Fluctuational Electrodynamics Research Articles

Parametric optimum design of a near-field electroluminescent refrigerator

A novel model of the irreversible near-field electroluminescent refrigerator (INFER) composed of an emitter and a receiver is proposed, where the heat transfers between the cold and hot sides and the reservoirs are taken into account. Based on the fluctuation electrodynamics, two critical formulas for the cooling power density (CPD) and cooling coefficient of performance (COP) of the INFER are derived. The optimum thermodynamic characteristics of the INFER are studied. Meanwhile, the effects of the vacuum gap on the performance of the INFER are discussed. By making a trade-off between the CPD and the COP, the parametric optimum design rules are presented. The parametric characteristics for homojunction and heterojunction structures are calculated and compared. An optimum design structure is determined. The results obtained here may provide some guidance for optimally designing and actually developing solid-state refrigerators.

Re-estimation of thermal contact resistance considering near-field thermal radiation effect

Thermal contact has always been a hot issue in many engineering fields and thermal contact resistance (TCR) is one of the important indicators weighing the heat transfer efficiency among the interfaces. In this paper, the contact heat transfer of conforming rough surfaces is theoretically re-estimated considering both the heat transfer from contact and non-contact regions. The fluctuational electrodynamics (an ab initio calculation) is adopted to calculate the thermal radiation. The contribution of the contact regions is estimated by the CMY TCR model and further studied by modelling specific surfaces with the corresponding surface roughness power spectrum. Several tests are presented where aluminum and amorphous alumina are mainly used in the simulations. Studies showed that there exists a significant synergy between the thermal conduction and near-field thermal radiation at the interface within a certain range of the effective roughness. When the effective roughness is near to the scales of submicron, the near-field thermal radiation effect should not be neglected even at room temperature.

Spectral redshift of the thermal near field scattered by a probe

The physics underlying spectral redshift of thermally generated surface phonon-polaritons (SPhPs) observed in near-field thermal spectroscopy is investigated. Numerically exact fluctuational electrodynamics simulations of the thermal near field emitted by a silicon carbide surface scattered in the far zone by an intrinsic silicon probe show that SPhP resonance redshift is a physical phenomenon. A maximum SPhP redshift of 19 cm-1 is predicted for a 200-nm-diameter hemispherical probing tip and a vacuum gap of 10 nm. Resonance redshift is mediated by electromagnetic gap modes excited in the vacuum gap separating the probe and the surface when the probing tip is much larger than the gap size. The impact of gap modes on the scattered field can be mitigated with a probing tip size approximately equal to or smaller than the vacuum gap. However, sharp probing tips induce important spectral broadening of the scattered field. It is also demonstrated that a dipole approximation with multiple reflections cannot be used for explaining the physics and predicting the amount of redshift in near-field thermal spectroscopy. This work shows that the scattered field in the far zone is a combination of the thermal near field emitted by the surface, and electromagnetic interactions between the probe and the surface. Spectroscopic analysis of near-field thermal emission thus requires a numerically exact fluctuational electrodynamics framework for modeling probe-surface interactions.

Towards fully self-consistent optoelectronic simulation of planar devices

Photon recycling plays an important role in various optoelectronic devices, such as thin-film solar cells and intracavity double-diode structures presently studied for electroluminescent cooling. However, a complete description of photon recycling requires developing fully self-consistent simulation tools of photon and electronic charge transport in realistic device structures. In this paper, we describe a possible route towards such simulation tools in planar devices by combining the radiative transfer (RT) equation of photon transport with the drift-diffusion (DD) equations of electron and hole dynamics. We investigate the feasibility of the approach by selected proof-of-principle device studies. The results indicate that combining the RT and DD models not only yields the expected device characteristics, but also produces new insight into the pertinent local emission and absorption properties within the device structures. In particular, the model allows to accurately investigate how emission directivity and saturation affect the coupling coefficient in the double diode structures, showing that the main contribution to the coupling coefficient arises from the reflectivity of the top contact. For completeness, we also discuss how interference affects photon transport in resonant devices by an example calculation using the quantized fluctuational electrodynamics framework, paving way for self-consistent modeling tools that also account for wave-optical effects.

On anomalously large nano-scale heat transfer between metals

The non-contact heat transfer between two bodies is more efficient than the Stefan-Boltzmann law, when the distances are on the nanometer scale (shorter than Wien's wavelength), due to contributions of thermally excited near fields. This is usually described in terms of the fluctuation electrodynamics due to Rytov, Levin, and co-workers. Recent experiments in the tip-plane geometry have reported "giant" heat currents between metallic (gold) objects, exceeding even the expectations of Rytov theory. We discuss a simple model that describes the distance dependence of the data and permits to compare to a plate-plate geometry, as in the proximity (or Derjaguin) approximation. We extract an area density of active channels which is of the same order for the experiments performed by the groups of Kittel (Oldenburg) and Reddy (Ann Arbor). It is argued that mechanisms that couple phonons to an oscillating surface polarisation are likely to play a role.

Gate voltage and doping effects on near-field radiation heat transfer in plasmonic heterogeneous pairs of graphene and black phosphorene.

Plasmon coupling and hybridization in 2D materials plays a significant role for controlling light–matter interaction at the nanoscale. We present a near-field radiation heat transfer (NFRHT) between vertically separated graphene and black phosphorene sheets at different temperatures in nanoscale separations. Radiation exchange from the theory of fluctuation electrodynamics is modulated by the carrier density of graphene and phosphorene. Direct comparison of NFRHT black phosphorene–graphene to symmetric graphene–graphene radiation exchange can be as much as 4 times higher for the selected doping range in both armchair (AC) and zigzag (ZZ) orientations of BP. The strong NFRHT enhancement of the specific optical properties of the heterogenous 2D material is due to the strong coupling of propagating surface plasmon polaritons as demonstrated by the distribution of the heat transfer coefficient. We also demonstrate that the magnitude of the near-field radiation enhancement is found to acutely depend on the vacuum gap of the graphene and BP pair. Interestingly, for separation distances below 200 nm, the total near-field heat transfer between black phosphorene and graphene exceeds that between graphene and graphene by 5 times. The radiation enhancement can be further tuned based on the orientation, AC, and ZZ of black phosphorene. These results prominently enable dynamic control of the total NFRHT relying on tunable anisotropic characteristics of BP irrespective of graphene's optical conductivity. Furthermore, the heterogeneous pairs of 2D materials potentially provide alternative platforms to achieve beyond super-Planckian radiation.

Coupled harmonic oscillator model to describe surface-mode mediated heat transfer

When two objects made of a material that 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 near-field radiative heat exchange has been traditionally and successfully described using fluctuational electrodynamics principles. Here, we describe an alternate coupled harmonic oscillator model approach, which can be used to model the coupling between surface modes and hence the resultant near-field heat transfer. We apply this theory to estimate the near-field heat transfer for the configurations of two metallic nanoparticles and two planar metal surfaces and compare the result with predictions from fluctuational electrodynamics theory.

Apparent Spectral Shift of Thermally Generated Surface Phonon-Polariton Resonance Mediated by a Nonresonant Film

Near-field radiative heat transfer between dissimilar materials is important in thermal management and energy-harvesting, but an in-depth physical analysis is needed. Using fluctuational electrodynamics, this study shows that the spectral redshift or blueshift of thermally generated surface phonon-polaritons (SPhPs) can be mediated by a nonresonant layer. The apparent shift is due to multiple reflections within the subwavelength gap separating resonant and nonresonant layers, which generate gap modes and decrease thermal emission around the SPhP resonance---valuable insight for applications based on near-field thermal radiation, such as thermophotovoltaics and thermal rectification.

Surface plasmon-enhanced near-field thermal rectification in graphene-based structures

We propose a thermal rectification structure composed of InSb and graphene-coated 3C-SiC separated by a nanoscale vacuum gap. To obtain an obvious thermal rectification effect, the permittivities of these materials are all considered to be temperature-dependent. Numerical calculations based on fluctuation electrodynamics reveal that the introduction of graphene into the structure enhances significantly near-field radiative heat flux and thermal rectification efficiency owing to the strong coupling of surface plasmon-polaritons between InSb and graphene. In general, the rectification efficiency above 60% can be maintained for the vacuum gap less than 70 nm. The rectification efficiency exceeding 95% is realized for a vacuum gap of 10 nm and a chemical potential of 0.1 eV. Increasing the emitter’s temperature leads to the drastic increase of the rectification efficiency in a wider temperature range. A lower chemical potential seems more favorable to raising rapidly the rectification efficiency. The above results might be helpful in designing a thermal diode with higher efficiency and wider vacuum gap.

Stored electromagnetic energy and radiated power by spherical thermal micro/nano-emitters: Radiation Q-factor

We examine theoretically (based on fluctuational electrodynamics) the stored electromagnetic energy and radiated power by a spherical thermal emitter. Moreover, we propose a measure for the radiation quality Q-factor for a polychromatic source such as a thermal emitter. We consider that the thermal emitter is made of tungsten and silicon carbide and we study in detail how the aforementioned radiative quantities depend on size and temperature of the antenna. Particularly, we obtain the emissivity (ratio of spectral radiated power by emitter and that by an ideal blackbody), and the spectral density of stored electromagnetic energy normalized with respect to that of a blackbody. For a SiC-emitter, the emissivity and the normalized spectral stored density energy exhibit multiple narrow peaks associated with surface phonon-polariton and whispering gallery mode resonances; while for a W-antenna, high ohmic losses yield broad spectra of the aforementioned quantities (only an interband resonance appears). These spectra depend strongly on particle size; the corresponding unnormalized spectra are perturbed by the temperature. There is an optimal size of the antenna for which the emissivity is maximal; the aforementioned materials yield an emissivity larger than one. The radiation Q-factor decreases as particle radius and temperature increase, implying that the radiation efficiency of a thermal emitter increases as these parameters grow. The Q-factor for a W-antenna is smaller than that for a SiC-antenna (same size and temperature) for nano-scale particles, whereas, for micrometric particles, the opposite happens over a certain temperature range. Our work might have implications for infrared sources and thermophotovoltaics.

Revisiting the Dipole Model for a Thermal Infrared Near-Field Spectroscope

We determine the scattered near-field and directly emitted power of a heated spherical nanoparticle above a sample within the framework of fluctuational electrodynamics using the dipole approximation. Our results deviate from previously obtained results. Additionally, we show that in a configuration where the nanoparticle is heated with respect to its environment, the scattered power of the near field of the sample is strictly zero. Only when the sample is heated or the temperature of the surroundings of the sample is lowered is there a contribution from the scattered power. Our results indicate that for the interpretation of near-field imaging setups as the thermal infrared near-field spectroscope not only the scattering of the near field but also the direct emission of the tip plays a role.

Magnetothermoplasmonics: from theory to applications

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 numbers m = +1 and m = -1. Some potential applications of these effects to thermal and magnetic sensing are also briefly discussed.

Limitations of kinetic theory to describe near-field heat exchanges in many-body systems

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 this difference becomes even greater than two orders of magnitude in the ballistic regime.

Dynamic near-field heat transfer between macroscopic bodies for nanometric gaps

Abstract The dynamic heat transfer between two half-spaces separated by a vacuum gap due to the coupling of their surface modes is modeled 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 that supports surface polaritons that can be excited at room temperature and the predicted heat transfer is compared to the steady-state heat transfer value calculated from the standard fluctuational electrodynamics theory. It is observed that for small time intervals the value of heat flux can be significantly higher than that of steady-state value.

Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit.

Radiative heat transfer (RHT) has a central role in entropy generation and energy transfer at length scales ranging from nanometres to light years1. The blackbody limit2, as established in Max Planck's theory of RHT, provides a convenient metric for quantifying rates of RHT because it represents the maximum possible rate of RHT between macroscopic objects in the far field-that is, at separations greater than Wien's wavelength3. Recent experimental work has verified the feasibility of overcoming the blackbody limit in the near field4-7, but heat-transfer rates exceeding the blackbody limit have not previously been demonstrated in the far field. Here we use custom-fabricated calorimetric nanostructures with embedded thermometers to show that RHT between planar membranes with sub-wavelength dimensions can exceed the blackbody limit in the far field by more than two orders of magnitude. The heat-transfer rates that we observe are in good agreement with calculations based on fluctuational electrodynamics. These findings may be directly relevant to various fields, such as energy conversion, atmospheric sciences and astrophysics, in which RHT is important.

Dynamic optical control of near-field radiative transfer.

Dynamic control of radiative heat transfer is of fundamental interest as well as for applications in thermal management and energy conversion. However, realizing high contrast control of heat flow without moving parts and with high temporal frequencies remains a challenge. Here, we propose a thermal modulation scheme based on optical pumping of semiconductors in near-field radiative contact. External photo-excitation of the semiconductor emitters leads to increases in the free carrier concentration that in turn alters the plasma frequency, resulting in modulation of near-field thermal radiation. The temporal frequency of the modulation can reach hundreds of kHz limited only by the recombination lifetime, greatly exceeding the bandwidth of methods based on temperature modulcation. Calculations based on fluctuational electrodynamics show that the heat transfer coefficient between two silicon films can be tuned from near zero to 600 Wm-2K-1 with a gap distance of 100 nm at room temperature.

Energy transfer between two vacuum-gapped metal plates: Coulomb fluctuations and electron tunneling

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 fluctuational electrodynamics. We go beyond the local equilibrium approximation to study the energy transfer in the crossover region from electron tunneling to Coulomb fluctuation based on a numerical calculation.

Precision Measurement of Phonon-Polaritonic Near-Field Energy Transfer between Macroscale Planar Structures Under Large Thermal Gradients.

Despite its strong potentials in emerging energy applications, near-field thermal radiation between large planar structures has not been fully explored in experiments. Particularly, it is extremely challenging to control a subwavelength gap distance with good parallelism under large thermal gradients. This article reports the precision measurement of near-field radiative energy transfer between two macroscale single-crystalline quartz plates that support surface phonon polaritons. Our measurement scheme allows the precise control of a gap distance down to 200nm in a highly reproducible manner for a surface area of 5×5 mm^{2}. We have measured near-field thermal radiation as a function of the gap distance for a broad range of thermal gradients up to ∼156 K, observing more than 40 times enhancement of thermal radiation compared to the blackbody limit. By comparing with theoretical prediction based on fluctuational electrodynamics, we demonstrate that such remarkable enhancement is owing to phonon-polaritonic energy transfer across a nanoscale vacuum gap.

Fluctuational electrodynamics for nonlinear materials in and out of thermal equilibrium

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, nonlinear surface, showing that Kirchhoff's must be applied carefully. We find that the spectral emissivity of a nonlinear nanosphere can in principle be negative, implying the possibility of heat flow reversal for specific frequencies.

Photonic thermal diode enabled by surface polariton coupling in nanostructures.

A novel photonic thermal diode concept operating in the near field and capitalizing on the temperature-dependence of coupled surface polariton modes in nanostructures is proposed. The diode concept utilizes terminals made of the same material supporting surface polariton modes in the infrared, but with dissimilar structures. The specific diode design analyzed in this work involves a thin film and a bulk, both made of 3C silicon carbide, separated by a subwavelength vacuum gap. High rectification efficiency is obtained by tuning the antisymmetric resonant modes of the thin film, resulting from surface phonon-polariton coupling, on- and off-resonance with the resonant mode of the bulk as a function of the temperature bias direction. Rectification efficiency is investigated by varying structural parameters, namely the vacuum gap size, the dielectric function of the substrate onto which the film is coated, and the film thickness to gap size ratio. Calculations based on fluctuational electrodynamics reveal that high rectification efficiencies in the 80% to 87% range can be maintained in a wide temperature band (~700 K to 1000 K). The rectification efficiency of the proposed diode concept can potentially be further enhanced by investigating more complex nanostructures such as gratings and multilayered media.