Nonlocal scattering matrix description of anisotropic polar heterostructures

Abstract

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.

Anisotropy and Modal Hybridization in Infrared Nanophotonics Using Low-Symmetry Materials

“…These effects have been recently observed by Ratchford et al within AlN/GaN short-period superlattices (TEM cross sections in Figure a,b), demonstrating a significantly modified IR reflectance (Figure c,d, blue curves), and thus, dielectric function and polaritonic dispersion. While ab initio simulations were initially employed to study crystalline hybrids, nonlocal dielectric theories have more recently been shown to correctly reproduce experimental features with limited computational requirements (Figure c,d, red curves), making it possible to include nonlocal effects in the design of SPhP devices. , Further, much like semiconductor quantum wells, this also provides the potential opportunity to inject free carriers in one of the constituents (e.g., GaN) to locally tune the SPhPs within the adjacent structure (e.g., AlN) through the electromagnetic hybrid effect . Thus, this could enable opportunities to actively tune polaritonic modes within materials where otherwise such effects are not possible.…”

Polaritonic quantization in nonlocal polar materials

“…where Cijkl is an effective elasticity tensor satisfying the symmetry conditions [18] Cijkl = Cjikl = Cklji ,…”

“…This unique property has led to LTPs being proposed as a platform for mid-infrared optoelectronics as a result of the possibility of exciting them through longitudinal electrical currents, while still outcoupling to transverse free-space radiation in the far-field [16]. A recent series of publications has studied LTPs in more general systems, demonstrating them to be a general feature of polar resonators at the nanoscale [17][18][19] and a similar phenomenology has also recently been observed in a Yukawa fluid [20]. These works follow the approach of nonlocal plasmonics, starting from the macroscopic Maxwell equations, introducing new macroscopic fields to describe phonon modes in the lattice and matching fields at material boundaries considering the flow of energy in the system.…”

Polaritonic quantisation in nonlocal polar material

“…This unique property has led to LTPs being proposed as a platform for mid-infrared optoelectronics as a result of the possibility of exciting them through longitudinal electrical currents, while still outcoupling to transverse free-space radiation in the far-field [16]. A recent series of publications has studied LTPs in more general systems, demonstrating them to be a general feature of polar resonators at the nanoscale [17][18][19] and a similar phenomenology has also recently been observed in a Yukawa fluid [20]. These works follow the approach of nonlocal plasmonics, starting from the macroscopic Maxwell equations, introducing new macroscopic fields to describe phonon modes in the lattice and matching fields at material boundaries considering the flow of energy in the system.…”