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We study the time harmonic Maxwell equations in a meta-material consisting of perfect conductors and void space. The meta-material is assumed to be periodic with period $eta > 0$; we study the behaviour of solutions $(E^{eta}, H^{eta})$ in the limit $eta to 0$ and derive an effective system. In geometries with a non-trivial topology, the limit system implies that certain components of the effective fields vanish. We identify the corresponding effective system and can predict, from topological properties of the meta-material, whether or not it permits the propagation of waves.
This paper provides a view of Maxwells equations from the perspective of complex variables. The study is made through complex differential forms and the Hodge star operator in $mathbb{C}^2$ with respect to the Euclidean and the Minkowski metrics. It
In this work, we are interested in the analysis of time-harmonic Maxwells equations in presence of a conical tip of a material with negative dielectric constants. When these constants belong to some critical range, the electromagnetic field exhibits
Let $V(t) = e^{tG_b},: t geq 0,$ be the semigroup generated by Maxwells equations in an exterior domain $Omega subset {mathbb R}^3$ with dissipative boundary condition $E_{tan}- gamma(x) ( u wedge B_{tan}) = 0, gamma(x) > 0, forall x in Gamma = parti
This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent initial bou
We study the homogenization of elliptic systems of equations in divergence form where the coefficients are compositions of periodic functions with a random diffeomorphism with stationary gradient. This is done in the spirit of scalar stochastic homog