Strong and Coherent Coupling between Localized and Propagating Phonon Polaritons

Christopher R. Gubbin, Francesco Martini, Alberto Politi, Stefan A. Maier, and Simone De Liberato

Phys. Rev. Lett. 116, 246402 – Published 17 June 2016

Abstract

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

Received 26 November 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.246402

Physics Subject Headings (PhySH)

Phonon polariton

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Christopher R. Gubbin^1,2, Francesco Martini², Alberto Politi², Stefan A. Maier¹, and Simone De Liberato²

¹Department of Physics, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
²School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, United Kingdom

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Issue

Vol. 116, Iss. 24 — 17 June 2016

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Images

Figure 1
(a) Fundamental dispersion of the surface mode is given by the black curve. Solid blue curves indicate surface mode folding from the edge of the first Brillouin zone (indicated by corresponding vertical dashed lines) for periodicities $5 - 7 μ m$ . The red curve shows the vacuum light line. The inset shows the electric field norm for a surface mode at an air/SiC interface. The gray shaded region in the inset shows the beginning of the Si substrate on which the SiC wafer we used is grown, highlighting that the surface mode is almost entirely localized into the SiC region. (b) Tight-binding dispersion of the monopolar mode of a pillar array is indicated by blue curves for a variety of periodicities. The red curve is the vacuum light line, with $c$ the speed of light. Insets show a slice of the mode electric field norm in an isolated SiC cylinder on substrate, calculated using comsol multiphysics, and a SEM image of a fabricated resonator. (c) SEM image of the fabricated array. (d) Electric field norm for a mode of the coupled array. The sinusoid indicates the surface mode wavelength.
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Figure 2
(a) Dispersion for array period $6.25 μ m$ and coupling constant $g_{0} = 1.63 meV$ ( $13.1 / cm$ ). Purple dotted lines are the constituent monopolar and folded surface phonon polariton branch, coupled normal modes are green dash-dotted lines. Blue dashed lines represent the two different angles $θ_{1}$ and $θ_{2}$ sampled by the dual illumination. Squares and circles are the fitted data points from the reflectance plots in the Supplemental Material [33]. (b) Illustration of the function of the grazing incidence objective. A Schwarzschild light path is indicated by angularly symmetric blue rays. The plane mirror at the bottom breaks the cylindrical symmetry of the objective rotating the light cone, initially at an incidence angle $θ$ , toward the sample. After reflecting upon the sample surface the beams strike a spherical mirror and are refocussed on the same spot before passing back into the objective. This results in a dual non-normal double-pass illumination at angles $θ_{1}$ and $θ_{2}$ . Notice that the separation between the two rays is exaggerated here for clarity purpose. The actual data for both the rays’ incidence angles and their angular spread can be found in the Supplemental Material [33].
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Figure 3
The top panel (a) shows the background subtracted experimental reflectance map of SiC cylinder arrays of varying period. The almost dispersionless mode at 113.75 meV ( $917.4 / cm$ ) is the transverse dipole resonance discussed elsewhere [4]. The peaks extracted from the reflectance map are given in the lower panels for the larger angle by blue squares and the smaller by red circles. Solid blue lines and dashed red lines are the corresponding fits, enacted using book values for the dielectric constants of SiC (b) [19], or fitting also the dielectric constants of SiC (c) as free parameters.
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