Comprehensive analysis of two different graded-index photonic-crystal lenses

Abstract

Abstract:We investigate two alternative approaches for implementing graded-index (GRIN) photonic-crystal (PC) structures that reveal a focusing effect. Gradient of the refractive index is achieved either using a symmetry-reduction approach (a structure of type I) or varying a filling fraction of PC elements (a structure of type II). We test the first structure for the frequencies located inside the first and second bands of the dispersion diagram. The focusing effect of the first structure characteristic for the frequencies located above the bandgap is stronger than that for the frequencies below the bandgap. It is demonstrated that variations of filling fractions of the elliptical air holes in the structure of type II produce a GRIN lens that manifests a pronounced focusing effect. We have also compared the focusing effects of the latter structure for the TE and TM polarizations. The both structures suggested in the present work can work in a broad enough band region.