Andreas Ioannidis

On the Error of the Optical Response Approximation in Chiral Media

We study the equations modelling the evolution of electromagnetic fields in chiral media with dispersion. We prove existence and uniqueness of solutions of these equations and provide estimates for the error of the optical response approximation for chiral media.

On the well-posedness of the Maxwell system for linear bianisotropic media

The time dependent Maxwell system is supplemented with the constitutive relations of linear bianisotropc media and is treated as a neutral integro-differential equation in a Hilbert space. By using the theory of abstract Volterra equations and strongly continuous semigroups we obtain general well-posedness results for the corresponding mathematical problem.

The propagation problem in a bi-isotropic waveguide

We investigate the problem of deflning propagating constants and modes in metallic waveguides of an arbitrary cross section, fllled with a homogeneous bi-isotropic material. The approach follows the guidelines of the classical theory for the isotropic, homogeneous, lossless waveguide: starting with the Maxwell system, we formulate a spectral problem where the square of the propagation constant shows up as the eigenvalue and the corresponding mode as the eigenvector. The di-culty that arises, and this is a feature of chirality, is that the eigenvalue is involved in the boundary conditions. The main result is that the problem is solvable whenever the Dirichlet problem for the Helmholtz equation in the cross section is solvable and two technical hypotheses are fulfllled. Our method, inspired by the null-fleld method, is quite general and has a good potential to work in various geometries.