Hyperbolic Region in an Array of Quantum Wires in a Planar Cavity

We calculated the dispersion relation of a system consisting of a periodic array of quantum wires embedded in a planar microcavity. When the parameters of the system support strong light matter coupling, the dispersion will have regions where the effective mass of the composite quasi-particle will have different signs along different axes. This is a criterion for hyperbolic metamaterials, and leads to interesting effects such as sustained kink solutions and nontrivial propagation of incident pulses.