Hybrid longitudinal-transverse phonon polaritons

Abstract

Phonon polaritons, hybrid light-matter quasiparticles resulting from strong coupling of the electromagnetic field with the lattice vibrations of polar crystals are a promising platform for mid-infrared photonics but for the moment there has been no proposal allowing for their electrical pumping. Electrical currents in fact mainly generate longitudinal optical phonons, while only transverse ones participate in the creation of phonon polaritons. We demonstrate how to exploit long-cell polytypes of silicon carbide to achieve strong coupling between transverse phonon polaritons and zone-folded longitudinal optical phonons. We develop a microscopic theory predicting the existence of the resulting hybrid longitudinal-transverse excitations. We then provide an experimental observation by tuning the resonance of a nanopillar array through the folded longitudinal optical mode, obtaining a clear spectral anti-crossing. The hybridisation of phonon polaritons with longitudinal phonons could represent an important step toward the development of phonon polariton-based electrically pumped mid-infrared emitters.

Fig. 1

Schematic of the ZLFO-SPhP hybridisation scheme. a Illustration of LO phonon dispersion parallel to the c-axis in 2H- and 4H-SiC. The wavevector is normalised over the 2H-SiC Brillouin zone border k_M = π/a where a is the length of the 2H-SiC unit cell along the c-axis. The shaded region illustrates the spectral range where SPhPs exist at a SiC/vacuum interface. Inset shows an illustration of the crystal structures of 2H- and 4H-SiC, the length of the 4H- unit cell is approximately twice that of the 2H- along the c-axis. b Sketch of the strong coupling between LO phonons, TO phonons, and photons, resulting in the creation of LTPPs, in a square array of 4H-SiC nanopillars

Fig. 2

Coupling between a ZFLO and a SPhP resonance at the interface of a polar dielectric halfspace. a TM polarised reflectance calculated for an a-cut, 4H-SiC substrate supporting a weak phonon mode at near normal incidence. The in-plane wavevector of the incident light is parallel to the crystal c-axis. The inset illustrates the physical system under study. b Colormap illustrates the dispersion of the surface phonon polariton on the bilayer interface calculated by Eq. (4). Overlaid dashed lines indicate the bare weak phonon and surface phonon polariton dispersions, while the green curves illustrate the coupled LTPP modes

Fig. 3

Experimental demonstration of strong coupling between a ZFLO and the monopolar mode of a nanopillar array. Upper panels illustrate the experimental reflectance from an array of 4H-SiC nanopillars with diameter (a) 300 nm (b) 500 nm and height 950 nm recorded as a function of the lattice period. The horizontal dashed line indicates the weak phonon resonance. The lower panel shows the magnitude of the reflectance dip extracted from the data. The shaded region indicates the region where the upper polariton is predominantly LO in character, demarcated by the vertical dashed line