Photonic crystal based polarization insensitive flat lens

The paper proposes a new design of an inhomogeneous artificially created photonic crystal lens structure consisting of annular dielectric rods to efficiently focus both transverse electric and transverse magnetic polarizations of light into the same focal point. The locations of each individual cell that contains the annular dielectric rods are determined according to a nonlinear distribution function. The inner and outer radii of the annular photonic dielectric rods are optimized with respect to the polarization insensitive frequency response of the transmission spectrum of the lens structure. The physical background of the polarization insensitive focusing mechanism is investigated in both spatial and frequency domains. Moreover, polarization independent wavefront transformation/focusing has been explored in detail by investigating the dispersion relation of the structure. Corresponding phase index distribution of the lens is attained for polarization insensitive normalized frequency range of a/lambda = 0.280 and a/lambda = 0.300, where a denotes the lattice constant of the designed structure and lambda denotes the wavelength of the incident light. We show the wave transformation performance and focal point movement dynamics for both polarizations of the lens structure by specially adjusting the length of the structure. The 3D finite-difference time domain numerical analysis is also performed to verifiy that the proposed design is able to focus the wave regardless of polarization into approximately the same focal point (difference between focal distances of both polarizations stays below 0.25 lambda) with an operating bandwidth of 4.30% between 1476 nm and 1541 nm at telecom wavelengths. The main superiorities of the proposed lens structure are being all dielectric and compact, and having flat front and back surfaces, rendering the proposed lens design more practical in the photonic integration process in various applications such as optical switch, attenuators and couplers, where the polarization insensitive focusing without any additional polarization control components plays an important role.