Vortices Formed by Two Counter-Propagating Waves for Surface Phonon Polaritons with Material Losses
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Vortices Formed by Two Counter‑Propagating Waves for Surface Phonon Polaritons with Material Losses Hyoung‑In Lee1 · Jinsik Mok2 Received: 1 September 2019 / Accepted: 3 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We examine the surface phonon polaritons established on resonance between lossy silicon carbide and vacuum over the Reststrahlen frequency range. To this goal, we investigate two waves counter-propagating along a planar material interface in terms of the orbital and spin parts of the Poynting vector. Vortices of the spin part are thus found to be generated near the collision point of the two waves. In addition, vortex pairs of opposite circulations are identified near the material interface. The locality of the electric permittivity plays an essential role in enabling our simple analysis by neglecting the spatial propagations of phonons while keeping the material damping. The resulting dynamics of the total displacement field turns out to be loss-free in the middle of the lossy dynamics of the other field variables, thus exhibiting a superfluid-like feature in an otherwise normal fluid. Keywords Surface phonon polaritons · Counter-propagating waves · Silicon carbide · Loss-induced phenomena · Spin part vortices · Locality · Total displacement
1 Introduction Here, we examine how vortices are formed by two counter-propagating classical electromagnetic (EM) waves in interactions with phonons. To this goal, we investigate the surface phonon polaritons that are established across a material interface between silicon carbide and dielectric when the operating frequency lies in the Reststrahlen band [1–9].
* Hyoung‑In Lee [email protected] 1
Research Institute of Mathematics, Seoul National University, 599 Gwanak‑Ro, Gwanak‑Gu, Seoul 08826, Republic of Korea
2
Department of Industrial and Management Engineering, Sunmoon University, 70 Sunmoon‑Ro‑221‑Gil, Tangjeong‑Myun, Asan‑See, Choongnam 31460, Republic of Korea
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Vol.:(0123456789)
Journal of Low Temperature Physics
Refer to Fig. 1a, where a lossy silicon carbide lies in the upper half-space, while a loss-free dielectric is placed in the lower half-space [2]. Let us take the simplest approach of associating the loss-free dielectric (vacuum or air) with a superfluid, while associating the lossy silicon carbide with a normal fluid. Hence, the lossy normal fluid and the loss-free superfluid are well separated by the interface, and they never interpenetrate each other unlike the superfluid liquid helium [10–14]. In this comparative description, the Poynting energy of EM waves enters the normal fluid across the fixed interface from our superfluid to compensate for the loss in our normal fluid. This picture of a superfluid and a normal fluid separated by the material interface holds true for the electric and magnetic fields as well as the mechanical displacement field in silicon carbide. It is essential to examine the total displacement consisting of both the electric field and the mechanical displacem
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