Nanophotonic control of thermal radiation for energy applications [Invited]

Wei Li; Shanhui Fan

doi:10.1364/OE.26.015995

1. Introduction

Thermal radiation represents a ubiquitous aspect of nature. Any object at finite temperatures emits thermal radiation due to the thermally induced motion of particles and quasiparticles. In Fig. 1, we highlight a few examples of such objects that are important for energy applications: The sun, at the temperature of 6000 K, represents the most important renewable energy resource. Every object that we encounter at everyday life, ranging from an incandescent light bulb where the filaments are heated up to 3000 K, to our own human body at a temperature near 310 K, emits thermal radiation. Therefore, thermal radiation provides radiative access to all heat sources. In addition, from a thermodynamic point of view for energy conversion purposes, a heat sink at low temperature is equally important as a heat source. We note that the universe, at a temperature of 3 K, represents the ultimate heat sink both in terms of its temperature, and its capacity. Moreover, from the earth surface, the coldness of the universe is accessible by thermal radiation through the atmosphere. In our quest to utilize various thermodynamic resources including both heat sources and heat sinks, therefore, the ability to control thermal radiation plays a fundamentally important role.

Fig. 1 Blackbody thermal radiation at temperatures of several important thermodynamic resources: sun at 6000 K, light bulb at 3000 K, human body at 310 K, and the universe at 3 K.

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Conventional thermal emitters have a set of common characteristics. The emitted radiations are typically incoherent, broadband, un-polarized, and the emission pattern is near-isotropic [1,2] [Fig. 2(a)]. Also, they are subject to a set of fundamental constraints [3]. For example, the spectral density of the thermal emission per unit emitter area is upper bounded by the Planck’s law of thermal radiation. In addition, thermal radiators are typically subject to the Kirchhoff’s law, which states that the angular spectral absorptivity and emissivity must be equal to each other. These characteristics and constraints impose strong restrictions on the capabilities for controlling thermal radiation.

Fig. 2 Nanophotonics for thermal radiation control. (a) Conventional thermal radiation is incoherent, broadband, un-polarized and near-isotropic in its directionality. (b)-(f) Nanophotonic structures could exhibit thermal radiation properties that are drastically different from conventional thermal emitters. (b) Nanophotonic structures could have control on coherence, bandwidth, polarization and directionality of thermal radiation. (c) Enhanced far field thermal radiation by thermal extraction. (d) Violation of Kirchhoff’s Law by breaking reciprocity. (e) Dynamic control of thermal radiation with nanophotonic structures. (f) Non-equilibrium and non-linear thermal radiation.

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Over the past 20 years, the development of nanophotonics, which utilizes engineered nanostructures where at least one of the structural features is at a wavelength or sub-wavelength scale, have challenged the conventional view of thermal radiation [4–9]. Nanophotonic structures have shown thermal radiation characteristics that are drastically different from the conventional thermal radiators. In Fig. 2(b)-2(f), we summarize the opportunities that nanophotonics offered for thermal radiation control. For example, nanophotonics structures could have coherent, narrowband, polarized and directional thermal radiation. One can also have enhanced, non-reciprocal, or dynamically tunable thermal radiation. These development of nanophotonic control thermal radiation leads to many exciting opportunities for new energy applications [10–13]. In our recent perspective article, we have highlighted some opportunities with thermal radiation control [14]. Here in this review article, we give a comprehensive overview of using nanophotonics to control the fundamental aspects of thermal radiation, as well as the related energy applications, including daytime radiative cooling, radiative cooling of solar cells, thermal textiles, and thermophotovoltaic systems.

2. Nanophotonics Control of Thermal Radiation

We start by providing a review of nanophotonic structures designed for the purpose of controlling thermal radiation. We will limit largely to the control of far-field thermal radiation, i.e. we will be primarily concerned with the thermal electromagnetic fields generated by these emitters at a distance that at least several wavelengths away from the emitter. Many exciting applications of near-field thermal radiation can be found in reviews such as [15,16].

The key quantities characterizing thermal emitters are the angular spectral absorptivity $α (ω, \hat{n}, \hat{p})$ , and the angular spectral emissivity $e (ω, \hat{n}, \hat{p})$ . The angular spectral absorptivity represents the absorption coefficient of the structure for incident light at a frequency $ω$ and direction $\hat{n}$ with a polarization vector $\hat{p}$ , and is typically measured by taking the ratio between the incident and the absorbed power per unit area. On the other hand, the angular spectral emissivity $e (ω, \hat{n}, \hat{p})$ measures the spectral emission power per unit area at a frequency $ω$ , to a plane wave propagating at the direction $\hat{n}$ , with a polarization vector $\hat{p}$ , normalized against the spectral emission power per unit area of a blackbody emitter at the same frequency to the same direction.

The vast majority of thermal emitters are made of reciprocal materials, i.e. materials characterized by symmetric permittivity and permeability tensors, including isotropic materials that are characterized by a scalar permittivity and permeability. Reciprocal emitters satisfy Kirchhoff’s law, which states that:

α (ω, \hat{n}, \hat{p}) = e (ω, \hat{n}, {\hat{p}}^{*})

Here the asterisk on the polarization vector denotes complex conjugate as required by a time-reversal operation. For such reciprocal thermal emitters, to control its emissivity it is sufficient to consider its absorptivity.

2.1 Spectral Control

In nanophotonic structures where the feature sizes are comparable to the wavelength of light, the wave interference effects lead to numerous possibilities to tailor their spectral responses. One can create structures for which the emissivity is drastically different from that of the underlying materials.

One can strongly enhance the emissivity of a material, with a variety of photonic resonators. A lossy resonator can be used to create a sharp spectral peak in the absorption spectrum. Consequently, such a resonator can be used to create a narrowband thermal emitter. A wide variety of resonant systems have been applied for this purpose. These include, for example, guided resonances in photonic crystal slabs [17–20] [Fig. 3(a) and 3(b)], arrays of metallic antennas [8,21] [Fig. 3(c)], surface plasmons [22], Fabry-Perot cavities [23–25], dielectric microcavities [26], and metamaterials [27,28].

Fig. 3 Nanophotonic structures for achieving narrowband thermal radiation. Each figure shows the emissivity/absorptivity spectrum for the structure shown in the inset. (a) A dielectric photonic crystal (orange region), separated by a vacuum spacing from a flat Tungsten surface (gray region), for the generation of narrowband thermal radiation, taken from [19]. As the size of the spacing increases, the system tunes through the critical coupling regime (blue curves) where the peak emissivity approaches unity. (b) Narrowband thermal emission generated from photonic crystal coupled with multiple quantum well structures, taken from [17]. (c) Gold antenna structures for the generation of narrowband thermal radiation, top: Experimental absorptivity of the single band metamaterial absorber. Bottom: Experimental absorptivity of the dual-band metamaterial absorber. Inset displays SEM images of one unit cell for the fabricated single and dual-band absorbers, taken from [8].

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In understanding the absorption and emission properties of a single resonance, the concept of critical coupling plays a significant role [19,29]. For a single resonance coupling to a single channel of externally incident wave, its absorptivity spectrum from that channel, and as a result its emissivity spectrum to that channel, has a Lorentzian lineshape:

α (ω) = e (ω) = \frac{4 γ_{e} γ_{i}}{{(ω - ω_{0})}^{2} + {(γ_{e} + γ_{i})}^{2}}

where

ω_{0}

is the resonant frequency,

γ_{e}

is the external radiative leakage rate of the resonance to the channel, and

γ_{i}

is the intrinsic loss rate of the resonance due to material absorption. Remarkably, no matter how small the material absorption is, i.e. no matter how small

γ_{i}

is, it is in principle always possible to achieve 100% absorption, at the resonant frequency

ω_{0}

, by satisfying the critical coupling condition:

γ_{e} = γ_{i}

Figure 3(a) illustrates the condition of the critical coupling [19]. The structure consists of a dielectric photonic crystal slab, assumed to be lossless, evanescently coupled to a uniform Tungsten slab which is lossy. As the spacing between the photonic crystal slab and the tungsten slab varies, the intrinsic loss rate $γ_{i}$ of the resonance varies, while the external leakage rate $γ_{e}$ largely remains a constant. The variation of the spacing therefore allows one to tune through the critical coupling point, resulting in narrowband thermal emission with a unity emissivity peak. At critical coupling, the resonance has a total linewidth of $2 γ_{i}$ . We note that at least in principle one can achieve thermal emission with bandwidth that is arbitrarily narrow. In this example, narrower emission linewidth can be achieved by increasing the distance between the slabs, and by adjusting the structural parameters of the photonic crystal slab such that the critical coupling is satisfied.

By utilizing multiple resonances [8,30–40], photonic structures can generate strong thermal emission with multiband or broadband characterstics. For example, one can combine two different resonators to form a bipartite checker board unit cell [8], to get dual-band emissivity [Fig. 3(c)]. One can also use sawtooth structure [30] [Fig. 4(a)], trapezoidal structures [31], or fractal structures [33] [Fig. 4(b)], all of which support multiple resonances, to get broadband response. In addition, an analogue of superradiance can arise in thermal radiation, when multiple resonances with similar resonant frequencies are placed together in a sub-wavelength volume [41]. In general, the understanding of resonances and resonant interactions provide a versatile conceptual framework for engineering thermal emissivity spectrum.

Fig. 4 Nanophotonic structures for achieving broadband enhancement and suppression of thermal radiation. Each figure shows the emissivity/absorptivity spectrum for the structure shown in the inset. (a) A sawtooth anisotropic metamaterial structure for achieving broadband absorption response, taken from [30]. (b) Metamaterial absorber with multiple resonance for achieving broadband absorption response, taken from [33]. (c) Periodic array of air holes in a Tungsten layer for broadband suppression of thermal radiation, taken from [42]. (d) Suppressing and enhancing thermal emission in different wavelength ranges with multi-layer metamaterial, taken from [28].

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Instead of enhancing thermal emissivity, one can also strongly suppress the emissivity of a material, over a range of wavelengths, for example, with the use of a photonic crystal structure that supports a photonic band gap. The gap corresponds to a frequency range where a structure has very little density of states. Within the gap the structure strongly reflects incident light. Such high reflectivity translates into a strongly suppressed thermal emissivity in the band gap. Strong suppression of thermal emissivity has been proposed and demonstrated in dielectric and metallic photonic crystal structures [4,5,43,44]. For example, Yeng et al considered an array of air holes in metal film [Fig. 4(c)]. Each air hole can be considered as a metallic waveguide with a cut-off frequency that is inversely proportional to the diameter of the holes. The array supports a band gap in the frequency range below the cut-off. The resulting structure therefore exhibits a strong suppression of thermal emissivity over a broad frequency range from near zero-frequency to the cut-off frequency [42].

Many nanophotonic structures simultaneously enhance emissivity in some wavelength ranges while suppress emissivity in other wavelength ranges. For example, the photonic crystal structure shown in Fig. 4(c), which suppresses emissivity in the gap as mentioned above, also enhances emissivity at the edge of the photonic bands. One can think of the enhancement as resulting from individual resonances supported by the holes in the metal. Alternatively, one can also construct metamaterial with effective bulk material properties to selectively enhance and suppress thermal radiation at different wavelengths. As an example, metamaterials consisting of alternating sub-wavelength layers of metals and dielectrics have been used to control thermal radiation [27,28,45–47]. Such metamaterials exhibit enhanced thermal emission when the effective dielectric function is in the ellipsoidal regime, and suppressed thermal emission when the effective dielectric function is in the hyperbolic regime [Fig. 4(d)] [31]. The transition wavelength between these two regimes can be controlled by choosing the thickness of the layers appropriately.

2.2 Polarization Control

Many nanophotonic structures have absorption spectra that are strongly polarization dependent. As a result, their thermal emission can be strongly polarized. This is in contrast with a conventional blackbody or gray-body thermal emitter from which the thermal emission is typically un-polarized. In the nanowire antenna as considered in [Fig. 5(a)] [48], for example, due to a mirror symmetry, the wire supports resonances that couple only to either TE polarization with electric field parallel to the wire, or TM polarization with electric field perpendicular to the wire. As a result, on resonance the emission from the wire can be highly polarized. Ingvarsson et al investigated the thermal radiation from individual platinum nano-antennas, which has a rectangular shape. They demonstrated that the properties of the thermal radiation from the antenna [Fig. 5(b)] [49] closely resemble that of a dipole radiator, with the orientation of the dipole strongly correlated with the orientation of nanoantenna. Hence the radiation again can be strongly polarized. Strongly polarized thermal emission can also be realized using grating structures [6], photonic crystal slabs [50] and cavities [51].

Fig. 5 Nanophotonic structures for polarization control of thermal radiation. (a) Linearly polarized thermal emission from SiC antenna, taken from [48]. (b) Thermal radiation signal from a rectangular shape Platinum nanoantenna as a function of polarizer rotating angle. The thermal radiation signal exhibits a dipole like behavior. If the antenna is rotated by 90 degrees the polarization pattern is shifted accordingly. The insets show scanning thermal microscope images of the nanoantenna, taken from [49]. (c) Circularly polarized thermal emission from photonic crystal structures. Thermal emission intensity (T = 300 K) of left-handed (LH) (black solid line) and right-handed (RH) (red dashed line) circularly polarized light at the normal direction, for the layer-by-layer photonic crystal structure (inset) placed on a thick tungsten plate. The blue dashed-dotted line indicates the emission from a blackbody at 300 K, taken from [52]. (d) Estimated degree of circular polarization of thermal infrared radiation emitted by an infrared-absorbing slab capped by the 2D chiral metasurface shown in the insets, taken from [53]. (e) Emission spectrum of a rod array measured at angle of 10 degrees, with a right-handed circular polarizer (red line), and with a left-handed circular polarizer (blue line). Inset displays SEM images of the rod array and a single rod. The orientation of the rods rotates in the array, taken from [54]. (f) Space-variant polarization manipulation of thermal emission: (i) SEM image of spiral sub-wavelength elements with polarization order numbers m = 1, 2, 3, and 4. Thermal emission images emerging from the SiO₂ spiral elements captured through a polarizer (ii) and without a polarizer (iii), for m = 1,2,3,4. The elements were uniformly heated to a temperature of 353 K. The lines indicate the local transverse-magnetic polarization orientation measured in the near-field, taken from [55].

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In addition to the linearly polarized thermal emission as discussed above, nanophotonic structures can also be designed to produce thermal emission that is circularly polarized. Chi et al constructed a chiral photonic crystal structure in a layer-by-layer fashion. The photonic crystal [Fig. 5(c)] exhibits a photonic band gap for one of two circular polarizations but not the other [52]. Within such a polarization-dependent gap, the thermal emission then becomes circularly polarized. Alternatively, it is known that a planar meta-surface structure where the unit cell does not possess any mirror plane symmetry can have a chiral response to electromagnetic field. Thus, one can use such metasurface to achieve strong absorption for only one of the two circular polarization [53,56]. The thermal emission from such meta-surface then become circularly polarized [Fig. 5(d)]. Finally, circularly polarized thermal emission and spin-dependent thermal emission have also been observed in spin-optical metamaterials and metasurfaces [54,57–60]. For example, a thermal antenna array where the orientation of the antenna slowly vary in space [54] [Fig. 5(e)] results in a photon-spin-dependent dispersion relation for the surface waves. The thermal excitation of such surface waves then leads to a circularly polarized thermal emission or spin-dependent thermal emission.

With the use of aperiodic array of thermal antenna structures, optical beams with more complex polarization properties, such as those where the polarization varies across the beam cross-section, can also be generated. As an example, Dahan et al demonstrated space-variant polarization manipulation of thermal emission using a aperiodic SiO₂ gratings where the pitch is at a subwavelength scale [55] [Fig. 5(f)]. By controlling the local orientation of the grating, they experimentally demonstrated thermal emission with an axially symmetric polarization distribution.

2.3 Angular Control

Closely related to the capability for spectral control of the emissivity, one can also tailor the angular or directional properties of the emissivity using nanophotonic structures. Greffet et al, in a pioneering work, demonstrated strong angular dependency of emissivity from a SiC grating structure. The SiC-air interface supports surface phonon-polaritons. The use of grating enables a wavevector-selective resonant excitation of such surface phonon-polaritons, and results in strong angular-dependent absorptivity [6] [Fig. 6(a)]. At a given frequency, unity emissivity is achieved at a specific direction while at other directions the emissivity is strongly suppressed. The angular width of the thermal emission cone from a resonant thermal emitter can also be controlled. Figure 6(b) shows the angle dependent thermal emissivity of a plasmonic metasurface consists of an array of Tungsten (W) disks placed on a silicon nitride (SiN) layer backed a Platinum (Pt) mirror [61]. Such a structure supports gap surface plasmon modes localized in between the two metallic layers. At normal incidence, the mode satisfies the critical coupling condition shown in Eq. (3). Therefore one observes near-unity absorption at ω = 2353 cm⁻¹ [mode i shown in Fig. 6(b)]. This frequency corresponds to a free space wavelength that is smaller than the period. Thus for normal incident light there is no higher diffraction order. On the other hand, as the incident angle increases, higher diffraction order can appear, which provides additional channels for radiation from the modes and hence the critical coupling condition is no longer fulfilled, leading to reduced absorptivity/emissivity at higher angle. Therefore, one can control the angular width of the emitter by changing the periodicity of the structure.

Fig. 6 Beaming of thermal radiation: direction control and thermal focusing. (a) Directional thermal radiation from SiC grating, taken from [6]. (b) Angle dependent thermal emission from a plasmonic metasurface: Direct measurement of the emissivity at 600 °C as a function of the frequency and the angle of the W/SiN/Pt metasurface. The emissivity peak is located at ω = 2353 cm⁻¹ and between 0° and 26°, taken from [61]. (c) Directional thermal emission from bull’s eye structure, taken from [63]. (d) Focusing of thermal radiation from a nanostructured SiC metasurface, taken from [68].

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Highly directional thermal beaming has also been proposed and demonstrated using other photonic structures such as bull’s eye structures [Fig. 6(c)] [62,63], a tungsten grating structure [64], and photonic crystal [7,65]. In addition, photonic structures that have been designed to achieve strong angular response, such as multilayer coating [66], or angular coupler [67], may also be combined with a thermal emitter to produce strong angular-selective thermal emission.

Benefitting from the recent advances in metasurface, which enable wave front control by manipulating the phase and amplitude responses of each element in an ultra-thin optical antenna array [69], one can construct metasurface to manipulate the wave front of thermal emission [57–60,68,70] as well. Chalabi et al [68] proposed thermal focusing from a SiC metasurface [Fig. 6(d)]. The idea is to design nanostructures on SiC surface to scatter thermally generated surface waves. To enable focusing, the size, shape, and spacing of the scattering elements on the surface are carefully chosen to obtain constructive interference of the scattered waves at a focal point of interest. With the degrees of freedom offered by metasurfaces, significant flexibility in thermal emission control can be achieved.

Both the spectral and angular control of thermal emission changes the coherent properties of thermal emitters. A narrowband thermal emitter results in enhanced temporal coherence, and a directional thermal emitter results in enhanced spatial coherence, as compared to the standard blackbody radiator.

2.4 Beyond Planck’s Law and Kirchhoff’s Law: Thermal Extraction and Non-reciprocal thermal radiation

Since the absorptivity $α (ω, \hat{n}) \leq 1$ , it follows from Eq. (1) that the emissivity $e (ω, \hat{n}) \leq 1$ . Since the ideal blackbody has an emissivity of $e (ω, \hat{n}) = 1$ , it follows that when directly emitting into free space, a thermal emitter with an area $A$ cannot emit more than a corresponding blackbody emitter with the same area. When integrated over all emission angles $\hat{n}$ , the spectral density of the total emission power $P$ of the emitter with an area $A$ must satisfy

P = e (ω, \hat{n}) \cdot P_{0} \leq P_{0} = A \cdot \frac{ω^{2}}{4 π^{2} c^{2}} \cdot \frac{ℏ ω}{e^{ℏ ω / K_{B} T} - 1}

Here

ω

is the angular frequency of the emission.

ℏ

and

K_{B}

are the reduced Planck constant, and the Boltzmann constant, respectively.

T

represents the temperature of the emitter.

c

is the speed of light in vacuum. The formula for

P_{0}

in Eq. (4), which describes the emission power of a blackbody emitter, is Planck’s radiation law.

We note that when using Eq. (4) to determine the upper bound of thermal emission power, the area A in fact needs to be taken as the absorption cross-section rather than the geometrical cross-section of the emitter. For an emitter with a macroscopic emitting area [Fig. 7(a)], when it is directly surrounded by vacuum, its absorption cross-section cannot significantly exceed its geometrical cross-section. As a result, the overall emission cannot exceed the constraint set by the Planck’s radiation law, independent of the internal structure within the emitter [71]. This result has been explicitly demonstrated numerically in a direct calculation of thermal emission from a photonic crystal using the formalism of fluctuational electrodynamics. The computed thermal emission of the photonic crystal falls below what is required by Planck’s law in spite of the significant modification of the density of states within the structure [72].

Fig. 7 Beyond Planck’s Law and Kirchhoff’s Law: thermal extraction and non-reciprocal thermal radiation. (a)-(b) Enhancing far-field thermal radiation by thermal extraction. (a) Far field thermal radiation of a macroscopic thermal emitter cannot exceed the blackbody thermal emission with the same emitter area. (b) With thermal extraction, far field thermal radiation of a macroscopic thermal emitter can significantly exceed the blackbody thermal emission with the same emitter area. The thermal radiation of (a) is plotted as dashed line for reference. (c),(d) Non-reciprocal thermal radiation. Energy flow diagram of (c) a reciprocal thermal emitter, and (d) a non-reciprocal thermal emitter. The thermal emitter interacts with two blackbodies A and B, respectively. The emitter and the blackbodies are at the same temperature T.

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However, when the blackbody emitter is placed in a transparent dielectric medium with a refractive index of $n$ , in Eq. (4), the speed of light $c$ needs to be replaced by $c / n$ , and hence the total emission is enhanced by a factor of $n^{2}$ [Fig. 7(b)]. Exploiting this fact, Yu et al developed a thermal extraction scheme that results in a far-field thermal emission from a macroscopic thermal emitter exceeding the blackbody emission with same emitter area, by placing the emitter in near-field radiative contact with a transparent semispherical dome [73]. The dome is made of ZnSe with a refractive index of 2.4 and as a result the total emission into the dome can be much larger than the emission into vacuum. The area of the dome is chosen to be significantly larger than the physical area of the emitter to ensure that all power emitted into the dome can be extracted to far field. In [74], Simovski et al further explored this thermal extraction scheme by using hyperbolic metamaterials to significantly enhance the far field thermal radiation.

As discussed in the beginning of Section 2, Kirchhoff’s law also plays a very significant role in understanding thermal radiation. However, it is important to note that Kirchhoff’s law is not the requirement of the Second Law of Thermodynamics, but rather arises from reciprocity. The second law requirement on the relation between absorptivity and emissivity can be understood by considering the energy balance of a thermal emitter interacting with two blackbodies, A and B, in both reciprocal [Fig. 7(c)] and non-reciprocal [Fig. 7(d)] cases, at thermal equilibrium [75]. The emitter absorbs part of the emission from blackbody A and B, as described by absorptivities $α_{A}$ and $α_{B}$ , respectively. The emitter also emits towards the blackbody A and B, as described by emissivities $e_{A}$ and $e_{B}$ , respectively. When the emitter, and the blackbodies, are at the same temperature T, the second law of thermodynamics then requires zero net energy flow in or out of the emitter, independent of whether or not the emitter is reciprocal. In the reciprocal case [Fig. 7(c)], $e_{A, B} = α_{A, B}$ , and as a result the second law of thermodynamics is satisfied.

In the more general case when reciprocity is not enforced [Fig. 7(d)], the emission from blackbody A is either absorbed by the emitter, with absorptivity $α_{A}$ , or reflected to blackbody B, with a reflectivity $r_{A \to B}$ . We thus have

α_{A} + r_{A \to B} = 1

On the other hand, in the absorption process, blackbody A receives emission from both the emitter and the part of emission from blackbody B that is not absorbed by the emitter. We have

e_{A} + r_{B \to A} = 1

Combining Eqs. (5) and (6) and similarly considering the energy balance of the blackbody B, we have

e_{A} - α_{A} = r_{A \to B} - r_{B \to A} = α_{B} - e_{B}

For nonreciprocal systems,

r_{A \to B} \neq r_{B \to A}

. As a result,

e_{A, B} \neq α_{A, B}

. Therefore the Second Law of Thermodynamics is satisfied but the Kirchoff’s law is violated.

The ability to break Kirchhoff’s law is of fundamental importance in thermal radiation harvesting. For example, to convert solar radiation to electricity one would need to design an efficient solar absorber. However, by Kirchhoff’s law, an efficient absorber will be also an efficient emitter. Thus such an absorber must radiate part of the energy back to the sun, which represents an intrinsic loss mechanism. It is in fact known that the Landsberg limit [76], which represents the upper limit of the efficiency for solar energy harvesting, can only be achieved with the use of non-reciprocal systems [77,78].

While the possibility for breaking Kirchhoff’s law is known, earlier works showed only a very small difference in the angular spectral absorptivity and emissivity [79]. Recently, Zhu et al numerically proposed a design based on magneto-optical photonic crystals, where near-complete violation of the Kirchhoff’s law was achieved [75]. For a given frequency and angle of incidence, the spectral angular absorptivity can reach unity, while the corresponding emissivity vanishes.

Since Kirchhoff’s law is not applicable for non-reciprocal systems, it is useful to relate absorption and emission in a more generalized situation. Miller et al described thermal radiation on a basis of orthogonal modes, and derived a generalized form of the Kirchhoff’s law that is applicable for both reciprocal and non-reciprocal systems [80].

2.5 From Static to Dynamic: active control of thermal radiation

So far, we have primarily focused on static thermal emitters. For many applications it would be useful to develop dynamic thermal emitters where the emission intensity can be modulated as a function of time. The conventional mechanism to modulate emission intensity is to adjust the temperature T of the thermal emitter. However, adjusting the temperature usually requires a significant amount of energy input especially for larger emitters. Moreover, the modulation rate with such a mechanism is limited by the heat exchange rate of the emitter and its surroundings which controls the thermal time constant of the emitter. On the other hand, based on Eq. (4), the spectral density of the total emission power $P$ of the emitter is also a function of emissivity $e (ω, \hat{n})$ . Therefore, to control emission intensity one can instead modulate the emissivity. In such a case, the energy input and the modulation rate are no longer limited by the heat capacity and the thermal time constant of the emitters. In recent years there have been significant efforts seeking to modulate emissivity. Below we highlight a few examples.

One way to actively control thermal emissivity is by modulating the material properties. For example, one can modify the material properties by changing the carrier densities in the materials. For typical dielectrics and metals, the frequency dependent material dielectric function $\tilde{ε_{r}} (ω)$ can be described by the Lorentz-Drude model:

\tilde{ε_{r}} (ω) = \tilde{ε_{r}} (\infty) + \frac{N q^{2}}{ε_{0} m_{e}} \sum_{m = 1}^{M} \frac{f_{m}}{ω_{0, m}^{2} - ω^{2} + j ω Γ_{m}}

where

\tilde{ε_{r}} (\infty)

is the permittivity at infinite frequency,

N

is the carrier density,

q

is the electron charge,

ε_{0}

is the vacuum permittivity,

m_{e}

is the electron mass.

f_{m}

,

ω_{0, m}

and

Γ_{m}

are the oscillator strength, resonance frequency and damping coefficient of each oscillator, respectively. Based on Eq. (8), the dielectric function is dependent on the carrier density

N

. Therefore, one can change the material dielectric function and consequently the emissivity by changing carrier density, for example in semiconductors by electrical carrier injection. For many materials, the amount of dielectric constant variation due to carrier injection is relatively modest. Thus for bulk materials, such an emissivity change due to carrier injection is usually small. However, with carefully designed resonant nanophotonic structures, such a carrier induced emissivity change could be greatly amplified.

Brar et al. demonstrated electrically modulated thermal emissivity using graphene plasmonic resonators on a silicon nitride substrate [81] [Fig. 8(a)]. The graphene resonators produce narrow spectral emission peaks in the mid-infrared due to its plasmonic resonances. The frequency and intensity of these spectral peaks can be modulated, by varying the voltage of an electrostatic gate which controls the carrier density in the graphene resonators. Inoue et al. demonstrated electronically controlled thermal emissivity by coupling quantum wells with a photonic crystal cavity. Their structure emits in the mid-infrared due to intersubband transition in quantum wells. The absorption spectrum and strength of such transition can be modulated by varying externally applied voltage. The variations in the material absorption properties then translate into a significant variation of the thermal emissivity through the resonant enhancement effects provided by the photonic crystal cavity [82] [Fig. 8(b)]. In such a structure emissivity can be varied from 0.74 to 0.24, with a modulation speed exceeding 1MHz, which is four to five orders of magnitude faster than the speed at which conventional thermal emitters can be modulated. Coppens et al. demonstrated optically controlled thermal emissivity on ZnO based metamaterials [83]. The modulation is based on carrier generation in ZnO induced by ultra-violet light. Due to the flexibility in controlling spatially and temporal profile of the UV excitation, a spatial and temporal emissivity control can be achieved in such a system.

Fig. 8 Dynamic modulation of thermal emission. (a) Tunable thermal emission by electrical modulation of carrier density in an array of graphene resonators, taken from [81]. (b) Tunable narrowband thermal emission by electrical modulation of carrier density in a photonic crystal slab incorporating GaAs/n-AlGaAs quantum wells, taken from [82]. (c) Tunable thermal emission from a MEMS metamaterial perfect absorber structure. The modulation is achieved by changing the gap distance between the top resonators and the bottom metal plane, taken from [84]. (d) Negative differential thermal emission, realized by using phase change material VO₂. As the temperature increases, the material undergoes a phase change, resulting in the decrease of the spectral radiance. Taken from [85]. (e) Super-Stephan-Boltzman increase of thermal emission using phase change materials GST, taken from [86].

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Another way to actively control the emissivity is to control the geometry of nanophotonic structure without changing the material properties [84,87,88]. Liu et al demonstrate active control of emissivity by integrating microelectromechanical system (MEMS) with a metamaterial absorber structure [Fig. 8(c)] [84]. The structure consists of top free-standing resonators and a bottom metallic ground plane, with the gap in between. The gap size can be controlled by the electrostatic force induced by the applied bias. Variation of the gap sizes tunes the coupling of the electric and magnetic resonances in the structure and hence modulates its emissivity. This concept can be used to construct a surface with individually reconfigurable MEMS metamaterial pixels, realizing an emitter array capable of displaying thermal infrared patterns with a modulation rate up to 110 kHz.

An emerging direction for the active control of thermal radiation is through the use of phase change materials [85,86,89–93]. Phase change materials such as vanadium dioxide (VO₂) and Ge₂Sb₂Te₅ (GST) can be switched between two material states with significantly different optical properties, as the temperature passes the transition point. By incorporating phase change materials into thermal emitter designs, Kats et al demonstrated a VO₂ based thermal emitter [Fig. 8(d)] which has reduced emissivity at higher temperature (100 °C) as compared to a lower temperature (74.5 °C). As a result, the total emission intensity decreases as the temperature increases and a negative differential thermal emittance is observed [85]. This is in contrast with blackbody emitters where the total emission intensity varies as T⁴, where T is the temperature of the emitter. Alternatively, one can also construct thermal emitters with emissivity increases at higher temperature, therefore exhibiting super Stefan-Boltzmann relation [Fig. 8(e)] [86,90]. Other interesting observations include the demonstration of radiative thermal runaway based on negative differential thermal emittance [91], the demonstration of zero-differential thermal emittance using samarium nickelate [92], and the proposal of a thermal homeostasis device based on VO₂ [93].

2.6 Non-equilibrium and non-linear thermal radiation

Most existing works on controlling of thermal radiation focuses on systems at local equilibrium or consisting of linear medium. The use of non-equilibrium or nonlinear systems offer new opportunities. For example, in a semiconductor under external electrical bias or optical excitation, the electrons and the holes can have different quasi-fermi levels. The photons emitted from such semiconductors then have a non-zero chemical potential $μ_{γ}$ that is equal to the quasi-Fermi level separation between the electrons and holes, and hence has a spectral energy density $ρ (ω)$ of the form [94–96].

ρ (ω) = \frac{ω^{2}}{π^{2} c^{3}} \cdot \frac{ℏ ω}{e^{(ℏ ω - μ_{γ}) / K_{B} T} - 1}

Equation (9) is valid for photon states with

ℏ ω - μ_{γ} > K_{B} T

. The effect of chemical potential on thermal radiation spectra is illustrated in Fig. 9(b). The Planck distribution is recovered at

μ_{γ} = 0

. At the same emitter temperature, photons with a positive or negative chemical potential has higher or lower energy spectral density for every frequency

ω

respectively. This phenomena can be utilized to realize electroluminescence cooling devices [97–102]. Recently, Greffet et al developed a local form of Kirchhoff’s Law associated with non-equilibrium thermal radiation [103]. In general, the combination of nanophotonic thermal radiation control and active semiconductor devices may enable manipulation of heat using optoelectronic technology.

Fig. 9 Non-equilibrium and non-linear thermal emission. (a) A schematic energy diagram for electrons in a semiconductor. The separation of quasi-Fermi levels for electrons η_c and holes η_v, result in emission of photons carrying positive chemical potential μ_γ = η_c - η_v. (b) Modification of Planck spectra (blue) upon positive (red) and negative (black) chemical potential for a blackbody at a temperature of 300 K. (c) Peak emissivity ε_max of a cavity coupled to an external bath, both at temperature T, as a function of nonlinear coupling |ζ| = |α|k_BTγ_e/γ², for different ratios of the linear dissipation γ_e and external coupling γ_d rates. The inset shows the emissivity ε(ω) for γ_e = γ_d, corresponding to a cavity with perfect linear emissivity, for multiple values of ζ, taken from [104]. (d) Peak (on-resonance) spectral transfer function Φ_max ≡ Φ(ω₀) normalized by the blackbody Φ_BB as a function of nonlinear coupling |ζ| = |α|k_BTγ_e/γ², for a system consisting of a cavity at temperature T_d coupled to an external bath at T_e = 0, for multiple configurations of γ_e/γ_d and Re α/Im α at T = T_d. The inset shows a cavity design supporting a mode at λ ≈2.09 μm with lifetime Q ≈10⁸ and modal volume V ≈0.8(λ/n)³, along with its corresponding H_z and E_y field profiles, taken from [104].

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In typical thermal emitters, the intensity of light is sufficiently low such that the material can be assumed to be in the linear regime. However, resonant nanophotonic structures can exhibit strong nonlinear optical effects and therefore could have interesting thermal radiation properties different from linear medium [104–107]. For example, Khandekar et al. developed a nonlinear fluctuation-dissipation theorem and studied thermal radiation effects in nonlinear χ⁽³⁾ photonic crystal cavities [104]. They showed that the presence of nonlinear coupling in such a photonic crystal cavity can modify the critical coupling condition as described by Eq. (3) and also significantly alter the spectral lineshape of the emissivity, resulting in asymmetric and non-Lorentzian lineshapes [Fig. 9(c)]. In addition, the emission from such a nonlinear cavity can also exceed that of a corresponding linear blackbody at the same temperature [Fig. 9(d)].

3. Energy applications

The fundamental advances in controlling thermal radiation have led to many new energy applications. In this section, we will discuss a few of such examples, including demonstrations of daytime radiative cooling [11], thermal textile for human body local thermal management [13], thermophotovolatic system [10] and thermophotonics [108] system. All these applications make extensive use of the fundamental capabilities of nanophotonic structures as discussed in Section 2 to tailor various properties of thermal radiation, especially the spectral and angular aspects. Since energy applications often require large-scale deployment, many of the examples shown here utilize structures, such as multilayer films or nanoporous materials, which are more amenable to large-scale fabrication. We expect that as large-scale lithographic approaches are developed, many of the lithographically-defined structures discussed in Section 2 may find use in these applications as well.

3.1 Daytime radiative cooling

The motivation of radiative cooling is to seek to exploit the coldness of the universe as a thermodynamic resource [Fig. 10(a)]. The universe, at a temperature of 3 K, represents the ultimate heat sink both in terms of its temperature and its capacity. Moreover, the earth atmosphere is highly transparent in the wavelength range of 8 – 13 μm. This transparency window coincides with the peak of blackbody radiation spectrum at typical ambient temperature near 300 K. Thus, any object on earth, given sky access, can radiate heat out to the universe and thus lower its temperature. Such a cooling effect is readily observed at night and has been known for centuries [109–111].

Fig. 10 Daytime radiative cooling (a) Major thermodynamic resources around the earth. (b) To achieve daytime radiative cooling, one needs to create a structure that achieves broadband reflection of sunlight and strong thermal emission in the transparency window of the atmosphere. (c) A multi-layer structure made of HfO₂ and SiO₂ deposited a silver mirror on top of a silicon wafer. The structure has a strong solar reflection and selective thermal emission in 8-13 μm, and functions as a daytime radiative cooler. (d) Roof-top measurement setup. (e) The blue curve shows the temperature of the radiative cooler structure as shown in (c), when placed in the setup as shown in (d). The cooler reaches a temperature of 5 °C below the ambient air, under direct peak sunlight, taken from [11].

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For cooling purposes, however, it would be more interesting to operate during the daytime under direct sunlight when typical objects become hot. For this purpose then, one will need a structure that reflects the entire solar spectrum, while generates strong thermal radiation at the wavelength range of 8-13 μm [Fig. 10(b)]. The first theoretical design for a photonic structure of such a spectrum was reported in [112]. Raman et al have designed and fabricated a multi-layer photonic structure, which consists of seven dielectric layers deposited on top of a silver mirror [Fig. 10(c)] [11]. These layers are designed using a systematic optimization process taking into account fabrication constraints. The top three layers, with thickness on the order of hundreds of nanometers, are responsible generating strong thermal radiation. The bottom four layers, with thicknesses on the order of tens of nanometers, are used to enhance the reflectivity of silver mirror especially in the ultra-violet wavelength range. This sample, when placed in a roof-top measurement setup [Fig. 10(d)], was able to reach a temperature that is 5 °C below the ambient air temperature, in spite of having about 900 W/m² of sunlight directly impinging upon it [Fig. 10(e)].

Daytime radiative cooling have subsequently been considered in various material systems and structures [113,114,116–120]. In [113], Hossain et al reported a design of a selective emitter with near unity emissivity in the 8-13 μm wavelength range, using an array of pillars each consisting of multilayers of Al and Ge forming a meta-material [Fig. 11(a)]. Radiative cooling has also been demonstrated in [114] with a SiO₂ layer as the emitter backed by a silver mirror, with a polydimethylsiloxane (PDMS) layer on top of the SiO₂ layer to further enhance the emissivity in the atmospheric transparency window [Fig. 11(b)]. As an important step towards large-scale deployment, In [115], Zhai et al reported the fabrication of a large-area metamaterial structure consists of silica sphere in a polymer matrix designed for radiative cooling purposes [115] [Fig. 11(c)]. There is also an intriguing observation of the possibility of daytime radiative cooling in silver ants that live in deserts [116] [Fig. 11(d)].

Fig. 11 Nanophotonic structures for daytime radiative cooling (a) Metal–dielectric conical metamaterial pillars with alternating layers of aluminum and germanium for selective emission in 8-13 μm, taken from [113]. (b) Schematic (left) and photo (right) of photonic radiative cooler made of 500 μm fused silica wafer with a 100 μm thick polydimethylsiloxane (PDMS) film on top and 120 nm thick silver film as a back reflector, taken from [114]. (c) Photo (top) and schematic (bottom) of large scale photonic radiative cooler containing micrometer-sized SiO₂ spheres randomly distributed in the matrix material of polymethylpentene, taken from [115]. (d) Radiative cooling photonic structures from silver ants, taken from [116].

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For experimental demonstration, and eventual applications of radiative cooling technology, it is important to combine the photonic design with thermal considerations that minimizes the parasitic heat gain of the cooler and enables the delivery of the cooling effect to where it is needed, such as inside the building [11]. Chen et al integrated radiative coolers with a vacuum system that eliminates most of the parasitic heat loss, and demonstrated passive cooling to a temperature that is far below freezing [118] [Fig. 12(a) and 12(b)]. Goldstein et al demonstrated the integration of radiative coolers into air-conditioning systems to perform sub-ambient non-evaporative fluid cooling [119] [Fig. 12(c)-12(e)], which represented an important step forward in deliver coolness obtained from radiative cooling into inside a modern building that tends to be well insulated thermally.

Fig. 12 Packaging system for daytime radiative cooling. (a),(b) Schematic and photos of a vacuum system for reaching deep sub-freezing temperatures by minimizing non-radiative heat loss, taken from [118]. (c)-(e) Schematics and photo of fluid cooling panel system for sub-ambient non-evaporative fluid cooling, taken from [119].

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3.2 Radiative cooling on solar cells

The concepts of daytime radiative cooling can also be generalized towards cooling of solar cell [121–123]. The heating of the solar cell has adverse consequences on both its performance and reliability [124]. It is therefore of interest to explore a strategy for passive cooling of solar cell and solar panel. For this purpose, one can consider placing a cooling layer on top of solar panel. The cooling layer is used to modify the absorptivity and emissivity of the entire solar cell stack for cooling purposes. Ideally, such a layer should have the following characteristics [121]: (1) It should have unity emissivity over the entire thermal radiation wavelength to maximize radiative cooling [106]. Here since the solar cell operates at a temperature above ambient, the entire thermal wavelength range can be used for radiative cooling purposes. This is in contrast with the case considered in Section 3.1, where, to reach sub-ambient temperature for the radiative cooler, it is important to use a selective emitter with strong emission only in the transparency window of the atmosphere. (2) It should have perfect transmission in the solar wavelength range above the solar cell band gap so that it does not interfere with the operation of the solar cells. (3) It should also have perfect reflection below the band gap to suppress the sub band gap parasitic solar absorption. These characteristics is schematically summarized in Fig. 13(a) [121]. A theoretical study shows that a multi-layer photonic coating designed to have the three characteristics as outlined above can reduce the operating temperature temperatures of an encapsulated silicon solar cell by 5.7 °C [121]. Experimentally, Zhu et al placed a silica photonic crystal on top a silicon wafer, and showed that under direct sunlight the use of such a photonic crystal can reduce the temperature of the silicon wafer by 13 °C, as compared to a bare silicon wafer, while actually enhances the absorption of sunlight in the silicon. A reduction of the silicon cell temperature by 10 °C can improve the cell efficiency by around 1% [125], and increase cell lifetime by a factor of 2 [126]. The development of radiative cooling technique therefore has a potential to positively impact both the efficiency and the cost of the solar cells.

Fig. 13 Radiative cooling of solar cells. (a) Three design considerations for a cooling layer placed on top of a solar cell: In solar wavelength range, perfect transmission above solar cell bandgap, perfect reflection below bandgap, and perfect thermal emission in the thermal wavelength, taken from [121]. (b) A photonic crystal structure made of silica, which is transparent in the solar wavelength range, and has near-unity thermal emissivity in the thermal wavelength rage, taken from [122]. (c) Experimental demonstration of cooling effect when the structure in b is placed on top of a silicon solar absorbers, taken from [122].

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3.3 Thermal radiative textile

Another emerging application of nanophotonic controlled thermal radiation is to develop thermal textiles for personal thermal management [13,127–134]. In contrast to conventional indoor thermal management where the air conditioning system cools the entire building, the idea of personal thermal management is to provide heating or cooling only to a human body and its local environment, which has the potential to significantly reduce the energy consumption for air conditioning. For a typical indoor scenario, thermal radiation heat dissipation from human skin (emissivity ≈0.98) contributes to over half of the total body heat loss [Fig. 14(a)] [127]. Therefore, designing thermal radiative textile to control radiative heat dissipation from human body offers an important avenue for personal thermal management. One can design textile to be infrared transparent to fully dissipate human body radiation for cooling purpose, or to be infrared reflective for heating purpose [Fig. 14(b)]. In both cases, the textiles need to be opaque in the visible spectrum. Achieving such spectrum for either cooling or heating purposes is difficult with conventional textiles. Thus, recent efforts have sought to achieve these spectral properties by introducing suitable nanostructures into textiles [13,127–132].

Fig. 14 Nanophotonic thermal textile for personal thermal management. (a) Schematic of heat dissipation pathways from a clothed human body to the ambient environment. Thermal radiation contributes to a significant part of total heat dissipation, in addition to heat conduction, and heat convection, taken from [127]. (b) Ideal spectrum for thermal textile for cooling (top) and heating (bottom) purposes. (c) Measured infrared transmittance of nanoporous polyethylene, normal polyethylene, and cotton. The nanoporous polyethylene is as transparent as normal polyethylene. Cotton, on the other hand, is completely opaque, taken from [13]. (d) Measured infrared reflectance of the metallic coating side of nano-Ag/PE, compared with existing textile materials including cotton, Mylar blanket and Omni-Heat, taken from [131].

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For cooling purposes, Tong et al theoretically designed an infrared transparent visibly opaque fabric using synthetic polyethylene fibers with an intrinsically low infrared absorption. These fibers were designed to minimize infrared reflection via weak Rayleigh scattering while maintaining visible opaqueness via strong Mie scattering [127]. Hsu et al experimentally demonstrated a cooling textile based on nanoporous polyethylene [Fig. 14(c)] [13]. The nanoporous polyethylene has interconnected pores with sizes comparable with visible light, which scatter visible light strongly and make the textile opaque to human eyes, while maintain the infrared transparency of polyethylene.

For heating purposes, Cai et al developed nanoporous Ag textiles with strong reflectivity in the inner surface to reflect human body thermal radiation, and strongly suppressed thermal emissivity of the outer surface to minimize the radiative heat loss from the textile [Fig. 14(d)] [131]. In addition to thermal radiative considerations, significant efforts have been made to satisfy the wearability consideration such as water-wicking rate and air permeability in these nanophotonic structured thermal textile in order for such textiles for be adopted in practical applications [13,131,132].

3.4 Solar Thermophotovoltaic (STPV) and Thermophotovoltaic (TPV) System

When harvesting the thermal radiation energy from the sun at 6000K, the efficiency of a single junction solar cell is subject to the Shockley–Queisser limit and cannot exceed 41% [135]. The Shockley-Queisser limit arises from a fundamental mismatch between the broadband solar radiation and the optoelectronic properties of semiconductors: photons with energy below the semiconductor bandgap cannot be used to generate electricity; photons with energy above the bandgap can only contribute part of its energy to electricity, since the photon-generated carriers must first relax to semiconductor band edges. As one of the important approaches for overcoming the Shockley-Queisser limit, in 1979 Richard Swanson introduced the concept of solar thermophotovoltaic (STPV) systems [136], in which an intermediate element is placed between the sunlight and the solar cell [Fig. 15(a)] [25,137]. The intermediate element includes an absorber that can absorb the entire solar spectrum and get heat up, as well as an emitter that can generate narrowband thermal radiation tailored to the bandgap of the solar cell. Using a single-junction cell and considering the solar radiation incident on the STPV system is the same as assumed in the Shockley–Queisser analysis, an ideal intermediate element could boost the overall system efficiency to 85%, more than double the Shockley–Queisser limit [138].

Fig. 15 Solar thermophotovolatic systems. (a) A schematic shows the general concept of STPV system. Between the sun and the photovoltaic cell, an intermediate material absorbs the sunlight, heats up and generates narrowband thermal radiation that matches the band gap of photovoltaic cell, taken from [25]. (b) A nanophotonic narrowband thermal emitter made of a tungsten slab with Si/SiO₂ multilayer stack. The black curve is the emissivity of the emitter structure at normal incidence (θ = 0). The dashed black curve is the emissivity at normal incidence of a tungsten crossed grating structure. The red curve is the scaled spectral radiance of a 2000 K blackbody, taken from [25]. (c) Experimental realization of a solar thermophotovoltaic system. The system consists of broadband absorber, narrowband emitter and a InGaAsSb cell, taken from [10]. (d) Top panel: Internal quantum efficiency (IQE) spectrum of the InGaAsSb photovoltaic cell and the emissivity spectrum of the emitter. Bottom panel: structure of the photonic crystal emitter, taken from [10]. (e) Conversion efficiency η_tη_tpv as a function of solar irradiance H_s. Contributions to η_tη_tpv relative to a greybody absorber–emitter: MWNT–1D PhC absorber–emitter (twofold improvement) and area ratio optimization (additional twofold improvement). Efficiencies approaching 20% were predicted with a scaled-up (10 × 10 cm²) STPV system utilizing a high-quality 0.55 eV photovoltaic module with a sub-bandgap reflector, taken from [10].

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Motivated by the substantial potential for efficiency improvement in solar thermophotovoltaic systems, significant theoretical and experimental efforts have been devoted to the study of using various nanophotonic structures as the intermediate element in such systems [25,43,139–144]. For example, Rephaeli et al proposed absorber and emitter designs for STPV systems [25]. The absorber, consisting of an array of tungsten pyramids, has near-unity absorptivity over all for the entire solar spectrum with wavelength up to 2 μm, and moreover has low thermal emissivity in the longer wavelength range, which is important for maximizing the temperature of the absorber under sunlight. The emitter, made of a tungsten slab with Si/SiO₂ multilayer stack, provides a sharp emissivity peak at the solar cell band gap while suppressing emission below the band gap [Fig. 15(b)]. Such a system is predicted to reach a maximum efficiency of ~50% at emitter temperature of 2130 K. On the other hand, nanophotonic structures that can sustain in high temperatures have been developed for practical implementation in STPV systems [43,141–143,145].

Significant progresses have also been made in experimental demonstration of STPV system [10,146]. In Lenert et al [10] ‘s experiment in 2014 [Fig. 15(c)], the absorber is made of vertically aligned multi-walled carbon nanotubes. The emitter is made of one-dimensional Si/SiO₂ photonic crystal. The thicknesses of Si and SiO₂ layers are optimized to provide a cut-off in the thermal emission right at the bandgap of the InGaAsSb photovoltaic cell, strongly suppressing sub-bandgap thermal radiation [Fig. 15(d)]. The absorber, emitter and the photovoltaic cells are integrated in a vacuum environment to minimize parasite heat loss due to convection and conduction. The resulting system demonstrates a solar-to-electricity efficiency of 3.2% [Fig. 15(e)]. In 2016, Bierman et al [146] demonstrated significantly improved solar-to-electricity efficiency of 6.8% through the suppression of 80% of unconvertible photons by pairing a one-dimensional photonic crystal selective emitter with a tandem plasma–interference optical filter.

Closely related to the concept of solar thermophotovolatic system, there are also efforts for developing nanophotonic structures for thermophotovolatic systems, which are designed to generate electricity from a wider range of heat sources [43,139,147–149]. Thermophotovoltaic systems are important for applications such as waste heat recovery and portable fuel-to-electricity conversion. For example, Chan et al [150] demonstrated combustion driven thermophotovoltaic system for portable fuel-to-electricity conversion applications, based on high temperature Tantalum Tungsten alloy photonic crystals [151].

3.5 Thermophotonics (TPX) System

In a thermophotovoltaic system, the emitter is at maintained at thermal equilibrium. The concept of thermophotonics (TPX) [108], proposed by Martin Green, seeks to improve upon the thermophotovoltaic system by replacing the emitter with a light emitting diode under external bias. As noted in Section 2.6, the emitted photons from a light emitting diode possesses a non-zero chemical potential. Under forward bias, the luminescence from a light emitting diode is significantly enhanced by the applied voltage V, as compared with a blackbody emitter at the same temperature. And moreover the emission from a light emitting diode is strongly peaked at the semiconductor band gaps. Both aspects are useful for increasing the efficiency and the electric power density of the photovoltaic cell. The voltage on the light emitting diode can be provided by recovering part of the voltage generated by the photovoltaic cell. Theoretically, it is shown that TPX system can potentially realize solar/heat-to-electrical energy conversion system with both efficiency and power density higher than TPV system [108]. And unlike TPV system where the emitted photon energy and power density is determined by the emitter temperature, TPX system has been theoretically shown to work at much lower temperature than TPV, for example 500-600K [Fig. 16(b) and 16(c)] [152,153], leading to potential applications such as low-grade waste heat recovery. There has not been, however, an experimental demonstration of a high-efficiency TPX system. One of the challenges is to achieve highly efficient LED emitters at elevated working temperatures [154,155].

Fig. 16 TPX system for power generation and cooling. (a) A schematic showing the concept of TPX system, taken from [108]. An emitter diode with an applied external bias is on the heat source side. And a PV cell is on the heat sink side. The electroluminescence from the LED is absorbed by the PV cell for generating electricity. (b),(c) Theoretically calculated efficiency and power generation of TPX system as a function of bias/bandgap ratio, at an emitter temperature of 600K, taken from [152]. (d) A TPX system works as a solid-state refrigerator, taken from [156]. In this case, the GaAs LED is on the cold side for cooling purpose. The generated electricity from Si PV cell is resupplied to drive the LED. (e), (f) Cooling power density and coefficient of performance (COP) of the device shown in (d), taken from [156].

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A LED at forward bias can be used as for cooling purpose through electroluminescence [97–102], since the emitted photon is at an energy of the band gap, whereas the injected electron-hole pair has a quasi-Fermi level separation Therefore, similar to the TPX system above, but placing the LED on the cold side with a lower temperature than the PV cell, TPX system can work as solid-state cooling device [156,157]. For example, Chen at al proposed a high performance electroluminescent refrigeration device based on a GaAs LED and Si PV cell [Fig. 16(d)] [156]. The electroluminescence from the GaAs LED removes the heat from the LED side and the Si PV cell absorbs the emitted photons, and generates electrical power, which can be fed back into the LED, thus reducing the required external power that is injected into the LED. Such a cooling device could have cooling power density over 10³ W/m² working in the far field [Fig. 16(e)], while maintaining an efficiency of about 10% of Carnot limit [Fig. 16(f)], comparable to thermoelectric coolers.

4. Concluding Remarks and Future Perspectives

The recent advances in thermal radiation control build upon the exciting developments made in the past 20 years on nanophotonic structures for the control of light. As evidenced in this review, all major conceptual developments in nanophotonics, such as photonic crystals, plasmonics, and metamaterials, have found significant impact in controlling of thermal radiation. And the development of nanophotonic thermal radiation control will also continually benefit from other advances in nanophotonics such as design optimization [158], structure fabrication [159–161] and applying new material systems [162,163].

While spectral control of thermal radiation has been quite prominent in many energy applications, controlling other fundamental properties of thermal radiation as outlined in this review, such as angular control, polarization control, thermal extraction, reciprocity control and dynamic control, could open exciting applications opportunities as well. In addition to the examples provides in this review, there are significant opportunities in negative illumination for harvesting the cold of universe for nighttime electricity generation [164]. Nanophotonic controlled non-reciprocal thermal radiation could play a significant role in improving the system efficiency of such nigh time energy harvesting [165].

Unlike many photonic applications where minimizing loss is a central issue, controlling thermal radiation requires a judicious management of loss – a structure that is completely lossless does not generate thermal radiation. The developments of nanophotonic thermal radiation control therefore significantly enrich the field of nanophotonics and could also benefit other nanophotonic applications [166–168].

In order for nanophotonics to make an impact in practical thermal radiation applications, it is important to be able to scale these structures up. In addition, it is also of crucial importance to be able to integrate these nanophotonic structures into practical thermal systems. We anticipate the development of nanophotonics will lead to many new opportunities for controlling thermal radiation, with tremendous opportunities for both fundamental advances and practical energy applications.

Funding

Global Climate and Energy Project at Stanford University; Department of Energy (DOE) Office of Basic Energy Sciences (Grant No. DE-FG02-07ER46426); DOE Advanced Project Research Agency-Energy (APRA-E) (Grants No. DE-AR0000316, DE-AR0000533, DE-AR0000731), DOE “Light-Material Interactions in Energy Conversion” Energy Frontier Research Center (Grant No. DE-SC0001293); National Science Foundation (CMMI-1562204).

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Nanophotonic control of thermal radiation for energy applications [Invited]

Abstract

1. Introduction

2. Nanophotonics Control of Thermal Radiation

2.1 Spectral Control

2.2 Polarization Control

2.3 Angular Control

2.4 Beyond Planck’s Law and Kirchhoff’s Law: Thermal Extraction and Non-reciprocal thermal radiation

2.5 From Static to Dynamic: active control of thermal radiation

2.6 Non-equilibrium and non-linear thermal radiation

3. Energy applications

3.1 Daytime radiative cooling

3.2 Radiative cooling on solar cells

3.3 Thermal radiative textile

3.4 Solar Thermophotovoltaic (STPV) and Thermophotovoltaic (TPV) System

3.5 Thermophotonics (TPX) System

4. Concluding Remarks and Future Perspectives

Funding

References and links

Cited By

Figures (16)

Equations (9)

Optics Express