Electromagnetic properties of a dielectric grating .1. Propagating, evanescent, and guided waves

Electromagnetic properties of nanostructured rectangular gratings of semiconductor materials are studied by exactly solving Maxwell's equations for a local dielectric function. Propagating, evanescent, and guided waves in unidimensional periodic lattices are computed, and their interference is discussed quantitatively. Nearly vanishing transmittance and nearly total reflectance can be obtained in extended frequency ranges, which can be tailored by suitably choosing grating parameters. The local electric field within, between, and below the dielectric wires is computed for ct broad range of grating parameters and for various angles of incidence of light: we find that the electric-field component parallel to the wires is always larger than that perpendicular to them within the wires. The last result is relevant for discussing photoluminescence experiments in the gratings of quantum-well wires.