Abstract
We describe a novel scheme for obtaining a superhigh numerical aperture gradient-index (SHNA GRIN) lens from multiple thin layers of two or more materials with large refractive-index contrast. Design procedures for the lens are described, including variation of the layer thickness to achieve focusing and of the thickness limit to reduce scattering loss. We use an exact numerical solution by the finite-difference time-domain method to evaluate the lens's performance. Specific examples of a SHNA GRIN lens with a SiO2-TiO2 material system designed for fiber coupling to a nanowaveguide are shown to have focusing FWHM spot sizes of 0.53-0.7 microm at lambda =1.55 microm (corresponding to a NA of approximately 1.6-1.1) with 2.7-2.4% more loss than an ideal continuous index profile GRIN lens. With this approach, a SHNA GRIN lens with a NA of > 1.5 and a length of <20 microm can be achieved with currently available thin-film deposition techniques.
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