Zero-index waveguides for metasurface applications

Metamaterials with a refractive index of zero have emerged as a new tool for phase control in nanophotonics. Waves propagate within such metamaterials with infinite phase velocity, resulting in uniform phase throughout. Recently two-dimensional zero-index metamaterials have been integrated with on-chip silicon photonics, allowing for phase-free propagation over large areas. However, zero-index modes are inherently lossy: since the momentum of the wave is zero, it lies above the light line, and therefore couples to waves in free space. In particular, momentum conservation implies that the light is scattered vertically, perpendicular to the surface. We can leverage this scattering to couple guided waves into free space while controlling the phase, treating the zero-index material as a metasurface. We use full-wave simulations to study the out-of-plane radiation from zero index metamaterials in the near-infrared. The metamaterial consists of a silicon photonic crystal on a silica substrate, where the geometry of the structure is tuned to achieve simultaneously zero electric and magnetic response. Controlling the nanostructure allows for fine control of the effective mode index over a continuous range of positive and negative values, corresponding to positive and negative refracted angles. Since the periodicity of the crystal is smaller than the free space wavelength, the beam scatters without diffraction. This platform provides additional flexibility beyond beam steering. By introducing spatial variation in the effective index, we can control the phase of scattered light to achieve more sophisticated wavefront engineering. We explore two examples: a graded index photonic crystal for focusing, and a spiral waveguide to generate orbital angular momentum.