Quasi-normal mode expansion of the scattering matrix

Abstract

Scattering problems in classical electrodynamics or quantum mechanics are characterised through the scattering matrix (S-matrix). For complex scenarios the underlying differential equations can only be solved numerically combined with an immense computational effort. Thus, calculating the S-matrix through these solutions is costly. Furthermore, the numerical routines hide the innerworkings of the studied problem. However, the discovery of so-called Quasi-Normal Modes (QNMs) and their connection to poles and zeros of the S-matrix indicate the existence of an expansion solely dependent on the asymptotic behaviour of these QNMs. Such an expansion would not only reconstruct the S-matrix faster, but also allow a more qualitative understanding of the scattering problem. This thesis continues previous work [1] by taking the last steps towards a full expansion of the scattering matrix in terms of QNMs and investigates its application to a selection of scattering systems.[1] F. Salihbegovic, “Reconstructing the Scattering Matrix Using the Quasi-Bound States,” Masters thesis, TU Wien, 2018.