Nonlocal Scattering Matrix Description of Anisotropic Polar Heterostructures

Polar dielectrics are a promising platform for mid-infrared nanophotonics, allowing for nanoscale electromagnetic energy confinement in oscillations of the crystal lattice. We recently demonstrated that in nanoscopic polar systems a local description of the optical response fails, leading to erroneous predictions of modal frequencies and electromagnetic field enhancements. In this Paper we extend our previous work providing a scattering matrix theory of the nonlocal optical response of planar, anisotropic, layered polar dielectric heterostructures. The formalism we employ allows for the calculation of both reflection and transmission coefficients, and of the guided mode spectrum. We apply our theory to complex AlN/GaN superlattices, demonstrating the strong nonlocal tuneability of the optical response arising from hybridisation between photon and phonon modes. The numerical code underlying these calculations is provided in an online repository to serve as a tool for the design of phonon-based mid-infrared optoelectronic devices.