Nonlinear optics in on-chip zero-index metamaterials

Optical metamaterials - composite materials whose electromagnetic properties are finely engineered by designing their constituents - have been shown to exhibit strange and exotic properties, such as negligible or negative indices of refraction and the direct control of the amplitude and phase of light. These properties have been used for innumerable applications, such as flat lenses, invisibility cloaks as well as previously unseen nonlinear interactions. Recently, our group has demonstrated the first on-chip metamaterial with a refractive index of zero. These isotropic structures exhibit a refractive index of zero for all in-plane propagation directions. The proposed devices are CMOS-compatible and can be fabricated using standard lithographic processes on an SOI wafer. We will present the theory behind this material as well as the experimental demonstration, and will conclude by discussing nonlinear propagation in a zero-index medium. This metamaterial exhibits surprising phase-matching behaviour, in particular, the simultaneous generation of forward- and backward- propagating light. Using full-wave simulations, we study the propagation and generation of nonlinear signals within these metamaterials and explore their unique phase-matching behaviour in multiple simultaneous directions. We leverage the 2-dimensional nature of these metamaterials to explore the dependence of the nonlinear signal on the size as well as shape of the nonlinear material. The presented results have important implications for future phase-matching schemes and integrated nonlinear applications.