Spectral analysis of dissipative Maxwell systems

The electromagnetic properties of a conductive, anisotropic material are described by the Maxwell’s equations with non-trivial conductivity. The presence of conductivity makes the problem dissipative rather than self-adjoint. Dissipation introduces significant hurdles in the spectral analysis of the system, compared to the self-adjoint case. For instance, spectral approximations (such as the Galerkin approximations or the domain truncation method) might be prone to spectral pollution. I will present a recent result establishing that discrete eigenvalues of the Maxwell system can be approximated without spectral pollution by domain truncation, even if they lie inside the numerical range of the operator.

Finally, I will briefly describe further results dealing with the case of lossy metamaterials, or the case of materials with ‘asymptotic anisotropy’. Based on joint works with S. Bögli, M. Marletta, and C. Tretter.