Multi-refractive-index metamaterials based on subwavelength waveguide arrays

We demonstrate a metamaterial that cannot be described by a single set of refractive-index and impedance values, even for fixed frequency and polarization. The metamaterial structure is a stack of dissimilar waveguides with subwavelength width and spacing, which guide light at different phase velocities. This multi-refractive-index metamaterial (MRIM) can be viewed as a spatial superposition of multiple homogeneous materials. Using full-wave simulations, we demonstrate several optical components based on MRIMs, including prisms that deflect light to multiple angles, lenses with multiple focal points, and multi-index Fabry-Perot etalons with an enhanced density of resonant modes. We provide a theoretical framework for analyzing MRIMs to determine effective refractive indices, fractions of power to each channel (i.e., to each refractive index), and transmittance.