Modeling the optical properties of Twisted Bilayer Photonic Crystals.

We demonstrate a photonic analog of twisted bilayer graphene that has ultra-flat photonic bands and exhibits extreme slow light behavior. Our twisted bilayer photonic device, which has an operating wavelength in C-band of the telecom window, uses two crystalline silicon photonic crystal slabs separated by a methyl methacrylate tunneling layer. We numerically determine the magic angle using a finite-element method and the corresponding photonic band structure, which exhibits a flat band over the entire Brillouin zone. This flat band causes the group velocity to approach zero and introduces light localization in a linear periodic photonic system. Using a plane-wave continuum model we find that photonic modes in twisted bilayer photonic crystals are not as tightly bound as their electronic counterparts in twisted bilayer graphene. In addition, the photonic system has a larger band asymmetry. The band structure can easily be engineered by adjusting the device geometry, giving significant freedom in the design of devices. Our work provides a fundamental understanding of the photonic properties of twisted bilayer photonic crystals and opens the door to nanoscale-based non-linear enhancement and superradiance.