Self-focusing media using graded photonic crystals: Focusing, Fourier transforming and imaging, directive emission, and directional cloaking

Abstract

Using numerical simulations, we investigate the realization of self-focusing media using two-dimensional graded photonic crystals and their applications for imaging and non-imaging purposes. The two-dimensional graded photonic crystals consist of spatially varying cylindrical holes drilled in a dielectric host. By controlling the gradient of the refractive index and the thickness of the self-focusing medium, it is possible to obtain either a focusing lens with Fourier transforming capabilities or an imaging lens, which produces inverted images. Non-imaging applications include a simple antenna for directive emission obtained from the focusing lens, whereas a directional cloak is obtained by modifying the imaging lens. Graded photonic crystal based devices work well up to the Bragg frequencies. They are compact, made from lossless dielectrics, and compatible with planar lithographic techniques, so they can find applications in a broad frequency range, even at the optical frequencies.