Generalized 4 ×\times 4 Matrix Formalism for Light Propagation in Anisotropic Stratified Media: Study of Surface Phonon Polaritons in Polar Dielectric Heterostructures

We present a generalized 4 $\times$ 4 matrix formalism for the description of light propagation in birefringent stratified media. In contrast to previous work, our algorithm is capable of treating arbitrarily anisotropic or isotropic, absorbing or non-absorbing materials and is free of discontinous solutions. We calculate the reflection and transmission coefficients and derive equations for the electric field distribution for any number of layers. The algorithm is easily comprehensible and can be straight forwardly implemented in a computer program. To demonstrate the capabilities of the approach, we calculate the reflectivities, electric field distributions, and dispersion curves for surface phonon polaritons excited in the Otto geometry for selected model systems, where we observe several distinct phenomena ranging from critical coupling to mode splitting, and surface phonon polaritons in hyperbolic media

Second Harmonic Generation from Critically Coupled Surface Phonon Polaritons

Mid-infrared nanophotonics can be realized using sub-diffractional light localization and field enhancement with surface phonon polaritons in polar dielectric materials. We experimentally demonstrate second harmonic generation due to the optical field enhancement from critically coupled surface phonon polaritons at the 6H-SiC-air interface, employing an infrared free-electron laser for intense, tunable, and narrowband mid-infrared excitation. Critical coupling to the surface polaritons is achieved using a prism in the Otto geometry with adjustable width of the air gap, providing full control over the excitation conditions along the polariton dispersion. The calculated reflectivity and second harmonic spectra reproduce the full experimental data set with high accuracy, allowing for a quantification of the optical field enhancement. We also reveal the mechanism for low out-coupling efficiency of the second harmonic light in the Otto geometry. Perspectives on surface phonon polariton-based nonlinear sensing and nonlinear waveguide coupling are discussed

Layer-Resolved Resonance Intensity of Evanescent Polariton Modes in Anisotropic Multilayers

Phonon polariton modes in layered anisotropic heterostructures are a key building block for modern nanophotonic technologies. The light-matter interaction for evanescent excitation of such a multilayer system can be theoretically described by a transfer matrix formalism. This method allows to compute the imaginary part of the p-polarized reflection coefficient Im$(r_{pp})$, which is typically used to analyze the polariton dispersion of the multilayer structure, but lacks the possibility to access the layer-resolved polaritonic response. We present an approach to compute the layer-resolved polariton resonance intensity in aribtrarily anisotropic layered heterostructures, based on calculating the Poynting vector extracted from a transfer matrix formalism. Our approach is independent of the experimental excitation conditions, and fulfills an empirical conservation law. As a test ground, we study two state-of-the-art nanophotonic multilayer systems, covering strong coupling and tunable hyperbolic surface phonon polaritons in twisted \MoO~double layers. Providing a new level of insight into the polaritonic response, our method holds great potential for understanding, optimizing and predicting new forms of polariton heterostructures in the future.Comment: 7 pages, 2 figure

Second Harmonic Generation from Phononic Epsilon-Near-Zero Berreman Modes in Ultrathin Polar Crystal Films

Immense optical field enhancement was predicted to occur for the Berreman mode in ultrathin films at frequencies in the vicinity of epsilon near zero (ENZ). Here, we report the first experimental proof of this prediction in the mid-infrared by probing the resonantly enhanced second harmonic generation (SHG) at the longitudinal optic phonon frequency from a deeply subwavelength-thin aluminum nitride (AlN) film. Employing a transfer matrix formalism, we show that the field enhancement is completely localized inside the AlN layer, revealing that the observed SHG signal of the Berreman mode is solely generated in the AlN film. Our results demonstrate that ENZ Berreman modes in intrinsically low-loss polar dielectric crystals constitute a promising platform for nonlinear nanophotonic applications

Corrections

Surface phonon polaritons (SPhP) and surface plasmon polaritons (SPP), evanescent modes supported by media with negative permittivity, are a fundamental building block of nanophotonics. These modes are unmatched in terms of field enhancement and spatial confinement, and dynamical all-optical control can be achieved e.g. by employing phase-change materials (PCMs). However, the excitation of surface polaritons in planar structures is intrinsically limited to p-polarization. On the contrary, waveguide modes in high-permittivity films can couple to both p- and s-polarized light, and in thin films, their confinement can become comparable to surface polaritons. Here we demonstrate that the s-polarized waveguide mode in a thin Ge3Sb2Te6 (GST) film features a similar dispersion, confinement, and electric field enhancement as the SPhP mode of the silicon carbide (SiC) substrate, while even expanding the allowed frequency range. Moreover, we experimentally show that switching the GST film grants non-volatile control over the SPhP and the waveguide mode dispersions. We provide an analytical model for the description of the GST/SiC waveguide mode and show that our concept is applicable to the broad variety of polar crystals throughout the infrared spectral range. As such, complementarily to the polarization-limited surface polaritons, the s-polarized PCM waveguide mode constitutes a promising additional building block for nanophotonic applications

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

Generalized 4x4 matrix algorithm for light propagation in anisotropic stratified media (Matlab files)

<p>The attached Matlab function allows to calculate reflection and transmission coefficients for any number of arbitrarily anisotropic or isotropc multilayer systems. The associated publication will be submitted shortly. Besides the transfer matrix function, we also provide a simple test script allowing to calculate specific predefined material systems presented in the upcoming publication.</p