Design of fused silica nanostructured gradient index microlenses

We present theoretical results for a quarter-pitch gradient index (GRIN) parabolic lens made of pure and Ge-doped fused silica glasses. An ideal radial GRIN lens has a continuous parabolic refractive index distribution. The typical method of fabrication of gradient index components is based on the ion exchange technique, however it is limited to some types of soft glasses only.
In this paper we present GRIN lenses with continuous change of effective index of refraction achieved using silica glass rods of subwavelength diameters. These rods are stacked in accordance with a particular pattern, calculated using Maxwell-Garnet effective medium mixing formula and developed using a standard stack-and-draw fiber drawing technique. The size of the subwavelength rods in the final GRIN lens structure is below λ/5=310 nm, while the diameter of final component equals to 37 µm. A length of the GRIN lens component determines its performance, such as collimation or focusing with various numerical apertures. Use of silica glass for GRIN lens development enables compatibility with standard fusion splicers for the development of miniaturized robust lensed fiber systems for telecom and sensor applications.