Design and analysis of thin optical lens composed of low-index subwavelength structures

We design a polarization-insensitive subwavelength optical lens capable of focusing plane waves of visible wavelength using traditional optical materials such as glass. Using analytical effective medium theory and finite difference time domain (FDTD) method, the phase of transmission of arrayed subwavelength inclusions is studied with respect to their size and shape. It is shown that the phase relations can be accurately predicted using an analytical method, simplifying the design process. A guideline is established for selecting a set of subwavelength inclusions so that complete phase coverage can be achieved. Analytical calculation of focal length using diffraction equations (Fresnel or Rayleigh-Sommerfeld) along with effective medium approximation is done and compared with FDTD and experimental results, showing high accuracy. Large-scale optical lenses with subwavelength thickness are designed and their performance analyzed using an analytical approach. The optical lenses show high focusing efficiency at small numerical apertures, insensitivity to polarization angle, and robustness to uncertainty in their structural parameters. This work shows that using an analytical method, thin optical lenses with subwavelength structure can be designed and studied.