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 give a detailed account of equilibrium and non-equilibrium fluctuational electrodynamics of hyperbolic metamaterials. We show the unifying aspects of two different approaches; one utilizes the second kind of fluctuation dissipation theorem and the other makes use of the scattering method. We analyze the near-field of hyperbolic media at finite temperatures and show that the lack of spatial coherence can be attributed to the multi-modal nature of super-Planckian thermal emission. We also adopt the analysis to phonon-polaritonic super-lattice metamaterials and describe the regimes suitable fo…
We develop fluctuational electrodynamics for media with nonlinear optical response in and out of thermal equilibrium. Starting from the stochastic nonlinear Helmholtz equation and using the fluctuation dissipation theorem, we obtain perturbatively a deterministic nonlinear Helmholtz equation for the average field, the physical linear response, as well as the fluctuations and Rytov currents. We show that the effects of nonlinear optics, in or out of thermal equilibrium, can be taken into account with an effective, system-aware dielectric function. We discuss the heat radiation of a planar, nonl…
We develop fluctuational electrodynamics for media with nonlinear optical response. In a perturbative manner, we amend the stochastic Helmholtz equation to describe fluctuations in a nonlinear setting, in agreement with the fluctuation dissipation theorem, and identify the local (Rytov) current fluctuations. We show how the linear response (the solution of the scattering problem) of a collection of objects is found from the individual responses, as measured in isolation. As an example, we compute the Casimir force acting between nonlinear objects which approaches the result for linear optics f…
We present an approach to describing fluctuational electrodynamic (FED) interactions, particularly van der Waals (vdW) interactions as well as radiative heat transfer (RHT), between material bodies of vastly different length scales, allowing for going between atomistic and continuum treatments of the response of each of these bodies as desired. Any local continuum description of electromagnetic (EM) response is compatible with our approach, while atomistic descriptions in our approach are based on effective electronic and nuclear oscillator degrees of freedom, encapsulating dissipation, short-…
Quantum and thermal fluctuations of electromagnetic fields, which give rise to Planck's law of blackbody radiation, are also responsible for van der Waals and Casimir forces, as well as near-field radiative energy transfer between objects. Electromagnetic waves transport energy, momentum, and entropy. For classical thermal radiation, the dependence of the above mentioned quantities on the temperature is well-known mainly due to Planck's work. When near-field effects, namely the collective influence of diffraction, interference, and tunneling of waves, become important, Planck's theory is no lo…
Dispersion forces between neutral material bodies are due to fluctuations of the polarization of the bodies. For bodies in equilibrium these forces are often referred to as Casimir-Lifshitz forces. For bodies in relative motion, in addition to the Casimir-Lifshitz force, a lateral frictional force ("quantum friction", in the zero temperature limit) comes into play. The widely accepted theory of the fluctuation induced forces is based on the "fluctuational electrodynamics" , when the Maxwell equations are supplemented by random current sources responsible for the fluctuations of the medium pola…
In chains of closely-spaced nanoparticles supporting surface polaritons, near-field electromagnetic coupling leads to collective effects and super-Planckian thermal radiation exchange. Researchers have primarily used two analytical approaches to calculate radiative heat transfer in these systems: fluctuational electrodynamics, which directly incorporates fluctuating thermal currents into Maxwell's equations, and a kinetic approach where the dispersion relation provides modes and propagation lengths for the Boltzmann transport equation. Here, we compare results from the two approaches in order …
When two objects made of a material which supports surface modes are brought in close proximity to each other such that the vacuum gap between them is less than the thermal wavelength of radiation, then the coupling between the surface modes provides an important channel for the heat transfer to occur which is different from that mediated by long range propagating electromagnetic waves. Indeed, the heat transfer then exceeds Planck's blackbody limit by several orders of magnitude, and consequently has been used for several energy applications such as near-field thermophotovoltaic systems. This…
We theoretically study the phenomenon of self-propulsion through Casimir forces in thermal non-equilibrium. Using fluctuational electrodynamics, we derive a formula for the self-propulsion force for an arbitrary small object in two scenarios, i) for the object being isolated, and ii) for the object being close to a planar surface. In the latter case, the self-propulsion force (i.e., the force parallel to the surface) increases with decreasing distance, i.e., it couples to the near-field. We numerically calculate the lateral force acting on a hot spheroid near a surface and show that it can be …
We review recent theoretical developments on the nanoscale radiative heat transfer in magneto-optical many-particle systems. We discuss in detail the circular heat flux, the giant magneto-resistance effect, the persistent heat current, and the thermal Hall effect for light in such systems within the framework of fluctuational electrodynamics, using the dipolar approximation. We show that the directionality of heat flux in such systems can in principle be understood by analyzing the competing contributions to the heat exchange of the magnetic-field-dependent dipolar resonances of quantum number…
The transport of heat mediated by thermal photons in hyperbolic multilayer metamaterials is studied using the fluctuational electrodynamics theory. We demonstrate that in comparison to bulk materials the flux inside layered hyperbolic materials can be transported at much longer distances, making these media very promising for thermal management and for near-field energy harvesting.
Spin and orbital angular momentum of light plays a central role in quantum nanophotonics as well as topological electrodynamics. Here, we show that the thermal radiation from finite-sized bodies comprising of nonreciprocal magneto-optical materials can exert a spin torque even in global thermal equilibrium. Moving beyond the paradigm of near-field heat transfer, we calculate near-field radiative angular momentum transfer between finite-sized nonreciprocal objects by combining Rytov's fluctuational electrodynamics with the theory of optical angular momentum. We prove that a single magneto-optic…
We investigate energy and momentum non-contact exchanges between two arbitrary flat media separated by a gap. This problem is revisited as a transmission problem of individual system eigenmodes weighted by a transmission probability obtained either from fluctuational electrodynamics or quantum field theory. An upper limit for energy and momentum flux is derived using a general variational approach. The corresponding optimal reflectivity coefficients are given both for identical and different media in interaction.
Using the fluctuational electrodynamics and nonequilibrium Green's function methods, we demonstrate the existence of a current-induced heat transfer in double-layer graphene even when the temperatures of the two sheets are the same. The heat flux is quadratically dependent on the current. When temperatures are different, external voltage bias can reverse the direction of heat flow. The drift effect can exist in both macroscopic and nanosized double-layer graphene and extend to any other 2D electron systems. These results pave the way for a different approach to the thermal management through r…
A theory of temperature dynamics in many-body systems driven by time-dependent external sources is introduced. The formalism based on the combination of the perturbation theory and the fluctuational-electrodynamics approach in many-body systems. By using response theory, explicit formula for the temperature and phase shifts is derived and expressed in terms of the amplitude and phase of external power sources. Although the proposed method is highly efficient because it can skip the transient response, it is valid when external powers are weak. As an illustration of this theoretical framework, …
In this work, we propose a near-field radiative thermal transistor made of two graphene-covered silicon carbide (SiC) plates separated by a nanometer vacuum gap. Thick SiC plates serve as the thermal "source" and "drain", while graphene sheets function as the "gate" to modulate the near-field photon tunneling by tuning chemical potential with applied voltage biases symmetrically or asymmetrically. The radiative heat flux calculated from fluctuational electrodynamics significantly varies with graphene chemical potentials, which can tune the coupling between graphene plasmon across the vacuum ga…
In the present work, we theoretically demonstrate that near field radiative transport between one dimensional periodic grating microstructures separated by nanometer vacuum gaps can be spectrally enhanced by exciting magnetic polariton. Fluctuational electrodynamics that incorporates scattering matrix theory with rigorous coupled wave analysis is employed to exactly calculate the near field radiative flux between two gold gratings. Besides the well known coupled surface plasmon polaritons, the radiative flux can be also spectrally enhanced due to magnetic polariton, which is excited in the gap…
We study the radiative heat transfer between two semi-infinite half-spaces, bounded by conductive surfaces in contact with vacuum. This setup is interpreted as a four-terminal mesoscopic transport problem. The slabs and interfaces are viewed as bosonic reservoirs, coupled perfectly to a scattering center consisting of the two interfaces and vacuum. Using Rytov's fluctuational electrodynamics and assuming Kirchhoff's circuital law, we calculate the heat flow in each bath. This allows for explicit evaluation of a conductance matrix, from which one readily verifies Büttiker symmetry. Thus, radiat…
Using the nonequilibrium Green's function (NEGF) formalism, we propose a microscopic theory for near-field heat transfer between charged metal plates focusing on the Coulomb interactions. Tight-binding models for the electrons are coupled to the electromagnetic field continuum through a scalar potential. Our approach differs from the established ones based on Rytov fluctuational electrodynamics, which deals with the transverse radiative field and vector potential. For a two quantum-dot model a new length scale emerges below which the heat current exhibits great enhancement. This length scale i…
The dynamic heat transfer between two half-spaces separated by a vacuum gap due to coupling of their surface modes is modelled using the theory that describes the dynamic energy transfer between two coupled harmonic oscillators each separately connected to a heat bath and with the heat baths maintained at different temperatures. The theory is applied for the case when the two surfaces are made up of a polar crystal which supports surface polaritons that can be excited at room temperature and the predicted heat transfer is compared with the steady state heat transfer value calculated from stand…
We investigate the radiative heat transfer along a chain of nanoparticles using both a purely kinetic approach based on the solution of a Boltzmann transport equation and an exact method (Landauer's approach) based on fluctuational electrodynamics. We show that the kinetic theory generally fails to predict properly the heat flux transported along the chain both at close (near-field regime) and large separation (far-field regime) distances. We report a deviation of a factor two between the heat fluxes predicted by the two approaches in the diffusive regime of heat transport and we show that thi…
In the present work, we theoretically demonstrate, for the first time, that near field radiative transport between 1D periodic grating microstructures separated by subwavelength vacuum gaps can be significantly enhanced by exciting magnetic resonance or polariton. Fluctuational electrodynamics that incorporates scattering matrix theory with rigorous coupled wave analysis is employed to exactly calculate the near field radiative heat flux between two SiC gratings. Besides the well known coupled surface phonon polaritons (SPhP), an additional spectral radiative heat flux peak, which is due to ma…
Enhanced Near-Field Thermal Radiation Driven by Multiple Corner and Edge Modes in Subwavelength Square Nanowires
Sorbonne Université, CNRS, Institut des Nanosciences de Paris, INSP（索邦大学，法国国家科学研究中心，巴黎纳米科学研究所）；Institute of Industrial Science, The University of Tokyo（东京大学工业科学研究所）；LIMMS, CNRS-IIS IRL 2820（中岛实验室，CNRS-IIS 国际联合研究实验室 2820）；Laboratoire des Solides Irradiés Ecole Polytechnique - UMR CNRS 7642 - CEA/DRF/IRAMIS（固体辐射实验室，巴黎综合理工学院，CNRS 联合研究单位 7642，CEA/DRF/IRAMIS）
Using the standard fluctuational electrodynamics framework, we analytically calculate the radiative heat current between two thin metallic layers, separated by a vacuum gap. We analyse different contributions to the heat current (travelling or evanescent waves, transverse electric or magnetic polarization) and reveal the crucial qualitative role played by the dc conductivity of the metals as compared to the speed of light. For poorly conducting metals, the heat current may be dominated by evanescent waves even when the separation between the layers greatly exceeds the thermal photon wavelength…
A normal-diffusion theory for heat transfer in many-body systems via carriers of thermal photons is developed. The thermal conductivity tensor is rigorously derived from fluctuational electrodynamics as a coefficient of diffusion term for the first time. In addition, a convection-like heat transfer behavior is revealed in systems of asymmetric distribution of particles, indicating violation of Fourier's law for such system. Considering the central role of thermal conductivity in heat transfer, this work paves a way for understanding, analysis and manipulation of heat transfer in nanoparticle s…
We perform a theoretical study of the near-field heat transfer between two atomically thin metallic layers, isolated galvanically but coupled by the Coulomb interaction, within the framework of fluctuational electrodynamics in the Coulomb limit. We clarify the role of disorder and spatial dispersion, and identify several distinct regimes of the heat transfer. We find that the plasmon contribution to the heat current is suppressed both in the clean and diffusive limits, but dominates in a parametrically wide crossover region at sufficiently high temperatures.
Recent experimental measurements for near-field radiative heat transfer between two bodies have been able to approach the gap distance within $2 \; \textrm{nm}$, where the contributions of Coulomb fluctuation and electron's tunneling are comparable. Using the nonequilibrium Green's function method in the $G_{0}W_{0}$ approximation, based on a tight-binding model, we obtain for the energy current a Caroli formula from the Meir-Wingreen formula in the local equilibrium approximation. Also, the Caroli formula is consistent with the evanescent part of the heat transfer from the theory of fluctuati…
It is shown that thermally excited plasmon-polariton modes can strongly mediate, enhance and \emph{tune} the near-field radiation transfer between two closely separated graphene sheets. The dependence of near-field heat exchange on doping and electron relaxation time is analyzed in the near infra-red within the framework of fluctuational electrodynamics. The dominant contribution to heat transfer can be controlled to arise from either interband or intraband processes. We predict maximum transfer at low doping and for plasmons in two graphene sheets in resonance, with orders-of-magnitude enhanc…
Active control of heat flow is of both fundamental and applied interest in thermal management and energy conversion. Here, we present a fluctuational electrodynamic study of thermal radiation between twisted bilayer graphene (TBLG), motivated by its unusual and highly tunable plasmonic properties. We show that near-field heat flow can vary by more than 10-fold over only a few degrees of twist, and identify special angles leading to heat flow extrema. These special angles are dictated by the Drude weight in the intraband optical conductivity of TBLG, and are roughly linear with the chemical pot…
A general theory of photon-mediated energy and momentum transfer in N-body planar systems out of thermal equilibrium is introduced. It is based on the combination of the scattering theory and the fluctuational-electrodynamics approach in many-body systems. By making a Landauer-like formulation of the heat transfer problem, explicit formulas for the energy transmission coefficients between two distinct slabs as well as the self-coupling coefficients are derived and expressed in terms of the reflection and transmission coefficients of the single bodies. We also show how to calculate local equili…
We use fluctuational electrodynamics to determine emissivity and van der Waals contribution to surface energy for various spherical shapes, such as a sphere, a bubble, a spherical shell and a coated sphere, in a homogeneous and isotropic medium. Near-field radiative transfer and momentum transfer between flat plates and curved surfaces have been studied for the past decades, however the investigation of radiative heat transfer and van der Waals stress due to fluctuations of electromagnetic fields for a single object is missing from literature. The dyadic Green's function formalism of radiative…
We study a one-dimensional model of radiative heat transfer for which the effect of the electromag- netic field is only from the scalar potential and thereby ignoring the vector potential contribution. This is a valid assumption when the distances between objects are of the order of nanometers. Using Lorenz gauge, the scalar field is quantized with the canonical quantization scheme, giving rise to scalar photons. In the limit as the speed of light approaches infinity, the theory reduces to a pure Coulomb interaction governed by the Poisson equation. The model describes very well parallel plate…
In this Letter we experimentally demonstrate that the radiative heat transfer between metallic planar surfaces exceeds the blackbody limit by employing the near-field and thin-film effects. Nanosized polystyrene particles were used to create a nanometer gap between aluminum thin-films of different thicknesses coated on 5x5 mm2 diced silicon chips while the gap spacing is fitted from the near-field measurement with bare Si chips. The experimental results are validated by theoretical calculation based on fluctuational electrodynamics. The near-field radiative heat flux between 13-nm Al thin-film…
Near-field and resonance effects have a strong influence on the nanoscale electromagnetic energy transfer, and detailed understanding of these effects is required for the design of new, optimized nano-optical devices. We provide a comprehensive microscopic view of electromagnetic energy transfer phenomena by introducing quantum Langevin heat baths as local noise sources in the equations of motion for the thermally fluctuating electric dipoles forming dielectric bodies. The theory is, in a sense, the microscopic generalization of the well-known fluctuational electrodynamics theory and thereby p…
We present a general microscopic first-principles method to study the Coulomb-interaction-mediated heat transfer in the near field. Using the nonequilibrium Green's function formalism, we derive Caroli formulas for heat transfers between materials with translational invariance. The central physical quantities are the screened Coulomb potential and the spectrum function of polarizability. Within the random phase approximation, we calculate the polarizability using the linear response density functional theory and obtain the screened Coulomb potential from a retarded Dyson equation. We show that…
We study the electrodynamics of spin triplet superconductors including dipolar interactions, which give rise to an interplay between the collective spin dynamics of the condensate and orbital Meissner screening currents. Within this theory, we identify a class of spin waves that originate from the coupled dynamics of the spin-symmetry breaking triplet order parameter and the electromagnetic field. In particular, we study magnetostatic spin wave modes that are localized to the sample surface. We show that these surface modes can be excited and detected using experimental techniques such as micr…
Beyond Electrons: A Theoretical Framework for Near-Field Radiative Thermal Computing and Neural-Network-Inspired Processing
Northeastern University（东北大学）；Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier（夏尔·库隆实验室 (L2C)，CNRS-蒙彼利埃大学联合研究单位 5221）；Institut Universitaire de France（法国高等研究院）
