Two-dimensional gradient-index metamaterial with sawtooth profile

Abstract

We investigate theoretically and experimentally a binary metal-dielectric metamaterial with a sawtooth profile. The structure consists of a two-dimensional array of pillars with submicrometer diameters. The pillar diameters linearly vary along one axis and are constant along the other. This furnishes a serrated spatial profile of effective refractive index along a single axis. We first present a set of analytical solutions defining the electromagnetic fields in such a structure. Further we give the results of our experimental fabrication of gradient metamaterial with a sawtooth spatial profile. The basic material for pillars was photoresist. Their geometry was defined using direct laser writing. Resist was overexposed in controlled manner in order to obtain pillars with diameters below the nominal resolution of the laser writer. The microfabricated pillars were coated by a sputter-deposited aluminum film. For characterization we utilized optical and atomic force microscopy and angledependent Fourier Transform infrared spectroscopy. We envision the applicability of our graded metasurfaces in transformation optics.