Nonlinear Phase-Matching in 2D Integrated Zero-Index Metamaterials

Nonlinear optics play an important role in many applications in photonics and quantum optics, such as in frequency conversion, sensing, and entangled-photon generation. The strong field confinement obtained by the transition to an integrated platform has led to unprecedented nonlinear figures of merit and the miniaturization of nonlinear devices. However, phase-matching remains an essential component to nonlinear processes and represents a significant obstacle, with many different free-space and on-chip techniques being developed to circumvent its constraints. Recently, a 1-dimensional metamaterial with a refractive index of zero has been applied to 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. We have designed a pair of 2D integrated metamaterials with an effective refractive index of zero: a square array of silicon rods on a silica substrate, and the inverse structure of a square array of air-holes in a silicon slab. These isotropic structures both 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. 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.