Here the asterisk on the polarization vector denotes complex conjugate as required by a timereversal operation. For such reciprocal thermal emitters, to control its emissivity it is sufficient to consider its absorptivity.
这里极化向量上的星号表示复共轭，这是时间反演操作所要求的。对于这种互易热辐射器，要控制其发射率，只需考虑其吸收率即可。

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.
在纳米光子结构中，当特征尺寸与光波长相当时，波干涉效应导致了对光谱响应进行定制的大量可能性。可以创建发射率与底层材料截然不同的结构。

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©], surface plasmons [22], Fabry-Perot cavities [23-25], dielectric microcavities [26], and metamaterials [27,28].
可以通过多种光子谐振器显著提高材料的发射率。有损耗的谐振器可用于在吸收光谱中创建尖锐的谱峰。因此，此类谐振器可用于创建窄带热辐射器。为此目的，已经应用了广泛的谐振系统。例如，包括光子晶体板中的导波谐振[17-20] [图 3(a)和 3(b)]、金属天线阵列[8,21] [图 3©]、表面等离子体[22]、法布里-珀罗腔[23-25]、介电微腔[26]和超材料[27,28]。

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:
在理解单个共振的吸收和发射特性时，临界耦合的概念起着重要作用[19,29]。对于单个共振与入射外部波的单个通道耦合，该通道的吸收光谱以及由此产生的对该通道的发射光谱具有洛伦兹线形：

where ${\omega }_0$${\omega }_0$omega_(0)\omega_{0} is the resonant frequency, ${\gamma }_e$${\gamma }_e$gamma_(e)\gamma_{e} is the external radiative leakage rate of the resonance to the channel, and ${\gamma }_i$${\gamma }_i$gamma_(i)\gamma_{i} is the intrinsic loss rate of the resonance due to material absorption. Remarkably, no matter how small the material absorption is, i.e. no matter how small ${\gamma }_i$${\gamma }_i$gamma_(i)\gamma_{i} is, it is in principle always possible to achieve $100\mathrm{\%}$$100\mathrm{\%}$100%100 \% absorption, at the resonant frequency ${\omega }_0$${\omega }_0$omega_(0)\omega_{0}, by satisfying the critical coupling condition:
${\omega }_0$${\omega }_0$omega_(0)\omega_{0} 为谐振频率， ${\gamma }_e$${\gamma }_e$gamma_(e)\gamma_{e} 为谐振到通道的外部辐射泄漏率， ${\gamma }_i$${\gamma }_i$gamma_(i)\gamma_{i} 为由于材料吸收引起的谐振固有损耗率。值得注意的是，无论材料吸收有多小，即无论 ${\gamma }_i$${\gamma }_i$gamma_(i)\gamma_{i} 有多小，只要满足临界耦合条件，原则上总是可以实现 $100\mathrm{\%}$$100\mathrm{\%}$100%100 \% 吸收，在谐振频率 ${\omega }_0$${\omega }_0$omega_(0)\omega_{0} 处。

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 ${\gamma }_i$${\gamma }_i$gamma_(i)\gamma_{i} of the resonance varies, while the external leakage rate ${\gamma }_e$${\gamma }_e$gamma_(e)\gamma_{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{\gamma }_i$$2{\gamma }_i$2gamma_(i)2 \gamma_{i}. We note that at least in principle one can achieve thermal emission with bandwidth that is arbitrarily narrow. In this example, narrower emission linewidth can be achieved by increasing the distance between the slabs, and by adjusting the structural parameters of the photonic crystal slab such that the critical coupling is satisfied.
图 3(a)展示了临界耦合[19]的条件。该结构由一个介电光子晶体板组成，假设为无损耗，以指数衰减的方式耦合到一个均匀的钨板，该钨板有损耗。随着光子晶体板和钨板之间的间距变化，共振的本征损耗率 ${\gamma }_i$${\gamma }_i$gamma_(i)\gamma_{i} 会变化，而外部泄漏率 ${\gamma }_e$${\gamma }_e$gamma_(e)\gamma_{e} 基本保持不变。因此，间距的变化允许通过临界耦合点进行调节，从而产生具有单位发射率峰值的窄带热辐射。在临界耦合时，共振的总线宽为 $2{\gamma }_i$$2{\gamma }_i$2gamma_(i)2 \gamma_{i} 。我们注意到，至少在原则上，可以实现对带宽任意窄的热辐射。在这个例子中，可以通过增加板之间的距离，并通过调整光子晶体板的几何参数，使得临界耦合得以满足，从而实现更窄的辐射线宽。

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]. © 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].
图 3. 实现窄带热辐射的纳米光子结构。每个图展示了嵌入图中所示结构的发射率/吸收率光谱。（a）一个介电光子晶体（橙色区域），通过真空间隙与平坦的钨表面（灰色区域）分离，用于产生窄带热辐射，取自[19]。随着间隙尺寸的增加，系统通过临界耦合区域（蓝色曲线）进行调谐，此时峰值发射率接近 1。（b）由光子晶体与多重量子阱结构耦合产生的窄带热辐射，取自[17]。©用于产生窄带热辐射的金天线结构。顶部：单带超材料吸收器的实验吸收率。底部：双带超材料吸收器的实验吸收率。嵌入图显示了制造的单带和双带吸收器的一个单元细胞的扫描电子显微镜图像，取自[8]。

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©]. 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.
通过利用多个共振[8,30-40]，光子结构可以产生具有多频带或宽带特性的强烈热辐射。例如，可以将两个不同的谐振器组合起来形成一个二分格子的晶胞[8]，以获得双频带发射率[图 3©]。还可以使用锯齿形结构[30][图 4(a)]、梯形结构[31]或分形结构[33][图 4(b)]，所有这些结构都支持多个共振，以获得宽带响应。此外，当将具有相似共振频率的多个共振放置在亚波长体积中时，热辐射中可以出现超辐射的类似现象[41]。总的来说，对共振和共振相互作用的理解为工程热辐射光谱提供了一个通用的概念框架。

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]. © 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].
图 4. 宽带增强和抑制热辐射的纳米光子结构。每个图展示了插入图中所示结构的发射率/吸收率光谱。（a）用于实现宽带吸收响应的锯齿形各向异性超材料结构，取自[30]。（b）具有多个共振的超材料吸收器，用于实现宽带吸收响应，取自[33]。©钨层中周期性空气孔阵列，用于宽带抑制热辐射，取自[42]。（d）利用多层超材料在不同波长范围内抑制和增强热辐射，取自[28]。

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]$$[4,5,43,44]$[4,5,43,44][4,5,43,44]. For example, Yeng et al considered an array of air holes in metal film [Fig. 4©]. Each air hole can be considered as a metallic waveguide with a cut-off frequency that is inversely proportional to the diameter of the holes. The array supports a band gap in the frequency range below the cutoff. The resulting structure therefore exhibits a strong suppression of thermal emissivity over a broad frequency range from near zero-frequency to the cut-off frequency [42].
通过增强热辐射率，也可以在波长范围内强烈抑制材料的热辐射率，例如，使用支持光子带隙的光子晶体结构。该带隙对应于结构密度态非常低的频率范围。在带隙内，结构强烈反射入射光。这种高反射率转化为带隙内强烈抑制的热辐射率。在介电和金属光子晶体结构中已经提出并证明了强烈抑制热辐射率的方法 $[4,5,43,44]$$[4,5,43,44]$[4,5,43,44][4,5,43,44] 。例如，Yeng 等人考虑了金属薄膜中的空气孔阵列 [图 4©]。每个空气孔可以被视为一个截止频率与孔直径成反比的金属波导。该阵列支持低于截止频率的频率范围内的带隙。因此，这种结构在从近零频率到截止频率的宽频率范围内表现出强烈抑制热辐射率 [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©, 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.
许多纳米光子结构同时在某些波长范围内增强发射率，而在其他波长范围内抑制发射率。例如，图 4©所示的 photonic crystal 结构，如上所述，在间隙中抑制发射率，同时在光子带边缘增强发射率。可以将这种增强视为由金属孔支持的个别共振引起的。或者，也可以构建具有有效本征材料特性的超材料，以选择性地在不同波长处增强和抑制热辐射。例如，由金属和介电材料交替的亚波长层组成的超材料已被用于控制热辐射[27,28,45-47]。当有效介电函数处于椭球状态时，这些超材料表现出增强的热辐射，而当有效介电函数处于双曲状态时，则抑制热辐射[图 4(d)] [31]。这两个状态之间的过渡波长可以通过适当选择层的厚度来控制。

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 nanoantennas, 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].
许多纳米光子结构的吸收光谱强烈依赖于偏振。因此，它们的红外辐射可以强烈偏振。这与传统的黑体或灰体红外辐射器形成对比，其红外辐射通常是未偏振的。例如，在[图 5(a)] [48]中考虑的纳米线天线中，由于镜面对称性，导线只支持与导线平行电场的 TE 偏振或与导线垂直电场的 TM 偏振的共振。因此，在共振时，导线的辐射可以高度偏振。Ingvarsson 等人研究了单个铂纳米天线的红外辐射，该天线呈矩形形状。他们证明了天线[图 5(b)] [49]的红外辐射特性与偶极子辐射器非常相似，偶极子的方向与纳米天线的方向强烈相关。因此，辐射又可以强烈偏振。使用光栅结构[6]、光子晶体板[50]和腔体[51]也可以实现强烈偏振的红外辐射。