Raman scattering of phonon polaritons under nanoscale confinement: the role of structure and environment

Abstract

Strong light-matter coupling gives rise to polaritons -- quasiparticles that combine both photonic and material characteristics. Here, we show that polar nanocrystals exhibit structure- and environment-dependent Raman scattering, enabled by their hybrid phonon polariton nature. Such dispersive behavior enables refractive index sensing in the mid-infrared range via visible-wavelength inelastic spectroscopy and draws parallels with molecular systems under vibrational strong coupling. Crucially, Raman scattering appears only under nanoscale confinement of phonon polaritons. For optimal structures, this leads to self-hybridization between localized phonon modes and surface phonon polaritons hosted by the same nanoparticle.

Figures (5)

• Figure 1: Optical constants, Raman and infrared spectra of bulk SiC.A, Analytical permittivity of SiC: real (blue) and imaginary (red) part, reproduced from Palik handbook choyke1997silicon. Inset demonstrates the zoom in part where the resonance condition is reached for a subwavelength sphere, $\varepsilon_1\simeq -2$ is valid for air medium. B, Infrared reflection (blue line, left axis) and Raman scattering (red line, right axis) of 6H-SiC crystal. Insets show the schematic of the crystal lattice.
• Figure 2: Raman scattering by surface phonon polaritons in SiC nanopillars: the effect of structure and environment.A, Typical experimental Raman scattering spectra for different diameters of nanopillars. Each spectrum has a removed baseline signal and normalized over TO peak intensity. The offset of 0.5 between neighboring spectra along the $y$-axis is artificial for visual perception.Inset shows the enlarged view of SPhP resonance peak shift. B, Tilted SEM images of the SiC nanopillars. Scale bars are 500 nm. The color matches the corresponding plots in A. The blue dashed line indicates a close-up cross-sectional ADF STEM image of the $\sim$ 10 nm diameter pillar. Scale bar for the STEM image is 50 nm. C, Statistically averaged Raman scattering fitting of the TO and SPhP peak positions. Error bars are from the standard deviation of the mean value. D, The ratio between SPhP or LO intensity and a TO intensity as a function of the diameter. Error bars are statistical error bars from fitting of 9 separate disks. E, Raman scattering spectra of a dense array of SiC $D=200$ nm nanopillars for different surrounding media -- air, water H$_2$O, heavy water D$_2$O, ethylene glycol (EG), and isopropanol (IPA). Similar normalization and offset as in A. Inset: Enlarged view of the SPhP resonance peak shift observed for different surrounding media. F, Schematic of the experiment where the sample was covered homogeneously with a liquid droplet. G, Raman scattering fitting of the TO and SPhP peak positions as a function of the real part of the media permittivity $\varepsilon'$ at 930 cm$^{-1}$. The dashed line is the linear fit of the SPhP peak spectral position. Error bars represent the 0.95 confidence interval. The dielectric function of heavy water at 10.75 $\mu$m is adopted from Ref. bertie1989infrared. H, The ratio between SPhP or LO intensity and a TO intensity as a function of the media permittivity. Error bars represent the 0.95 confidence interval.
• Figure 3: Raman scattering by surface phonon polaritons in SiC dimer and elliptical nanopillars.A, Typical Raman spectra of the dimer nanopillars of $D$ = 100 nm diameter and 25, 50, 100, and 2000 (single pillar) nm gap size ($\delta$). Normalization and offset are made similar to Figure \ref{['fig:environment']}A. Inset shows the enlarged view of SPhP resonance peak shift with different gap sizes. B, Schematic of the dimensions of the structure and typical SEM images of the dimers. Scale bars are 500 nm. Boxes colors correspond to frames color from A$\delta$ = 25, 50, 100 nm. C, Statistically averaged over 9 dimers per gap reference TO Raman peak (red squares) and SPhP peak (blue circles) positions as functions of gap size $\delta$. D, The relative intensity of SPhP (blue circle) and LO (red triangles) peaks to TO peak for each gap size, averaged over 9 dimers per gap. E, Typical Raman spectra of the elliptical nanopillars of $D$ = 200 nm diameter and 1 to 5 aspect ratio (AR) of the corresponding color of the frames in F. Normalization and offset are made similarly to Figure \ref{['fig:environment']}A. Inset shows the enlarged view of SPhP resonance peak shift with different aspect ratios. F, A graphical image schematically showing the AR correspondence to the diameter and tilted SEM images of the SiC nanopillars. Scale bars are 500 nm. Colors of the frames correspond to spectra color AR = 1 -- 5. G, Statistically averaged over 9 elliptical pillars per AR value reference TO Raman peak position (red squares) and SPhP peak position (blue circles) as functions of AR. H, Relative intensity of SPhP and LO peaks to TO peak intensity for each AR value, averaged over 9 ellipsoids per AR.
• Figure 4: Comparison of infrared and Raman spectra for SiC nanopillars of various diameters.A, Infrared reflection spectra of a pillar array of various diameters from 30 to 500 nm. The center-to-center pitch size is 2 $\mu$m. The inset is the schematic of the experiment. The arrows and markers indicate the position of the respective modes -- TO, LO (indicates the border of the Reststrahlen band), SPhP, and lattice resonances from the periodic nature of the sample and mid-IR excitation. B, Experimental Raman scattering of the single nanopillar array from A. The markers and arrows indicate the same set of modes, but the longitudinal resonances are absent in the Raman scattering. C, Numerically simulated reflection map of SiC pillar array on the SiC substrate. The incident light is a $p$-polarized plane wave excitation with a $\theta$=20$\degree$ angle with respect to the normal. D, Numerically simulated reflection map of SiC pillar array on the SiC substrate. The incident light is a $s$-polarized plane wave excitation with a $\theta$=20$\degree$ angle with respect to the normal. The parameters of simulated SiC pillars closely approximate the experimental ones. The markers and arrows indicate the same set of modes, but the lattice resonances are not present in the Raman scattering.
• Figure 5: Raman scattering by surface phonon polaritons in subwavelength 4H-SiC nanostructures.A, Raman spectra for different diameters of nanopillars with $L=270$ nm. Diameters given in the legends are the design diameters. B, Tilted-view SEM images of SiC nanopillars. Scale bars are 200 nm. C, Fitted peak position of Raman scattering spectra for corresponding pillars. Diameter values on the $x$-axis represent the average of the top and bottom diameters of the nanopillars, extracted from the corresponding SEM images. Error bars indicate the standard deviation calculated from six to nine pillars for each diameter. [$\star$] symbol marks an unidentifiable peak position, caused by the limited fitting accuracy in this case, due to the low signal-to-noise ratio in the Raman spectrum. For some diameters, error bars are smaller than symbols. D, Typical Raman spectra for elliptical nanopillars with minor axis $\approx$ 75 nm and height of 270 nm. Aspect ratio is shown as AR = 1 -- 4. E, Tilted-view SEM images for elliptical nanopillars with minor axis $\approx$ 75 nm. Scale bars are 200 nm. F, Fitted peak position of Raman scattering spectra for elliptical nanopillars. The major axes on the $x$-axis represent the average of the top and bottom major axes of the nanopillars, extracted from the corresponding SEM images. Error bars indicate the standard deviation calculated from six to nine pillars for each elliptical nanopillar. For some pillars, error bars are smaller than symbols. G, Effect of different thicknesses of Al$_2$O$_3$ (0-12 nm) on Raman spectra of elliptical nanopillars with aspect ratio 3 (AR = 3) and height 270 nm). Orange spectrum shows the recovery of the SPhP peaks after cleaning the Al$_2$O$_3$ layer. H, Graphical image of elliptical nanopillar. Inset is the top view SEM image of the particle minor axis $\approx$ 75 nm and AR = 3 with 3 nm Al$_2$O$_3$ deposited by ALD. Scale bar is 200 nm. I, Fitted peak position of SPhP with varying Al$_2$O$_3$ thicknesses for the presented spectra in G. The data corresponding to a 12 nm Al$_2$O$_3$ thickness is excluded because the SPhP Raman peak is poorly defined and shows a pronounced blue shift with increasing Al$_2$O$_3$ thickness.