Design of flat lens-like graded index medium by photonic crystals: Exploring both low and high frequency regimes

In this manuscript, we propose the design of an inhomogeneous artificially created graded index (GRIN) medium to enrich the optical device functionalities of light by using periodic all-dielectric materials. Continuous GRIN profile with hyperbolic secant index distribution is approximated using two-dimensional photonic crystal (2D PC) dielectric rods with a fixed refractive index. The locations of each individual cell that contain dielectric rods of certain radii are determined based on the results of the frequency domain analysis. The desired index distribution is attained at long wavelengths using dispersion engineering approach. The frequency response of the transmission spectrum exhibits high transmission windows appearing at both larger and smaller wavelengths regions. Two regions are separated by a local band gap that blocks the incident light for a certain frequency interval. Light manipulation characteristics such as focusing, de-focusing and collimation are systematically and quantitatively compared for artificially designed GRIN medium within low and high frequency regimes. We show different field manipulation capabilities and focal point movement dynamics of the GRIN medium by special adjustment of the length of the structure. In addition, an analytical formulation based on ray theory is derived to investigate the focusing, de-focusing and collimation properties of proposed GRIN medium. The analytical approach utilizes Ray theory and computational tools are based on plane wave expansion and finite-difference time-domain methods. Implementing the GRIN medium by periodic optical materials provides frequency selectivity and strong focusing effects at higher frequency region. The designed structure can be used in integrated nanophotonics as a compact optical element with flat surfaces.