2022/06/04 by Malcolm Brown, Tomáš Dohnal, Brown, Malcolm +5 · 1 citation
Mathematics · Computer Science · #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2206.02037
The paper determines and classifies the spectrum of a non-self-adjoint operator pencil generated by the time-harmonic Maxwell problem with a nonlinear dependence on the frequency for the case of two homogeneous materials joined at a planar interface. We study spatially one-dimensional and two-dimensional reductions in the whole space ℝ and ℝ2. The dependence on the spectral parameter, i.e. the frequency, is in the dielectric function and we make no assumptions on its form. These function values determine the spectral sets. In order to allow also for non-conservative media, the dielectric function is allowed to be complex, yielding a non-self-adjoint problem. The whole spectrum consists of eigenvalues and the essential spectrum, but the various standard types of essential spectra do not coincide in all cases. The main tool for determining the essential spectra are Weyl sequences.