Application of the QCTO technique to design flat fresnel GRIN lenses

Abstract

The quasi-conformal transformation optics (QCTO) technique is employed to design flat TO gradient-index (GRIN) Fresnel-type lenses. Because the targeted Fresnel lenses possess complex curvatures and contour profiles with sharp corner boundaries, the QCTO algorithm cannot be applied directly to transform them into a flat TO GRIN lens. This is due to the fact that the QCTO technique is based on a discrete coordinate transformation (DCT) strategy, which relies on the property that the local coordinates of the virtual space and physical space systems remain as near-orthogonal meshes. A novel approach is proposed here to solve the limitations of the application of QCTO to the design of Fresnel lenses, that is: (a) the Fresnel lens is first divided into several sections; (b) the QCTO method is then applied to each section of the lens with homogeneous media and curved shapes; (c) the resulting flat TO GRIN lenses sections are partially truncated on the left/right end sides, then; (d) followed by a stretching transformation along the horizontal direction to yield the same size as the original TO lens sections. Next, (e) the refractive index of the resulting flat TO GRIN lens sections are multiplied by an optimized scaling factor; (f) finally all the modified flat TO lens sections are integrated to form the final flat TO GRIN lens. The imaging performances of the Fresnel lenses and their flat TO GRIN lens counterparts are simulated by use of an in-house graphical processing unit (GPU)-based body of revolution finite-difference time-domain (BOR-FDTD) code. Numerical results demonstrate that flattened TO GRIN lenses have the same focusing properties as free-space Fresnel lens or one mounted on a substrate, for both normally and obliquely incident plane waves.