Propagation of extremely short pulses of electromagnetic field (electromagnetic spikes) is considered in the framework of the total Maxwell-Duffing model where anharmonic oscillators with cubic nonlinearities (Duffing model) represent the material medium and wave propagation is governed by the 1-d bidirectional Maxwell equations. This system of equations has a one parameter family of exact anal...

In this paper the authors extend their previous work on Boundary Perturbation methods for scattering calculations from families of diffraction gratings to three dimensions and the full vector electromagnetic Maxwell equations. This extension is non-trivial in both its algorithmic implementation (not only are new terms added to the recursions, but also the full, coupled, vector Maxwell equations...

In this paper, we consider near cloaking for the full Maxwell equations. We extend the method of [5, 6], where the quasi-static limit case and the Helmholtz equation are considered, to electromagnetic scattering problems. We construct very effective near cloaking structures for the electromagnetic scattering problem at a fixed frequency. These new structures are, before using the transformation...

The extension of the conventional finite-difference time-domain solution of the full vector Maxwell equations to modeling femtosecond optical-pulse propagation in a nonlinear Kerr medium that exhibits a finite response time is presented. Numerical results are given for nonlinear self-focusing in two space dimensions and time; the technique can be generalized to three space dimensions with adequ...

We present in this paper a numerical Maxwell–Schrödinger model to simulate intense ultrashort laser pulses interacting with a H 2 -gas in the nonlinear non-perturbative regime. After presentation of the model and a short mathematical study, we propose a numerical approach for its computation. In particular we focus on the polarization computation allowing the coupling between the Maxwell and Sc...

In this paper the Maxwell equations in an exterior domain with the generalized impedance boundary conditions of Engquist-N ed elec are considered. The particular form of the assumed boundary conditions can be considered to be a singular perturbation of the Dirichlet boundary conditions. The convergence of the solution of the Maxwell equations with these generalized impedance boundary conditions...

We study a nonoverlapping domain decomposition method for the harmonic Maxwell equations with a new kind of interface condition. Using Fourier analysis we derive suitable families of transmission conditions in R3 that involve second order tangential differential operators and that guarantee convergence for both propagative and evanescent modes. Such families depend upon parameters that are chos...