We analyze a homogenization limit for the linear wave equation of second order. The spatial operator is assumed to be of divergence form with an oscillatory coefficient matrix aε that is periodic with characteristic length scale ε; no spatial symmetry properties are imposed. Classical homogenization theory allows to describe solutions uε well by a non-dispersive wave equation on fixed time inte...

In order to obtain a unified approach for the FiniteDifference Time-Domain (FDTD) analysis of dispersive media described by a variety of models, the coordinate stretched Maxwell’s curl equation in time domain is firstly deduced. Then the FDTD update formulas combined with the semi-analytical recursive convolution (SARC) in Digital Signal Process (DSP) technique for general dispersive media are ...

We demonstrate optical nonlinearities due to the interaction of weak optical fields with the collective motion of a strongly dispersive ultracold gas. The combination of a recoil-induced resonance in the high gain regime and optical waveguiding within the dispersive medium enables us to achieve a collective atomic cooperativity of 275+/-50 even in the absence of a cavity. As a result, we observ...