Dispersions of polariton and radiative decay rate in a quantum wire grating

In order to study the polariton dispersions and their radiative decays in a semiconductor quantum wire grating, we have calculated the electromagnetic modes generated by the grating when the light incident plane is parallel to the wires. By using Greenʹs function techniques and solving Maxwellʹs equations with a non-local susceptibility, exciton-polarizations induced in quantum wires are then calculated. Dispersion curves show not only exciton-polariton resonances but also the dispersion of the gratingʹs electromagnetic modes. For a given wire dimension, the polariton can decay radiatively even for higher grating electromagnetic modes. Our model can be also applied for a three-dimensional semiconductor photonic crystal having confined excitons.