Gradient refractive index lens-like media are implemented using two-dimensional graded photonic crystals. They were considered as effectively homogeneous media in the long-wavelength approximation. Specified distribution of the gradient refractive index was realized using rods with spatially varying radii and applied for a design of a focusing and imaging lens. The validity of the proposed method was confirmed using full-wave numerical simulations. Planar versions of the presented lenses can find applications in integrated nanophotonics.
"Graded photonic crystals for implementation of gradient refractive index media," Journal of Nanophotonics 5(1), 051806 (1 January 2011). https://doi.org/10.1117/1.3586783