Block course, 1 week
Maxwell's equations; measurement modalities; Helmholtz decomposition; function spaces for a cavity problem; exterior Calderon operators; surface scattering problems; Floquet–Bloch transform; problem sessions.
This course conveys a comprehensive understanding of electromagnetic wave scattering from surface structures in optics, of practically relevant technical measurement setups, and of mathematical tools to tackle the corresponding scattering problems analytically. To this end, the course starts by introducing Maxwell's equations as the fundamental physical model of electrodynamics, together with the most important experimental measurement setups for light scattering. The mathematical part of the course puts special emphasis on the construction of suitable Sobolev spaces for electromagnetic problems and their density and trace problems, as those differ considerably from, e.g., the well-known -spaces. Using these spaces together with the Helmholtz decomposition allows to tackle Maxwell's equations in bounded domains. To be able to further consider scattering from unbounded surfaces, suitable exterior Calderon operators for domain truncation are constructed. Finally, the scattering problem on an unbounded domain is reduced to a bounded domain by the Floquet–Bloch transform. Participants will become familiar both with theoretic and numeric concepts of the lecture by working on tutorials in the problem sessions.
- D. Colton, R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. 3rd ed., Springer-Verlag New York, 2013.
- P. Monk. Finite Element Methods for Maxwell's Equations. Cambridge University Press, Cambridge, 2003.