Focusing element formed by scattering structures in a planar dielectric waveguide

A design process for creating integrated diffractive focusing elements for use in planar waveguides is presented. The elements consist of a linear array of holes etched into the core layer of a planar dielectric waveguide. A complete element is a few micrometers in size, while the individual holes are sub-micrometer. The focusing element was designed using analytical Mie theory. The performance of the complete 3D structure was then evaluated using 3D finite difference time domain (FDTD) method. A focal spot width of 227 nm (full width at half maximum) was predicted by 3D FDTD simulations with a peak intensity more than 10x the incident intensity and back-reflections lower than 1%. The focusing elements were fabricated using electron beam lithography and plasma etching. Fluorescence imaging was used to map the intensity in the waveguide core. The experimentally measured intensity maps were in good agreement with the simulations when the finite spatial resolution of the imaging system was taken into account.