and Bandlow et al (2008), the calculation of the Brillouin diagram for periodic metamaterials is realized using a scattering matrix approach. An approach with a Taylor approximation is shown in Klindworth and Schmidt (2014) for band structures in photonic crystals. For photonic crystals, the band structure is calculated using model order reduction (MOR) in Scheiber et al (2011). A sensitivity analysis for a waveguide eigenvalue problem has been demonstrated in Burschäpers et al (2011), here with permittivity values as parameters in the context of a simple inverse problem
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