Perspective on Near-Field Radiative Heat Transfer Mariano Pascale1Maxime Giteau1and Georgia T. Papadakis1 ICFO-Institut de Ciencies Fotoniques The Barcelona Institute of Science and Technology Castelldefels Barcelona 08860

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Perspective on Near-Field Radiative Heat Transfer

Mariano Pascale,1Maxime Giteau,1and Georgia T. Papadakis1

ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860,

Spain

(*Electronic mail: georgia.papadakis@icfo.eu)

Although near-ﬁeld radiative heat transfer was introduced in the 1950’s, interest in the ﬁeld has recently revived,

as the effect promises improved performance in various applications where contactless temperature regulation in the

small-scale is a requirement. With progress in computational electromagnetics as well as in nanoinstrumentation,

it has become possible to simulate the effect in complex conﬁgurations and to measure it with high precision. In this

Perspective, we highlight key theoretical and experimental advances in the ﬁeld, and we discuss important developments

in tailoring and enhancing near-ﬁeld thermal emission and heat transfer. We discuss opportunities in heat-to-electricity

energy conversion with thermophotovoltaic systems, as well as non-reciprocal heat transfer, as two of many recent

focus topics in the ﬁeld. Finally, we highlight key experimental challenges and opportunities with emerging materials,

for probing near-ﬁeld heat transfer for relevant technologies in the large-scale.

I. INTRODUCTION

All objects at non-zero temperature emit thermal radiation

due to the thermally excited motion of particles and quasipar-

ticles. Thermal radiation is exchanged between objects sepa-

rated by large distances, such as the earth and the sun or outer

space. Controlling this energy exchange enables applications

in solar energy harvesting, including solar photovoltaics1–4

and daytime radiative cooling5–10. The ability to understand

and control thermal radiation is key in all scenarios where ra-

diative heat transfer (RHT) prevails over thermal conduction

and convection. Examples include thermal protection systems

for spacecrafts11 and high-temperature heat exchangers12,13.

Tailoring thermal radiation, thus, impacts a plethora of areas

of science and engineering, and research in thermal photonics

is setting new frontiers for novel and disruptive technologies

in the years to come 14,15.

Besides being one of the ﬁrst successes of quantum physics,

Planck’s law of thermal radiation 16 has been the cornerstone

of modern nanophotonics at mid-infrared (IR) frequencies.

The law states that a blackbody, an idealized object that per-

fectly absorbs radiation at all frequencies, radiates an elec-

tromagnetic spectrum which depends only on its tempera-

ture, and peaks at the thermal wavelength λth =α/T, with

α≈2898 µmK, as dictated by Wien’s displacement law17.

At room temperature, λth is roughly 10 microns.

When two objects are separated by a distance dmuch

greater than λth (Fig. 1 (a)), the Stefan-Boltzmann law, a

direct consequence of Planck’s law, predicts that the upper

bound on the net radiative heat ﬂux is σ(T4

1−T4

2), where σ

is the Stefan-Boltzmann constant, and T1≥T2are the temper-

atures of the two objects exchanging heat. This heat is ex-

changed via far-ﬁeld propagating electromagnetic modes that

oscillate harmonically as seen in Fig. 1 (a).

When the heat-exchanging objects, however, are in close

proximity with respect to the thermal wavelength (dλth),

evanescent modes can mediate the RHT, hence Planck’s law as

well as the Stefan-Boltzmann law cease to hold 15,18–21. Near-

ﬁeld radiative heat transfer (NFRHT) can exceed the far-ﬁeld

predictions by several orders of magnitude, owing to these

evanescent electromagnetic modes. Such excitations are sur-

d≫λth

(a)

d≪λth

(b)

101102103104105

Gap-size d[nm]

100

101

102

103

104

Thermal Conductance [W/m2K]

Far-Field

λth

SiC-SiC, T=300 K

Black-body

Near-Field

∝1/d2

(c)

FAR-FIELD

NEAR-FIELD

FIG. 1. RHT between two bulk planar layers at different tempera-

tures, separated by a vacuum gap of size dmuch greater than the

thermal wavelength λth (far-ﬁeld) is mediated by propagating waves

(a). When the two layers are brought at a distance dλth (near-

ﬁeld), RHT can be mediated by evanescent modes (b). In panel (c),

the radiative thermal conductance (or heat transfer coefﬁcient, h) per

unit area for two semi-inﬁnite planar layers of SiC near room temper-

ature (T=300K) is shown. For dλth, with λth ≈10 µm marked

by a vertical line, hundergoes a ∝d−2enhancement (red curve). For

dλth,hsaturates at its far-ﬁeld value (blue line), which is smaller

than the blackbody limit ≈6W/m2K (grey line).

face plasmon polaritons (SPPs) or surface phonon polaritons

(SPhPs), and they carry large photon momenta19,22–29, termed

wavenumbers henceforth. Unlike propagating modes that me-

diate RHT in the far-ﬁeld, near-ﬁeld excitations exhibit maxi-

mum intensity at the interface between two media, and decay

exponentially away from it, as schematically depicted in Fig. 1

(b). By placing two such interfaces in close proximity, pho-

ton tunneling occurs, explaining the large heat transfer rates

predicted in the near-ﬁeld as compared to the far-ﬁeld20,30,31.

This is shown in panel (c) of Fig. 1, by plotting h, the ther-

mal conductance per unit area (or heat transfer coefﬁcient).

We note that his plotted in logarithmic scale, due to the con-

siderable difference in the heat transfer rates in the near-ﬁeld

as compared to the far-ﬁeld. The results in Fig. 1 pertain to a

temperature gradient near 300 K, and the material considered

in these calculations is SiC, because it supports a prominent

arXiv:2210.00929v3 [physics.optics] 8 Mar 2023

TABLE I. Scaling laws for NFRHT as a function of the gap-size d

for typical canonical geometries.

PLATE-

PLATE SPHERE-

PLATE TIP-

PLATE SPHERE-

SPHERE

d230,38 1

d[ad]36,65–67 logd68(left) 1

d[ad]69,70

d3[a<d]71 137,66,72

dα∈[0.3,2](right) 1

d6[ad]69,70

SPhP mode near 12 microns. As can be seen, far-ﬁeld RHT

is independent of the distance between the bodies exchanging

heat. In contrast, NFRHT is inversely dependent on the sepa-

ration distance, d. The upper bound of hbetween two planar

interfaces separated in the near-ﬁeld can be approximated as

σ0

d2(T2

1−T2

2)27,32–34, where σ0is only dependent on universal

constants. As can be seen in Fig. 1 (c), for gap sizes be-

low 100 nm, heat transfer undergoes a transition and scales as

1/d2with respect to its far-ﬁeld value. Recent developments

in nanoinstrumentation35 now make it practically possible to

separate objects such small distances, for which the effect has

been measured various times36–39, as discussed below.

The scaling law describing how NFRHT depends on d

varies for different conﬁgurations. In Table I, we summa-

rize this law for some canonical conﬁgurations. Furthermore,

some analytical methodologies have been developed for arbi-

trary shapes 40,41. We note that the results in Table I are valid

within a macroscopic description of thermal ﬂuctuations. To

properly model how NFRHT scales in the limit d→0, of-

ten expressed as the "extreme near-ﬁeld", one ought to con-

sider effects relevant at microscopic scales, e.g., non-local

electromagnetic response as well as transport properties of the

materials42–45.

The enhancement of RHT in the near-ﬁeld discussed

above becomes relevant in applications ranging from con-

tactless cooling46–48 to harvesting energy with thermophoto-

voltaic (TPV) systems 23,49,50, thermal lithography13,33,51–53,

thermally-assisted magnetic recording54–56, thermal logic cir-

cuitry57–62 and scanning thermal microscopy63,64. In this per-

spective, we review experimental as well as theoretical ap-

proaches to measure NFRHT and compute the effect in com-

plex conﬁgurations, respectively. We present our recent con-

tributions ranging from fundamental ﬁndings such as the an-

alytical description of NFRHT in planar structures, to more

applied concepts such as actively tailoring NFRHT, opportu-

nities of NFRHT for thermophotovoltaic systems that convert

heat to electricity, and non-reciprocal heat transfer. Follow-

ing, we discuss foreseen challenges for the development of

NFRHT-related technologies, including achieving large-scale

vacuum gaps, approaches to access spectrally and angularly-

resolved information of thermal emission in the near-ﬁeld, and

improving the quality of narrow-bandgap semiconductors for

TPV systems.

II. OVERVIEW

In this section, we carry out a brief review of experimen-

tal advances in measuring NFRHT, as well as theoretical ap-

proaches to model the effect and predict device performances

and fundamental limits. We start by emphasizing that vari-

ous research groups have recently achieved impressively small

(down to few tens of nanometers) vacuum gaps, and have car-

ried out highly precise calorimetric measurements, which has

signiﬁcantly contributed to the development of the ﬁeld.

A. Measuring RHT at the nanoscale

NFRHT measurements are rather challenging to perform in

practice. They require ﬁne control of the separation between

objects at the nanoscale 19, as well as ensuring a uniform tem-

perature gradient across interfaces. One of the ﬁrst NFRHT

experiments was performed in the late 1960s by Domoto et

al.73, measuring the heat exchange between two parallel cop-

per disks at cryogenic temperatures. At such temperatures,

the thermal wavelength is of the order of hundreds of mi-

crons. The authors observed RHT that surpassed the black-

body limit when the disks were placed within tens of microns

from each other. The following decades have witnessed im-

portant advances in nanofabrication and nanoinstrumentation

techniques35. Thus, truly nanometric vacuum gaps have been

achieved and the measurement of NFRHT has been possible

near room-temperature.

An important prototypical conﬁguration for NFRHT, on

which most theoretical studies are based, is that of two par-

allel plates separated by a vacuum gap (Fig. 1). Though it is

arguably the simplest geometry to treat theoretically as well

as a relevant one for applications, the plane-to-plane conﬁgu-

ration is challenging to experimentally realize. This is due to

the requirement of a uniform nanometric vacuum gap between

smooth parallel surfaces19,35. Such nanometric vacuum gaps

in planar conﬁgurations have been previously achieved via

suspended parallel plates, for example using micro-electro-

mechanical systems (MEMS)38, as well as by separating the

plates using nanospheres or micropillars (Fig. 2(b-d)74–76.

Key NFRHT measurements reported in the literature be-

tween macroscopic plates (area λ2

th) are presented in

Fig 2(a), as a function of the vacuum gap size. For any gap-

dependent experiment, NFRHT follows the expected 1/d2

trend. Remarkably, even though the materials and conﬁgu-

rations have varied signiﬁcantly in these reports, all measure-

ments performed at room temperature (i.e., all data points ex-

cept Domoto et al.73 and Kralik et al.77) fall close to the same

1/d2line. Results that currently stand out are those by Sali-

hoglu et al.78, Rincón-García et al.79, and Fiorino et al.38, who

achieved a vacuum gap of merely 7 nm, 19 nm and 25 nm, re-

spectively, between parallel silica surfaces, leading to up to 4

orders of magnitude enhancement over the blackbody limit.

Although still in progress, within the last decade, efforts to

achieve large-scale nanometric vacuum gaps have been note-

worthy, with important demonstrations so far80.

Other than achieving a nanometric vacuum gap, to measure

101102103104

Gap-size d[nm]

102

103

104

RHT normalized to blackbody limit

∝1/d2

Domoto197073

Hu200886 Ottens201183

Kralik201277

Feng201384

Fiorino201838

Lang201787

Sabbaghi202074

Watjen201675

Ito201789

Yang201890

DeSutter201981

Tang202076

Lim201585

Bernardi201682 Ito201588

Song201695

Rinc´on-Garc´ıa202279

Salihoglu202078

(b)

(c)

(d)

(a)

FIG. 2. (a) Radiative heat ﬂux normalized to the blackbody limit

as a function of the minimum gap-size dfor several planar conﬁgua-

tions experimetally studied in the reported references. The vacuum

gap has been achieved: (b) without any interposed supporting struc-

ture (blue markers)38,73,77–79,82–85, for example using a MEMS38;

micropillars75,76,81,88–90 (green markers). A qualitative 1/d2-trend

for experiments at room temperature is also shown with a dashed

line.

NFRHT, one ought to carry out a calorimetric measurement

by applying and maintaining, throughout the measurement, a

temperature gradient between two objects. In 38,81, to achieve

this and measure NFRHT, the temperature of the receiver plate

was maintained constant with a thermoelectric cooler while

a thermoelectric heat pump was used to heat up the emitter.

The receiver’s and emitter’s temperatures were monitored us-

ing thermistors. The heat transferred between the two plates

for a given temperature difference was thus estimated from

the power supplied to the heater. Alternatively, the temper-

ature of the emitter and receiver can be maintained constant

using thermoelectric heat pumps, and the heat transfer can be

estimated directly from the supplied power82.

To measure radiative heat transfer, an additional challenge

is to remove the contributions of heat convection and conduc-

tion. Suppressing convection requires the measurements to be

performed in high vacuum, while suppressing conduction re-

quires minimal physical contact between a hot emitter and a

cold receiver. In all cases, convection and conduction con-

tributions should be subtracted from the total measured heat

transfer75,81.

Some of the alignment and positioning constraints imposed

by the plate-to-plate conﬁguration can be relaxed by replacing

one of the plates with a tip91,92 or a sphere36,67,86,93. Indeed,

initial modern experiments on NFRHT considered sphere-

to-plane conﬁgurations94. Scanning thermal microscopy

(SThM), which employs a tip-to-plane conﬁguration, is one

on the most notable applications of NFRHT as a measurement

technique72,91,95–97. Akin to scanning tunneling microscopy

and atomic force microscopy, SThM probes the surface of a

sample through the near-ﬁeld heat exchange between a heated

tip and the sample’s surface. This conﬁguration provides

access to the integrated heat-ﬂux in the extreme near-ﬁeld

regime, for gap-sizes below 10nm72,92,96,97. For instance, Kit-

tel et al.92 reported SThM measurements of NFRHT from

surfaces of Au or GaN for tip-to-surface distances down to

∼1nm.

B. Theoretical and computational methods

NFRHT is comprehensively described within the frame-

work of ﬂuctuational electrodynamics, as proposed by Rytov

in the 1950s98,99 and reﬁned by Polder and Van Hove in the

1970s20. Within this theory, thermal radiation originates from

thermally excited ﬂuctuating currents obeying the ﬂuctuation-

dissipation theorem100,101. The latter links the currents’ spa-

tial correlation to both the dielectric properties of the medium

emitting photons as well as the temperature. These micro-

scopic ﬂuctuating currents induce an electromagnetic ﬁeld

that transfers thermal energy via radiation and can be calcu-

lated via the macroscopic Maxwell’s equations.

The effect of NFRHT between two- and many-body sys-

tems is, in principle, fully described within the framework of

ﬂuctuational electrodynamics 15,102. Yet, analytical solutions

have been derived only in a few highly symmetric conﬁgu-

rations, involving canonical structures such as spheres69,71,

planes30 and cones68. Solving the RHT problem in com-

plex geometries is theoretically and computationally complex,

requiring advanced numerical approaches. Nevertheless, by

leveraging well-established computational techniques inher-

ited from classical electromagnetic scattering theory103, some

computational methods have been established. These rely on

spectral and ﬁnite element methods, according to the choice

of delocalized or localized functions, respectively, as basis

constituents for the scattering operators15,19,104–107. Methods

include the scattering matrix approach 108–110 as well as sur-

face111–113 and volume114–116 current formulations, including

the thermal discrete-dipole approximation66,117 and the ﬁnite

difference time domain approach118,119.

Finally, recent works have carried out in-depth analyses of

the upper bound limit of NFRHT in various conﬁgurations

27,34,40,41,120–122, demonstrating the important role of both in-

trinsic material properties as well as structural geometry for

maximizing NFRHT.

III. RECENT CONTRIBUTIONS

A. Analytical framework for polariton-mediated NFRHT

In section I, we established that NFRHT is optimal when

evanescent excitations, such as SPPs or SPhPs, are available

to transfer radiative heat across a vacuum gap. Thus, plas-

monic materials and polar dielectrics, respectively, are excel-

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PerspectiveonNear-FieldRadiativeHeatTransferMarianoPascale,1MaximeGiteau,1andGeorgiaT.Papadakis1ICFO-InstitutdeCienciesFotoniques,TheBarcelonaInstituteofScienceandTechnology,Castelldefels(Barcelona)08860,Spain(*Electronicmail:georgia.papadakis@icfo.eu)Althoughnear-eldradiativeheattransferwasintrodu...

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Perspective on Near-Field Radiative Heat Transfer Mariano Pascale1Maxime Giteau1and Georgia T. Papadakis1 ICFO-Institut de Ciencies Fotoniques The Barcelona Institute of Science and Technology Castelldefels Barcelona 08860

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