Phonon Polaritons and Epsilon Near Zero Modes in Sapphire Nanostructures

TL;DR

The paper investigates light–matter interactions in sapphire nanostructures within the LWIR Reststrahlen bands, using a nanocone-array resonator platform. By combining Fourier-transform infrared spectroscopy, confocal Raman mapping, and full-wave finite-element simulations, it identifies three surface phonon polariton (SPhP) modes, two hyperbolic volume phonon polaritons (HVPhPs), and an epsilon-near-zero (ENZ) mode, demonstrating strong sub-diffraction confinement. Spatial Raman measurements reveal mode-dependent enhancements and phonon–polaritons coupling, supported by symmetry-based Raman selection rules and modeling of the polarizability. The results establish sapphire nanocone arrays as a promising IR nanophotonic platform with potential applications in sensing, imaging, and magneto-phononic devices, by harnessing IR-active phonons, SPhPs, HVPhPs, and ENZ phenomena.

Abstract

Surface phonon polaritons (SPhPs) are promising candidates for enhanced light--matter interactions due to their efficient and low-loss light confinement features. In this work, we present unique light-matter interactions in saphhire within its Reststrahlen bands (RBs) across the long-wave infrared (LWIR) spectrum ($ω= 385$-$1050~\mathrm{cm}^{-1}$). Particularly, we investigated the nanocone-patterned sapphire resonator array, with specific attention to its in-plane and out-of-plane permittivity components. Through Fourier transform infrared spectroscopy measurement and full-wave photonic simulations, we identified a range of optical excitations in the RBs, including three SPhPs, two hyperbolic volume phonon polaritons (HVPhPs), and one epsilon-near-zero (ENZ) mode. The depth-resolved confocal Raman spectroscopy revealed strongly enhanced Raman signals on the nanostructured surface, suggesting the mode coupling between phonons and phonon-polaritons, which was further confirmed by the finite element modeling of polarizability. This exploratory study provides in-depth insights into the dynamics of LWIR phonon polaritons and ENZ modes in the nanostructured sapphire, indicating its great potential for innovative nanophotonic applications.

Figures (10)

• Figure 1: (a) Schematic of the crystallographic unit cells for $\alpha$-$\ce{Al2O3}$. The left panel shows the 3D atomic structure, while the right panels show $xy$ and $xz$ orientations. The black and red circles indicate aluminum and oxygen atoms, respectively. (b) Angle-dependent reflectance measurements for $s$-polarized excitation (polarization is perpendicular to the optic axis) and (c) for $p$-polarized excitation (polarization is parallel to the optic axis) for the bulk material. (d) Reflectance measurements for $s$ and $p$-polarized excitations for the bulk material with $\theta = 45^\circ$. (e) The real part of permittivity components for (001) sapphire ranging from 385 cm$^{-1}$ to 1050 cm$^{-1}$. The blue curve shows permittivity in $x$ and $y$ directions (perpendicular to the optic axis), and the red curve indicates the permittivity along $z$ direction (parallel to the optic axis). Color coding indicates various RBs of the material which are metallic (cyan), hyperbolic type $\mathrm{I}$ (magenta), and type $\mathrm{II}$ (green).
• Figure 2: Optical properties of nanocone-structured sapphire(a) Reflection spectra for the bulk and nanocone-structured material for the oblique $s$-polarized and (b) $p$-polarized incidence with angle of $\theta = 45^\circ$. The solid curves show reflection measurements for the bulk and nanostructured samples, and the dashed curves represent the simulation results obtained from modeling of the nanocone arrays using COMSOL Multiphysics. (c) The SEM images indicate the side view (left panel) and the top view (right panel) of the nanocone-structured sample. The nanostructure dimensions and the periodic rectangular unitcell used in the simulation shown on the images. (d) Reflection spectra for the bulk and nanostructured samples for $p$-polarized incidence with angles of $\theta = 45^\circ$ and $\theta = 70^\circ$ within the spectral range of 482 cm$^{-1}$ to 511 cm$^{-1}$ where the material exhibits hyperbolic type I behavior. The solid curves represent reflection measurements for the bulk and nanostructured samples, and the dashed curves demonstrate simulation results.
• Figure 3: E-field spatial distribution in NCA sapphire system. $E_z$ simulated cross-sectional plots for HvPhP at (a) 495 cm$^{-1}$, and (b) 500 cm$^{-1}$ with near grazing incidence of $\theta = 70^\circ$. The normal incidence $E_y$ simulated cross-sectional plots for (c) ENZ mode at 565 cm$^{-1}$, and for $s$-polarized SPhP resonances at (d) 763 cm$^{-1}$, and (e) 800 cm$^{-1}$. Normal incidence $E_z$ surface plot for $p$-polarized SPhP at (f) 794 cm$^{-1}$.
• Figure 4: Mapping PhPs in Al2O3 NCA. (a) Measured Raman at three different points (as shown in the inset) across the NCA indicating the spatial dependence of Raman modes. $ZY$ cross sectional view of Raman intensity obtained from experimental measurements for (b) $A_{1g}$ phonon mode at $\omega= 418~cm^{-1}$, and (c) $E_{g}$ phonon mode at $\omega= 751~cm^{-1}$ for three adjacent NCs. Theoretically simulated Raman intensity shown in $ZY$ cut plane for (d) $A_{1g}$ and (e) $E_{g}$ phonon modes. The dashed green lines indicate the NCs-air interface.
• Figure S1: (a) A (001) sample cut from a hexagonal crystal unit cell, with the optic axis ($c$-axis) oriented perpendicular to the sample’s surface. (b) Polarized components of a normal incident light beam. Here, the $p$-polarized light is in the $YZ$ plane, while the $s$-polarized light is positioned in $XZ$ plane, perpendicular to the plane of incidence.