Theory of Optical Nonlocality in Polar Dielectrics

Sub-wavelength confinement of mid-infrared light can be achieved exploiting the metal-like optical response of polar dielectric crystals in their Reststrahlen spectral region, where they support evanescent modes termed surface phonon polaritons. In the past few years the investigation of phonon polaritons localised in nanoresonators and layered heterostructures has enjoyed remarkable success, highlighting them as a promising platform for mid-infrared nanophotonic applications. Here we prove that the standard local dielectric description of phonon polaritons in nanometric objects fails due to the nonlocal nature of the phonon response and we develop the corresponding nonlocal theory. Application of our general theory to both dielectric nanospheres and thin films demonstrates that polar dielectrics exhibit a rich nonlocal phenomenology, qualitatively different from the one of plasmonic systems, due to the negative dispersion of phononic optical modes.Comment: 13 pages, 6 figure

Theory of four-wave-mixing in phonon polaritons

Third order anharmonic scattering in light-matter systems can drive a wide variety of practical and physically interesting processes from lasing to polariton condensation. Motivated by recent experimental results in the nonlinear optics of localised phonon polaritons, in this Letter we develop a quantum theory capable of describing four-wave mixing in arbitrarily inhomogeneous photonic environments. Using it we investigate Kerr self-interaction and parametric scattering of surface and localised phonon polaritons, showing both processes to be within experimental reach.Comment: 20 pages, 3 figure

Real-space Hopfield diagonalization of inhomogeneous dispersive media

We introduce a real-space technique able to extend the standard Hopfield approach commonly used in quantum polaritonics to the case of inhomogeneous lossless materials interacting with the electromagnetic field. We derive the creation and annihilation polaritonic operators for the system normal modes as linear, space-dependent superpositions of the microscopic light and matter fields, and we invert the Hopfield transformation expressing the microscopic fields as functions of the polaritonic operators. As an example, we apply our approach to the case of a planar interface between vacuum and a polar dielectric, showing how we can consistently treat both propagative and surface modes, and express their nonlinear interactions, arising from phonon anharmonicity, as polaritonic scattering terms. We also show that our theory can be naturally extended to the case of dissipative materials

Electrical Generation of Surface Phonon Polaritons

Efficient electrical generation of mid-infrared light is challenging because of the dearth of materials with natural dipole-active electronic transitions in this spectral region. One approach to solve this problem is through quantum-engineering of the electron dispersion to create artificial transitions, as in quantum cascade devices. In this work we propose an alternative method to generate mid-infrared light, utilizing the coupling between longitudinal and transverse degrees of freedom due to the nonlocal optical response of nanoscopic polar dielectric crystals. Polar crystals support transverse sub-diffraction photonic modes in the mid-infrared. They also support longitudinal phonons, which couple efficiently with electrical currents through the Fr\"ohlich interaction. As we have shown in previous theoretical and experimental works, these two degrees of freedom can hybridize forming longitudinal-transverse polaritons. Here we theoretically demonstrate that longitudinal-transverse polaritons can be efficiently generated by electrical currents, leading to resonant narrowband photonic emission. This approach can therefore be utilised to electrically generate far-field mid-infrared photons in the absence of dipole-active electronic transitions, potentially underpinning a novel generation of mid-infrared optoelectronic devices.Comment: 14 pages, 6 figure

Theoretical Investigation of Phonon Polaritons in SiC Micropillar Resonators

Of late there has been a surge of interest in localised phonon polariton resonators which allow for sub-diffraction confinement of light in the mid-infrared spectral region by coupling to optical phonons at the surface of polar dielectrics. Resonators are generally etched on deep substrates which support propagative surface phonon polariton resonances. Recent experimental work has shown that understanding the coupling between localised and propagative surface phonon polaritons in these systems is vital to correctly describe the system resonances. In this paper we comprehensively investigate resonators composed of arrays of cylindrical SiC resonators on SiC substrates. Our bottom-up approach, starting from the resonances of single, free standing cylinders and isolated substrates, and exploiting both numerical and analytical techniques, allows us to develop a consistent understanding of the parameter space of those resonators, putting on firmer ground this blossoming technology.Comment: 10 Pages, 8 Figure

Coherent coupling between localised and propagating phonon polaritons

Following the recent observation of localised phonon polaritons in user-defined silicon carbide nano-resonators, here we demonstrate coherent coupling between those localised modes and propagating phonon polaritons bound to the surface of the nano-resonator's substrate. In order to obtain phase-matching, the nano-resonators have been fabricated to serve the double function of hosting the localised modes, while also acting as grating for the propagating ones. The coherent coupling between long lived, optically accessible localised modes, and low-loss propagative ones, opens the way to the design and realisation of phonon-polariton based quantum circuits

Second harmonic generation from strongly coupled localized and propagating phonon-polariton modes

We experimentally investigate second harmonic generation from strongly coupled localized and propagative phonon polariton modes in arrays of silicon carbide nanopillars. Our results clearly demonstrate the hybrid nature of the system's eigenmodes and distinct manifestation of strong coupling in the linear and nonlinear response. While in linear reflectivity the intensity of the two strongly-coupled branches is essentially symmetric and well explained by their respective localized or propagative components, the second harmonic signal presents a strong asymmetry. Analyzing it in detail, we reveal the importance of interference effects between the nonlinear polarization terms originating in the bulk and in the phonon polariton modes, respectively.Comment: 7 pages, 4 figure

Strong Coupling of Epsilon-Near-Zero Phonon Polaritons in Polar Dielectric Heterostructures

We report the first observation of epsilon near zero (ENZ) phonon polaritons in an ultrathin AlN film fully hybridized with surface phonon polaritons (SPhP) supported by the adjacent SiC substrate. Employing a strong coupling model for the analysis of the dispersion and electric field distribution in these hybridized modes, we show that they share the most prominent features of the two precursor modes. The novel ENZ-SPhP coupled polaritons with a highly propagative character and deeply sub-wavelength light confinement can be utilized as building blocks for future infrared and terahertz (THz) nanophotonic integration and communication devices

Electrical generation of surface phonon polaritons

Efficient electrical generation of mid-infrared light is challenging because of the dearth of materials with natural dipole-active electronic transitions in this spectral region. One approach to solve this problem is through quantum-engineering of the electron dispersion to create artificial transitions, as in quantum cascade devices. In this work we propose an alternative method to generate mid-infrared light, utilizing the coupling between longitudinal and transverse degrees of freedom due to the nonlocal optical response of nanoscopic polar dielectric crystals. Polar crystals support sub-diffraction photonic modes in the mid-infrared. They also support longitudinal phonons, which couple efficiently with electrical currents through the Fröhlich interaction. As we have shown in previous theoretical and experimental works, these two degrees of freedom can hybridize forming longitudinal-transverse polaritons. Here we theoretically demonstrate that longitudinal-transverse polaritons can be efficiently generated by electrical currents, leading to resonant narrowband photonic emission. This approach can therefore be utilised to electrically generate far-field mid-infrared photons in the absence of dipole-active electronic transitions, potentially underpinning a novel generation of mid-infrared optoelectronic devices