  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.
