Thermal metamaterials based on surface phonon-polaritons
Laurent Tranchant1, José Ordonez-Miranda1 , Sebastian Voltz1, Bruno Palpant2, Thomas
Antoni1,2.
1
Laboratoire d’Énergétique Moléculaire et Macroscopique, Combustion, UPR CNRS 288, École
Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry, France
2
École Centrale Paris, Laboratoire de Photonique Quantique et Moléculaire, CNRS (UMR
8537), École Normale Supérieure de Cachan, Grande Voie des Vignes, F-92295 ChâtenayMalabry cedex, France
Presenting author's e-mail address: [email protected]
1. Surface phonon-polaritons on nanofilms
Surface phonon-polaritons (SPhPs) are electromagnetic waves propagating at the interface
between a dielectric and a polar material that features spontaneous electrical dipoles due to the
relative motion ofions in its lattice cell. The oscillations of these lattice ionsquantized in the form
of phonons, produce an electromagnetic field characterized by a dispersion mainly located
bellow the light line of the dielectric. SPhP arehence trapped at the materials interface while they
propagate in the in-plane directions with huge energy densities.
At the interface between two semi-infinite media, SPhPs have very short propagation length,
on the order of their wavelength (10 µm for SiO2), and only exist within a narrow spectral
bandwidth (1 µm SiO2), so that their contribution to thermal transport is often negligible. By
contrast, when they propagate along layers with a thickness on the order of hundreds of
nanometers, their spectral bandwidth as well as their propagation length increases dramatically,
providing the material with a new heat transfer channel that can exceeds the one of bulk thermal
conduction [1,2].Furthermore, at these nanoscales, the SPhPs propagation turns out to be
coherent [3] and consequently, their dispersion can be tailored using bandgap structures, like
surface gratings.
To model such structures, we have developed numerical simulations of SPhP based on the
electromagnetic finite-difference in time-domain MEEP code. In particular, we investigated two
structures exhibiting unnatural properties and for this reason called metamaterials: the first one
exhibits thermal anisotropy at equilibrium, whereas the other mimics a material with negative
index of refraction.We will focus our study on SiO2 systems since this material exhibits SPhP
resonances near 10 µm, which corresponds to the maximum of the thermal emission at ambient
temperature.
1. Numerical modeling
To investigate the propagation of SPhPs on realistic structures, with arbitrary shapes, we took
advantage of the electromagnetic nature of those waves to use MEEP code for finite-difference in
time-domain (FDTD). In such electromagnetic codes, materials are described by their sole
dielectric permittivity. Their phononic properties can be entirely embedded into the dielectric
permittivity since phonons are here responsible for the absorption of the electromagnetic field.
Hence the standard Lorentz model for permittivity can be used with resonances corresponding to
the phonons frequencies.
2. SPhP-based metamaterials
As thermal radiation becomes coherent when transported by SPhPs, it is possible to use the
wide variety of bandgap structures to manipulate it and design new materials with unnatural
properties. Here, we will focus on two nanostructured devices.
The first structure is a combination of two gratings, a first one enablesthe coupling of SPhP
with propagative fields while the second one creates a micro-cavity to trap the SPhP energy. This
second grating simply consists in a Bragg grating with a defect, so that the bandgap will prevent
the SPhP from propagating out of the defect. Based on FDTD simulations, we proved that, when
uniformly illuminated with a laser beam in stationary regime, the cavity generates a temperature
gradient on the order of 104 mK/µm (Figure 1) du to energy trapping.
The physical mechanisms at play in the second structure rely on the existence of modes with
negative group velocity at the surface of Bragg gratings. We expect that the coupling of such
modes with radiative ones result in negative refraction of incoming wave in the thermal infrared
domain.
Figure 1: Energy trapping in a SPhP microcavity. The figure represents the electromagnetic energy inside the
structure, obtained with an FDTD code.
3. References
[1] José Ordonez-Miranda, Laurent Tranchant, Takuro Tokunaga, Beomjoon Kim, Bruno Palpant, Yann Chalopin,
Thomas Antoni, Sebastian Volz, “Anomalous thermal conductivity by surface phonon-polaritons of polar nano thin
films due to their asymmetric surrounding media”, Journal of Applied Physics 113, pp. 084311 (2013).
[2] José Ordonez-Miranda, Laurent Tranchant, Takuro Tokunaga, Beomjoon Kim, Yann Chalopin, Thomas Antoni,
Sebastian Volz, “Quantized Thermal Conductance of Nanowires at Room Temperature Due to Zenneck SurfacePhonon Polaritons”, Physical Review Letters 114, pp. 055901 (2014).
[3] Jean-Jacques Greffet, Rémi Carminati, Karl Joulain, Jean-Philippe Mulet, Stéphane Mainguy, and Yong
Chen,“Coherent emission of light by thermal sources”, Nature 416, pp. 61-64 (2002).