We study the near-field heat exchange between hyperbolic materials and demonstrate that these media are able to support broadband frustrated modes which transport heat by photon tunnelling with a high efficiency close to the theoretical limit. We predict that hyperbolic materials can be designed to be perfect thermal emitters at nanoscale and derive the near-field analog of the blackbody limit.PACS numbers: 44.40.+a;81.05.Xj A black body is usually defined by its property of having a maximum absorptivity and therefore also a maximum emissivity by virtue of Kirchhoff's law [1]. The energy transmission between two black bodies having different temperatures obey the well-known Stefan-Boltzmann law. This law sets an upper limit for the power which can be transmitted by real materials, but it is itself a limit for the far-field only, since it takes only propagating modes into account. In terms of the energy transmission between two bodies the black body case corresponds to maximum transmission for all allowed frequencies ω and all wave vectors smaller than ω/c, where c is the vacuum light velocity. This means that all the propagating modes are perfectly transmitted across the separation gap.In the near-field regime, i.e., for distances smaller than the thermal wavelength λ th = c/k B T (2π is Planck's constant, k B is Boltzmann's constant, and T is the temperature) the radiative heat flux is not due to the propagating modes, but it is dominated by evanescent waves [2-4] and especially surface polaritons as confirmed by recent experiments [5][6][7][8][9][10][11]. The common paradigm is that the largest heat flux can be achieved when the materials support surface polaritons which will give a resonant energy transfer restricted to a small frequency band around the surface mode resonance frequency [3,4,12,13]. Many researchers have tried to find materials enhancing the nanoscale heat flux due to the contribution of the coupled surface modes by using layered materials [14,15] In the present work the aim is twofold: (i) We show, that materials supporting a broad band of evanescent frustrated modes can outperform the heat flux due to surface modes. This provides new possibilies for designing materials giving large nanoscale heat fluxes which could be used for thermal management at the nanoscale for instance. (ii) We derive a general limit for the heat flux carried by the frustrated modes and show that it is, in fact, the near-field analog of the usual black body limit. For the evanescent modes a near field analog of a black body can be defined in the sense that the energy transmission coefficient must be equal to one for all frequencies and all wave vectors larger than ω/c. With today's nanofabrication techniques it is possible to manufacture artificial materials such as photonic band gap materials and metamaterials which exhibit very unusual material properties like negative refraction [23]. Due to such properties they are considered as good candidates for perfect lensing [24,25], for repulsive Casimir forces [26][27][28][...

A general fluctuational-electrodynamic theory is developed to investigate radiative heat exchanges between objects which are assumed small compared with their thermal wavelength (dipolar approximation) in N -body systems immersed in a thermal bath. This theoretical framework is applied to study the dynamic of heating/cooling of three-body systems. We show that many-body interactions allow to tailor the temperature field distribution and to drastically change the time scale of thermal relaxation processes.

We study super-Planckian near-field heat exchanges for multilayer hyperbolic metamaterials using exact S-matrix calculations. We investigate heat exchanges between two multilayer hyperbolic metamaterial structures. We show that the superPlanckian emission of such metamaterials can either come from the presence of surface phonon-polaritons modes or from a continuum of hyperbolic modes depending on the choice of composite materials as well as the structural configuration.In the last few years several fascinating experiments have demonstrated that for small separation distances compared with the thermal wavelength the thermal radiation exchanged between two hot bodies out of thermal equilibrium increases dramatically compared with what we observe at large distances and can even exceed the well-known Stefan-Boltzmann law by orders of magnitude 1-6 . Accordingly, thermal emission is in that case also called super-Planckian emission emphasizing the possibility to go beyond the classical black-body theory. There are several promising applications of super-Planckian emitters ranging from thermal imaging 7-9 and thermal rectification/management 10-12 to near-field thermophotovoltaics 13-17 . This has triggered many studies on the possibilities of tailoring and controlling the super-Planckian radiation spectrum by means of designing the material properties 18-23 , using phase-change materials 24 or 2D systems such as graphene 25,26 , for instance.Recently, it was shown that hyperbolic metamaterials can lead to broad-band photonic thermal conductance inside the material itself 27 and between two hyperbolic materials only separated by a vacuum gap 28 . Further Nefedov et al. considered nanorod-like structures

The heat transport mediated by near-field interactions in networks of plasmonic nanostructures is shown to be analogous to a generalized random walk process. The existence of superdiffusive regimes is demonstrated both in linear ordered chains and in three-dimensional random networks by analyzing the asymptotic behavior of the corresponding probability distribution function. We show that the spread of heat in these networks is described by a type of Lévy flight. The presence of such anomalous heat-transport regimes in plasmonic networks opens the way to the design of a new generation of composite materials able to transport heat faster than the normal diffusion process in solids.

Here, we address the question of the validity of an effective description for hyperbolic metamaterials in the near-field region. We show that the presence of localized modes such as surface waves drastically limits the validity of the effective description and requires revisiting the concept of homogenization in near-field. We demonstrate from exact calculations that one can find surface modes in spectral regions where the effective approach predicts hyperbolic modes only. Hence, the presence of surface modes which are not accounted for in the effective description can lead to physical misinterpretations in the description of hyperbolic materials and their related properties.