Time-Periodic Waves for Maxwell Equations with Nonlinear Polarization

22.05.2024 14:45 - 16:30

Wolfgang Reichel (Karlsruher Inst. f. Technologie)

The Maxwell equations govern the propagation of electromagnetic waves in matter. In many cases the material
properties do not change when an electromagnetic wave propagates through them. However, for a class of materials, the refractive changes in a nonlinear way in the presence of a
sufficiently strong electric field E. In this talk I will consider a model for a class of materials with nonlinear polarization properties. I will further consider special geometries where one can prove the existence of propagating time-periodic electromagnetic waves which are localized in directions orthogonal to the propagation direction. This problem leads to a quasilinear hyperbolic nonlinear partial differential
equation for the electric field E. Solutions with the above properties (localized, time-periodic, propagating) will be found by a variational principle. Numerical simulations will also be shown.
This is joint work with Sebastian Ohrem (KIT).

R.I. Bot, A. Constantin, J. Weber

Sky Lounge, 12. OG, OMP 1