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Recent advances in quantum circuits and hybrid quantum well systems have been enabled by leveraging the strong coupling regime in hybrid material heterostructures. Quanta of light-matter interactions are polaritons, the coupled modes of photons and a material excitation, such as plasmons, excitons, or phonons. Due to their short wavelength, polariton lasers operating via intersubband polariton transitions in cascaded quantum wells have shown great promise as terahertz and mid-infrared sources with low threshold energies, with phonon-polariton lasers having applications in nanostructure fabrication and inspection. Hexagonal boron nitride (hBN) has come to the forefront of metamaterial research due to its polar van der Waals crystal structure and two infrared active phonon modes exhibiting hyperbolicity. Because of the small lattice mismatch (less the 22% of the GaN lattice constant) between [0001] oriented wurtzite GaN and hBN, hBN has been used as a substrate and mechanical release layer for GaN and AlGaN with minimal damage to the crystalline quality. Intersubband phonon-polaritons have already been detected in GaN/graphene heterostructures and intersubband excitonpolaritons have been detected in GaN/AlN heterostructures; due to the similar nature of these materials, we believe hBN will be a suitable barrier material for gallium nitride wells. In this study, the conduction band structure of the aforementioned heterostructure will be calculated using a self-consistent Schrödinger-Poisson solver. Intersubband phonon-polariton transitions in a layered hBN/GaN lattice via and Finite Element Method (FEM) simulation of the reflectivity and polaritonic dispersion will be evaluated.
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