Thermal radiative properties of metamaterials and other nanostructured materials: A review

Abstract

The ability to manufacture, control, and manipulate structures at extremely small scales is the hallmark of modern technologies, including microelectronics, MEMS/NEMS, and nano-biotechnology. Along with the advancement of microfabrication technology, more and more investigations have been performed in recent years to understand the influence of microstructures on radiative properties. The key to the enhancement of performance is through the modification of the reflection and transmission properties of electromagnetic waves and thermal emission spectra using one-, two-, or three-dimensional micro/nanostructures. This review focuses on recent developments in metamaterials–manmade materials with exotic optical properties, and other nanostructured materials, such as gratings and photonic crystals, for application in radiative energy transfer and energy conversion systems.

Keywords

metamaterial / nanostructured material / thermal radiative property / radiative energy transfer

Introduction

Wavelength-selective materials have enormous applications in photonic and energy conversion systems such as photodetectors [1], solar cells and solar absorbers [2,3], thermophotovoltaic devices [4], and radiation filters and emitters [5-7]. Pattern-induced radiative property variations can be an important problem for wafer temperature measurement and temperature uniformity control during integrated-circuit manufacturing [8,9]. In addition, light diffraction can be used to monitor etching depth and other features during microfabrication and lithographic processes [10,11]. It should be emphasized that surface electromagnetic (EM) waves, or polaritons, can be excited with periodic grooves or corrugated structures, resulting in coherent thermal emission with a SiC grating [12,13] and enhanced light transmission through subwavelength apertures [14].

Metamaterials refer to the class of artificially ordered structures that display exotic properties, not readily observed in naturally occurring materials. Electromagnetic metamaterials are synthesized materials with novel electric and magnetic properties. In some cases, these materials can exhibit a negative refractive index in a certain region of the electromagnetic spectrum. Before 2000, very sparse reports existed on negative index materials (NIMs). Shelby et al. [15] first demonstrated that a metamaterial exhibits negative refraction at x-band microwave frequencies. In a NIM, the phase velocity of an electromagnetic wave is opposite to its energy flux, and the refracted light from air to the NIM will bend to the same side as the incident light (negative refraction). The study of the effect of micro/nanostructures on optical properties of materials has become a frontier of photonics and imaging optics [16]. More recently, a negative refractive index in optical frequency have been observed by several groups [17-19].

Because of the potential applications of metamaterials on radiative energy transfer and energy conversion devices, the study of engineered surfaces with desired thermal radiative characteristics using controlled micro/nanostructures has recently received great attention. Zhang et al. [20] gave a comprehensive review on the radiative properties of semiconductor materials, with microroughness and periodic nanostructures. The present review focuses on recent development in periodic structures including metamaterials for tailoring thermal radiative properties. In what follows, the theoretical background is summarized in Section 2. The optical and radiative properties of metamaterials are discussed in Section 3. Section 4 addresses the application of periodic gratings for controlling radiative properties. Section 5 focuses on one-dimensional photonic crystals for use as coherent emission sources. Future challenges and directions are outlined in Section 6.

Basic theory

Negative index

In the late 1960s, Veselago [21] postulated the concept of negative refractive index (n < 0) for a hypothetical material having a negative electric permittivity (e) and a negative magnetic permeability (m). Note that e and m used here are relative to those of free space. However, contrast to materials with positive refractive indices or positive index materials (PIMs), the lack of simultaneous occurrence of negative e and m in natural materials hindered any further study on negative index materials (NIMs) for some 30 years. Pendry [22] conceived that a NIM slab with e = m = -1 performs the dual function of correcting the phase of the propagating components and amplifying the evanescent components, which normally exist only in the near field of the object. The combined effects could make a perfect lens which will eliminate the limitations on image resolution imposed by diffraction for conventional lenses. Potential applications range from nanolithography to novel Bragg reflectors, phase-compensated cavity resonators, forward couplers in transmission lines, waveguides, and enhanced photon tunneling for microscale energy conversion devices [23]. A brief discussion of the basic theory of metamaterials is given below, and more details can be found from Fu [24] and Zhang [25].

Real materials possess losses, and hence, both e and m are complex and frequency dependent. The negative index can be realized by considering the complex plane, as illustrated in Fig. 1. Note that \widetilde{ϵ}={ϵ}^{\prime }+\mathrm{i}{ϵ}^{"}=r_{ϵ}{\mathrm{e}}^{\mathrm{i}{\varphi }_{ϵ}} and \tilde{\mu }={\mu }^{\prime }+\mathrm{i}{\mu }^{\prime }=r_{\mu }{\mathrm{e}}^{\mathrm{i}{\varphi }_{\mu }}, so the complex refractive index becomes

(1)\tilde{n}=n+\mathrm{i}\kappa =r_n{\mathrm{e}}^{\mathrm{i}{\varphi }_n}=\sqrt{r_{ϵ}{r}_{\mu }}{\mathrm{e}}^{\mathrm{i}({\varphi }_{ϵ}+{\varphi }_{\mu })/\mathrm{2}}.

Therefore, if both {ϵ}^{\prime } and {\mu }^{\prime } are negative (or at least one is negative and {\varphi }_{ϵ}+{\varphi }_{\mu }>\mathrm{\pi }), n will be negative, but κ will always be positive. Generally speaking, one would like to see all the phase angles to be close to \pi in order to minimize losses or dissipation. Many metals and polar dielectrics have a negative {ϵ}^{\prime } in the visible and near-infrared. Periodic structures of thin metal wires or strips can dilute the average concentration of electrons and shift the plasma frequency to the far-infrared or longer wavelengths. At optical frequencies, negative-m materials rarely exist in nature, but can be obtained using complex materials (i.e., metamaterials) consisting of split-ring resonator structures. These structures and their alternatives, originally demonstrated at microwave frequencies, can be scaled down to achieve negative {\mu }^{\prime } toward higher frequencies. The combination of repeated unit cells of interlocking copper strips and split-ring resonators makes a metamaterial exhibit a negative {ϵ}^{\prime } and {\mu }^{\prime } simultaneously. Based on an effective-medium approach, the relative permittivity and permeability of a NIM can be expressed as functions of the angular frequency w as follows [26,27]:

(2)ϵ(\omega )=\mathrm{1}-{\displaystyle \frac{{\omega }_{\mathrm{p}}^{\mathrm{2}}}{{\omega }^{\mathrm{2}}+\mathrm{i}{\gamma }_{\mathrm{e}}\omega }},

and

(3)\mu (\omega )=\mathrm{1}-{\displaystyle \frac{F{\omega }^{\mathrm{2}}}{{\omega }^{\mathrm{2}}-{\omega }_{\mathrm{0}}^{\mathrm{2}}+\mathrm{i}{\gamma }_{\mathrm{m}}\omega }},

where {\omega }_{\mathrm{p}} is the effective plasma frequency, {\omega }_{\mathrm{0}} is the effective resonance frequency, {\gamma }_{\mathrm{e}} and {\gamma }_{\mathrm{m}} are the damping terms, and F is the fractional area of the unit cell occupied by the split ring. From Eqs. (2) and (3), both negative ϵ and \mu can be realized in a frequency range between {\omega }_{\mathrm{0}} and {\omega }_{\mathrm{p}} for adequately small {\gamma }_{\mathrm{e}} and {\gamma }_{\mathrm{m}}. Here, the values of {\omega }_{\mathrm{0}}, {\omega }_{\mathrm{p}}, {\gamma }_{\mathrm{e}}, {\gamma }_{\mathrm{m}} and F depend on the geometry of the unit cell that constructs the metamaterial.

Evanescent waves and photon tunneling

Total internal reflection occurs when a beam is incident from an optically denser material to another material at incidence angles greater than the critical angle determined by the ratio of the refractive indices of the two materials. Under this condition, no energy is transferred into the second medium, but there exist electromagnetic fields that decay exponentially away from the interface. The decaying electric fields are called evanescent waves. The mechanism of photon tunneling is related to total internal reflection. When a third medium with sufficiently large refractive index is placed close to the first medium such that the second medium becomes a thin layer, photons can tunnel through the second medium into the third. This phenomenon is called frustrated total internal reflectance. From the transmission point of view, it is called photon tunneling or radiation tunneling. The tunneled energy, however, is significant only when the distance between the two interfaces is shorter than the wavelength of the incident radiation.

Consider the following example: a plane wave is incident from a semi-infinite medium (medium 1) with an incidence angle of {\theta }_{\mathrm{1}}, as shown in Fig. 2(a). The thickness of the second medium (vacuum or air) is d₂, and the third medium is another semi-infinite medium. The transmittance from medium 1 to medium 3 at {\theta }_{\mathrm{1}}={\mathrm{45}}^{\mathrm{°}} are plotted in Fig. 2(b) for both s- and p-polarizations as a function of d_{\mathrm{2}}/\lambda, where l is the wavelength of the incident radiation invacuum . Note that for s-polarization, the electric field is perpendicular to the plane of incidence, which is also called TE wave; while for p-polarization or TM wave, the magnetic field is perpendicular to the plane of incidence. In the calculation, it is assumed that media 1 and 3 are nonmagnetic and with the same refractive index of n_{\mathrm{1}}=n_{\mathrm{3}}=\mathrm{1.5}. Note also that the critical angle in this case is {\theta }_{\mathrm{c}}={\sin }^{-\mathrm{1}}(\mathrm{1}/n_{\mathrm{1}})\approx {\mathrm{42}}^{\mathrm{°}}. For a fixed wavelength l, there is a strong dependence of the transmittance on the thickness d₂ of the second layer. The mechanism of photon tunneling can be understood as the coupling (or interference) of a forward evanescent wave with a backward evanescent wave. The rapid decrease of transmittance with increasing d₂ is that evanescent waves decay exponentially from the first interface and cannot reach the second interface for large d₂. Applications of photon tunneling can be in photon scanning tunneling microscopy and in micro/nanoscale radiation heat transfer and energy conversion [28-32].

Surface electromagnetic waves

Plasmons are quasiparticles associated with oscillations of plasma, which is a collection of charged particles such as electrons in a metal or a semiconductor. Plasmons are longitudinal excitations that can occur either in the bulk or at the interface. The charges oscillate along the surface, and such an excitation is called a surface plasmon or surface plasmon polariton. The field associated with a plasmon is localized at the surface, and the amplitude decays away from the interface. Such a wave propagates along the surface; and therefore, it is called a surface electromagnetic wave, similar to surface waves in fluids or the acoustic surface waves. Surface plasmons can be excited by electromagnetic waves and are important for the study of optical properties of metallic materials especially near the plasma frequency, which usually lies in the ultraviolet region. The requirement of evanescent waves on both sides of the interface prohibits the coupling of propagating waves in air to the surface plasmons. For this reason, surface waves are often regarded as nonradiative modes. The attenuated total reflectance (ATR) arrangements are commonly used to excite surface plasmons. When light is incident from the prism, it is possible for evanescent waves to occur simultaneously in underneath metallic and air layers, as shown in Fig. 3, for the two typical configurations [33].

In addition to the requirement of evanescent waves on both sides of the interface, the polariton dispersion relations must be satisfied, which can be expressed as follows when both media extend to infinity in the z-direction:

(4)\begin{array}{ll}{\displaystyle \frac{k_{\mathrm{1}z}}{{ϵ}_{\mathrm{1}}}}+{\displaystyle \frac{k_{\mathrm{2}z}}{{ϵ}_{\mathrm{2}}}}=\mathrm{0}\hfill & \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{T}\mathrm{M}\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}\hfill \end{array},

(5)\begin{array}{ll}{\displaystyle \frac{k_{\mathrm{1}z}}{{\mu }_{\mathrm{1}}}}+{\displaystyle \frac{k_{\mathrm{2}z}}{{\mu }_{\mathrm{2}}}}=\mathrm{0}\hfill & \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{T}\mathrm{E}\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}\hfill \end{array}.

This means that the sign of permittivity must be opposite for media 1 and 2 in order to couple a surface polariton with a TM wave. On the other hand, a magnetic material is needed with negative permeability for a TE wave to be able to couple with a surface polariton. Both TE and TM waves may excite surface plasmon polaritons with a NIM, as predicted by Ruppin [34].

Surface plasmons play an important role in near-field microscopy, nanophotonics, and biomolecular sensor applications [35-37]. Surface plasmons usually occur in the visible or near-infrared region of the electromagnetic wave spectrum for highly conductive metals such as Ag, Al, and Au. In some polar dielectric materials, phonons or bound charges can also interact with the electromagnetic waves in the mid-infrared spectral region and cause resonance effects near the surface; these resonant modes are called surface phonon polaritons, which have applications in tuning the thermal emission properties [12,13] and nanoscale nondestructive imaging [38].

Periodic gratings

Diffraction grating is considered as one of the simplest and most important devices in optical metrology. Many studies have been performed on the effect of gratings on radiative property modification [39,40]. The importance of grating on nanooptics is obviously owing to the ability to fabricate complete diffraction elements and the applications in sensors and surface diagnostics. Patterned semiconductor microelectronics has periodic structures on the surface with a period below 100 nm [41]. Understanding radiative properties is essential for thermal processing and modeling in semiconductor manufacturing as the feature size continues to shrink.

As shown in Fig. 4, a plane TE wave is incident on a 1-D grating surface from free space, region I with {ϵ}_{\mathrm{I}}=n_{\mathrm{I}}=\mathrm{1}\mathrm{a}\mathrm{n}\mathrm{d}{\kappa }_{\mathrm{I}}=\mathrm{0}. Region II is composed of binary materials A and B so that its dielectric function is a periodic function of x with a period of L, i.e., the grating period. The filling ratio f is the volume fraction of material A, and the lateral extension of the grating is assumed to be infinite. Region III is the substrate with a dielectric function of {ϵ}_{\mathrm{Ⅲ}}.

The wave vector BoldItalic defines the direction of incidence. The angle between BoldItalic and the surface normal \widehat{z} is the angle of incidence q, also called the polar angle. The grating vector BoldItalic is defined in the positive x direction with a magnitude of K = 2p/L. For simplicity, it is assumed that the incident wave vector is on the x-z plane, i.e., the y-component of BoldItalic is zero. For s-polarization, the electric field BoldItalic is parallel to the y-direction and perpendicular to the grating vector BoldItalic. The magnitude of the incident electric field, after normalization, can be expressed as \exp (\mathrm{i}{k}_{x}x+\mathrm{i}{k}_{z}z-\mathrm{i}\omega t). The magnitude of BoldItalic in regions I and III can be expressed as

(6)k_{\mathrm{I}}={\displaystyle \frac{\mathrm{2}\mathrm{\pi }{n}_{\mathrm{I}}}{\lambda }}={\displaystyle \frac{\mathrm{2}\mathrm{\pi }}{\lambda }}=k,k_{\mathrm{I}\mathrm{I}\mathrm{I}}={\displaystyle \frac{\mathrm{2}\mathrm{\pi }{n}_{\mathrm{I}\mathrm{I}\mathrm{I}}}{\lambda }}=n_{\mathrm{I}\mathrm{I}\mathrm{I}}k,

where n_{\mathrm{III}} is the refractive index of region III. There exists a phase difference of \mathrm{2}\mathrm{\pi }\mathrm{\Lambda }\sin \theta /\lambda =k_x\mathrm{\Lambda } between the incident wave at (x,z) and that at (x+\mathrm{\Lambda },z) due to a path difference of \mathrm{\Lambda }\sin \theta. This condition must also be satisfied by each diffracted wave, i.e., the magnitude of the j th-order reflected wave can be written as r_j\exp (\mathrm{i}{k}_{x,j}x-\mathrm{i}{k}_{\mathrm{I}z}z-\mathrm{i}\omega t), where r_j is the reflection coefficient, and k_{x,j} is determined by the Bloch-Floquet condition [39,40]:

(7)k_{x,j}={\displaystyle \frac{\mathrm{2}\mathrm{\pi }}{\lambda }}\sin \theta +{\displaystyle \frac{\mathrm{2}\mathrm{\pi }}{\mathrm{\Lambda }}}j=k_x+Kj\mathrm{.}

The previous equation can be expressed in terms of the angle of reflection given by

(8)\sin {\theta }_j=\sin \theta +{\displaystyle \frac{j\lambda }{\mathrm{\Lambda }}\mathrm{.}}

where {\theta }_j=\arcsin (k_{x,j}/k) is the j th-order diffraction angle for reflection. Equation (8) is the well-known grating equation. When k_{x,j}>k_{\mathrm{I}}, \sin {\theta }_j>\mathrm{1} and the jth-order reflected wave decays exponentially toward the negative z direction. The fact that gratings can induce evanescent waves is key to the excitation of surface waves with gratings, in place of prisms.

Rigorous-coupled wave analysis (RCWA) and finite-difference time domain (FDTD) are commonly used methods for solving the grating equations to determine radiative properties as well as field distribution. Detailed discussion of RCWA and FDTD can be found from Lee et al. [42] and Fu et al. [43]. In addition to the rigorous approaches, when the wavelength is much greater than the grating period, effective-medium theory (EMT) or method of homogenization, is often applied to periodic structures. In this case, all high-order diffracted waves are evanescent and only the zeroth-order diffraction gives a propagating wave that is responsible to far-field radiative properties. The grating region is treated as a homogeneous material with the dielectric function that depends on polarization [25,41].

Photonic crystals

Recently, the unique features of periodic microstructures (i.e., photonic crystals) have been utilized in several studies to engineer the radiative properties for specific applications [44,45]. A photonic crystal (PC) is a periodic array of unit cells (i.e., photonic lattices in analogy to those in real crystals) which replicate infinitely into one, two, or three dimensions. From the analogy of the electron movement in crystals, wave propagation in a PC should also satisfy the Bloch condition as in real crystals [46]. Similarly, due to the periodicity, a PC exhibits band structures consisting of pass and stop bands when the frequency is plotted against the wave vector. In the pass band, for instance, waves can propagate inside a PC. Whereas in the stop band, no energy-carrier waves can exist inside a PC, and only oscillating but evanescently decaying fields possibly exist. The existence of stop bands enables a PC to be used in many optoelectronic devices such as band-pass filters and waveguides [47-49]. Most of the 1-D PCs have been found to consist of alternating layers with two lossless dielectrics, while metallic PCs have also been researched extensively. In some cases, the dimension may be smaller than 100 nm for tuning the visible properties.

While 3D PCs with complicated structures can be fabricated and used in a number of applications, the fundamental physics can be illustrated using 1D PCs and can easily be generalized for 2D or 3D structures. The 1D PC, illustrated in Fig. 5(a), is a periodic multilayer structure, whose unit cell is composed of alternating dielectrics with different refractive indices of n_{\mathrm{a}}\mathrm{a}\mathrm{n}\mathrm{d}{n}_{\mathrm{b}}, where \mathrm{\Lambda }=d_{\mathrm{a}}+d_{\mathrm{b}} is the period of the PC or photonic lattice constant. The reflectance of the 1D PC structure with different numbers of periods (n= 30 and 300) is shown in Fig. 5(b), where the wavelength is normalized to the period L. The reflectance approaches unity in the stop band (when n >30). In the pass band, interference effects affect the free spectral range of oscillation and, thus, the oscillation frequency increases with the number of periods of the PC structure. A special type of 1D PC is the Bragg reflector, which is composed of alternating high- and low-index films, each at a thickness of one-quarter of the wavelength in the film, i.e., d_{\mathrm{a}}=\lambda /(\mathrm{4}{n}_{\mathrm{a}}) and d_{\mathrm{b}}=\lambda /(\mathrm{4}{n}_{\mathrm{b} }).

Metamaterials

Photon tunneling and transmittance enhancement

Photon tunneling and transmittance enhancement achieved by application of layers made of metamaterials were motivated by the concept of Pendry’s [22] perfect lens. Because photon tunneling depends strongly on the vacuum gap width between the two media as shown in Fig. 2(a) and the transmittance by photon tunneling is negligibly small when the vacuum gap width d_{\mathrm{2}} is larger than the incidence wavelength, techniques that can enhance the transmittance by photon tunneling will make it more promising to be used in photon scanning tunneling microscope [28,29] and in microscale thermophotovoltaic devices [31,32]. Zhang and Fu [49] studied the enhancement of photon tunneling using a NIM slab in the structure shown in Fig. 6(a) which is similar to that in Fig. 2(a) except that a NIM slab of thickness d_{\mathrm{3}} is inserted between the vacuum gap and the bottom semi-infinite medium. Transmittance by photon tunneling through the structure was derived and the results for both TE and TM waves at incidence angle {\theta }_{\mathrm{1}} equal to 45 and 60 degrees can be seen in Fig. 6(b). It is interesting to find that application of the NIM slab with {ϵ}_{\mathrm{3}}={\mu }_{\mathrm{3}}=-\mathrm{1} gives the transmittance equal to unity as long as the thickness of the NIM slab d_{\mathrm{3}} is the same as the thickness of the vacuum gap d_{\mathrm{2}}. Furthermore, application of the NIM slab can result in a unity transmittance not only for photon tunneling, but for electromagnetic waves at any incidence angle, provided that conditions {ϵ}_{\mathrm{3}}={\mu }_{\mathrm{3}}=-\mathrm{1} and d_{\mathrm{3}}=d_{\mathrm{2}} can be satisfied [50]. The function of the NIM slab in this case is the same as that for the perfect lens, that is, to correct the phase of the propagating components and amplify the evanescent components.

The physical mechanism behind the amplification of evanescent components is due to excitation of surface polaritons at the vacuum/NIM interface. However, the values of ϵ and \mu of a NIM are both frequency-dependent [21] and the frequency at which excitation of surface polaritons occurs varies with the incidence angle. Therefore, enhancement of transmittance by excitation of surface polaritons may be possible only at certain frequencies and may further deteriorate due to the dissipation inside the NIM. Equations (2) and (3) have been proposed [26,27] to describe the frequency-dependent ϵ and \mu of an artificial NIM, which is constructed with repeated unit cells of inter-locking metal strips and split-ring resonators. It should be noted that the values of ϵ and \mu given by Eqs. (2) and (3) are complex numbers at any frequency due to the two damping terms {\gamma }_{\mathrm{e}} and {\gamma }_{\mathrm{m}}, which are responsible for the dissipation inside the material. Nevertheless, negative real parts of both ϵ and \mu can be achieved within a certain range of frequency. Fu et al. [51] developed an algorithm for calculating radiative properties of multilayers including NIMs and calculated the transmittance of the structure illustrated in Fig. 6(a), but with {ϵ}_{\mathrm{3}} and {\mu }_{\mathrm{3}} obtained from Eqs. (2) and (3), respectively. In their calculations, the parameters ω_0/ω_p and F are respectively equal to 0.5 and 0.785. The results are shown in Fig. 7 for s- and p-polarized plane wave incident at 45°, along with the transmittance without the NIM layer (d₃ =0) for comparison. Transmittance enhancement due to excitation of surface polaritons is manifested by the high peak of the transmittance curve for either polarization. The effect of damping on the enhancement is clearly seen from the curves corresponding to different values of \gamma (here, {\gamma }_{\mathrm{e}} is assumed equal to {\gamma }_{\mathrm{m}}). It should also be noted that the series of small peaks at lower frequencies are not due to excitation of surface polaritons, but to wave interference inside the NIM slab. In the case when the two end media as shown in Fig. 6(a) are dissimilar, not only surface polaritons, but also bulk polaritons inside the NIM slab can be excited. The dispersion relations of both surface and bulk polaritons related to NIMs were discussed by Park et al. [52]. The study on unusual photon tunneling and enhanced transmittance using NIMs and single-negative metamaterials in multilayer structures and photonic crystals for different application purposes has become an active research area over the past several years [53-57].

Coherent emission

Thermal emission is a spontaneous process that occurs in any real object. Electromagnetic radiation emitted from heated objects is generally manifested by a broad spectrum and quasi-isotropic angular behavior [58]. However, surface microstructures can strongly affect the directional behavior of absorption and emission due to multiple reflections and diffraction, allowing the radiative properties to be controlled [59-65]. The key to the enhancement of performance is the modification of the reflection and emission spectra using one-, two-, or three-dimensional micro/nanostructures [20].

Coherent thermal emission is associated with a sharp spectral peak (temporal coherence) and/or angular lobes into well-defined directions (spatial coherence). This research has drawn much attention lately for applications in thermophotovoltaic devices, optoelectronics, and space thermal management. Coherent thermal emission has been demonstrated using gratings [12,13,66] by excitation of surface polaritons. With gratings, the excited surface polaritons couple with and enhance the thermal radiation in the direction of \theta determined by Eq. (8) for a particular wavelength (frequency). It should be noted that coherent thermal emission source constructed by etching a grating on the surface of a normal material is possible only for p-polarization because normal materials do not support surface polaritons of s-polarization.

Recently, Fu et al. [67] proposed a method to achieve coherent emission of radiation from a planar heterogeneous structure that pairs single-negative materials, as shown in Fig. 8(a). Coherent emission of radiation from such a heterogeneous structure without grating is possible for both s- and p-polarizations. The mechanism for coherent thermal emission is still due to excitation of surface polaritons, but at the interface of the paired single-negative materials. Materials with negative ϵ but positive \mu can be found in metals and polar dielectrics. Metamaterials with negative \mu but positive ϵ can be artificially made with different methods, which will be discussed in detail in Section 3.3. The emissivity of the planar heterogeneous structure can be indirectly calculated from the reflectance subtracted from unity if the negative \mu layer is thick enough for the whole structure to be opaque, according to Kirchhoff’s law [58]. Assuming that {ϵ}_{\mathrm{2}} and {\mu }_{\mathrm{3}} of the materials shown in Fig. 8(a) can be respectively described by Eqs. (2) and (3), the calculated emissivity of the structure is shown in Fig. 8(b) for s-polarization at angles of emission equal to 30° and 60°, respectively. Here, other parameters used are {\mu }_{\mathrm{2}}=\mathrm{1}, {ϵ}_{\mathrm{3}}=\mathrm{4}, F = 0.785, {\omega }_{\mathrm{0}}=\mathrm{0.5}ω_p, {\gamma }_{\mathrm{e}}={\gamma }_{\mathrm{m}}=\mathrm{0.0025}{\omega }_{\mathrm{p}}, and d_{\mathrm{2}} is taken as \mathrm{0.425}{\lambda }_{\mathrm{p}} ({\lambda }_{\mathrm{p}} is the corresponding wavelength of {\omega }_{\mathrm{p}}) in order to obtain optimized emissivity. A very high emissivity can be seen in a narrow frequency band centered at the surface polariton resonance frequency. At frequencies outside the narrow band, the emissivity is nearly zero. The inset illustrates the emissivity plotted as a function of the angle of emission for different surface polariton resonance frequencies. Angular emission lobes are clearly seen. Similar results can be obtained for p-polarization.

A slightly more complicated structure can be constructed by adding another layer denoted by {ϵ}_{\mathrm{4}} and {\mu }_{\mathrm{4}} to the bottom of the structure illustrated in Fig. 8(a). Consider the case when {ϵ}_{\mathrm{4}}={ϵ}_{\mathrm{2}} and {\mu }_{\mathrm{4}}={\mu }_{\mathrm{2}}, coupling of surface polaritons excited at the two interfaces of the paired single-negative layers occurs at small thickness d_{\mathrm{3}} of the mid-layer. As a consequence, the surface polariton resonance frequency splits into two distinct ones. Therefore, d_{\mathrm{3}} serves as an extra parameter that can be adjusted to tune the frequency (wavelength) and direction of coherent emission. Figure 9 shows the calculated emissivity of this trilayer structure for p-polarization at angles of emission equal to 30° and 60°, respectively. In the calculation, the values of {ϵ}^{\prime }\mathrm{s} and {\mu }^{\prime }\mathrm{s} are the same as those in Fig. 8(b) except that {\mu }_{\mathrm{3}}=\mathrm{2}. It can be seen that coherent emission occurs at two distinct frequencies for given values of d_{\mathrm{2}} and d_{\mathrm{3}}. Notice that the relative emissivity peaks can be tuned by changing the value of d_{\mathrm{2}}. Furthermore, the emissivity shown in Fig. 9 indicates that the coherent emission at the higher resonance frequency is highly directional but the coherent emission at the lower frequency is highly angle-independent (diffuse) [68]. Alternatively, coherent emission of radiation from gratingless surface for both s- and p-polarizations has also been shown to be achievable using one-dimensional photonic crystal coated with a polar dielectric, as will be discussed in Section 5.

Structures consideration

How to construct negative m' materials in the infrared? When a time-varying magnetic field is parallel to the axis of a spiral coil of metal wire, an induced magnetic field will occur due to the resultant current in the coil according to Lenz’s law. Diamagnetism can also occur with the split-ring resonator, as shown in Fig. 10(a) [27,69]. The actual structures used straight wires, as shown in Fig. 10(b), to ease the fabrication [15,70]. In order to scale the diamagnetic response to the near infrared, the single split-ring and U-shape cells shown in Figs. 10(c) and (d) were successfully employed [71,72]. With these artificial structures, sometimes called “magnetic atoms,” electromagnetic waves can interact with materials via both electric and magnetic fields. In fact, diamagnetic response can occur with a pair of conducting wires due to the anti-parallel currents induced by a time-varying magnetic field perpendicular to the plane of the wires; see Fig. 10(e) [73,74]. Metamaterials have been demonstrated in the near-infrared and the red light with paired metal strips [75-78]. Another successful variation is the so-called fishnet double-layer structure which has been used to produce NIM in the infrared region [79,80]. Recently, the fishnet structure has been extended to multilayers for negative refraction in the optical frequencies [19]. These recent advances have encouraged the proposal of novel ideas to tailor the thermal emission and absorption characteristics in order to realize spectral and directional selection based on metamaterials.

The magnetic response existing between the metallic strips and the film allows the structure to behave as a single-negative material, with a negative permeability (real part) and a positive permittivity. Meanwhile, the bulk metallic film also serves as a nonmagnetic material with a negative permittivity (real part) and a positive permeability in the near infrared. Consequently, surface magnetic polaritons can be excited in the proposed structure, resulting in coherent thermal emission as discussed in the preceding section. Consider the structure that is made of periodic metal strips with a dielectric spacer deposited on a metallic film, as depicted in Fig. 11(a). Without the spacer, it is simply a binary grating. For simplicity, silver is selected as the material for the strips and (opaque) film, and silicon dioxide is used as the spacer. In practice, the silver film, whose thickness is much greater than the radiation penetration depth, can be deposited on a substrate (not shown). The calculated reflectance using RCWA of the structure is shown in Fig. 11(b) for geometric parameters L = 500 nm, w = 250 nm, and h = d = 20 nm. The dotted line shows the reflectance of a simple grating (d = 0). A sharp reflectance dip near n = 13780 cm^-1 is attributed to surface plasmon polariton that occurs for both structures. On the other hand, if a 20 nm SiO₂ spacer is added, several additional reflectance dips at n = 5670, 11490, and 16095 cm^-1, corresponding respectively to the fundamental, the second, and the third harmonic modes, appear in addition to the one caused by the surface plasmon. These reflectance dips are attributed to the excitation of magnetic polaritons, as demonstrated by Lee et al. [81]. Magnetic polaritons can be viewed as a resonance with a magnetic response (negative permeability) that is coupled to a nonmagnetic medium [82]. Lee et al. [81] also showed that surface polaritons result in narrow spectral band and in a well-confined direction. However, the dispersion curves for magnetic polaritons are rather flat, resulting in isotropic (diffuse) coherent emission.

Periodic gratings

Energy conversion application

The conversion efficiency for thermophotovoltaic devices can be enhanced by modified reflection and emission spectra using micro/nanostructures [83]. 1D and 2D gratings can support cavity modes as well as surface polaritons. As mentioned in the previous section, the excitation of surface waves using gratings can result in coherent thermal emission [12,13,66]. The cavity resonance modes and surface polaritons can interplay for the development of thermal emission source with specific requirements. For example, a TPV radiator is a thermal emitter that usually works in the operating wavelength region of typical GaSb-related TPV cells, which transfer the photon energy into electricity. A number of periodic microstructures have been developed to enhance the performance of TPV radiators. Heinzel et al. [5] fabricated 2D tungsten gratings and achieved an emittance of 0.7 at the wavelength of 1.6 μm with the help of thermally excited surface plasmons. Sai et al. [84] developed 2D deep periodic tungsten microcavities and measured an emittance higher than 0.8 at wavelengths from 0.5 to 1.8 μm and emission angles between 0° and 30°, and an emittance higher than 0.65 at 60°. Chen and Zhang [85] proposed a concept of complex gratings, based on the superposition of two simple binary gratings, for potential application as thermophotovoltaic (TPV) radiators. They showed that by carefully selecting the parameters, the emittance peak from the 1D complex grating can be enhanced and is insensitive to the direction. In another study, Chen and Zhang [86] used the concept of complex gratings with doped silicon to enhance the performance of infrared detectors. Fu and Tan [87] proposed a photovoltaic conversion device in which silicon layer and a metallic grating is formed in a way as shown in Fig. 12(a). Note that the silicon dioxide layer on top of the silicon layer serves as an antireflection coating. Numeric simulations indicate that cavity modes can be excited inside the grooves of the grating, resulting in selectively enhanced absorption of photons with energy above the silicon gap energy in the silicon if the geometries of the grating are selected suitably, as shown in Fig. 12(b). It is suggested by noting the difference in the silicon layer thickness when the structure is with and without the grating that this structure may help to reduce the thickness of the silicon layer in convectional Si-based solar cells.

Application in materials processing

Temperature non-uniformity is a critical problem in rapid thermal processing (RTP) of wafers because it leads to uneven diffusion of implanted dopants and introduces thermal stress. One cause of the problem is non-uniform absorption of thermal radiation, especially in patterned wafers, where the optical properties vary across the wafer surface. Recent development in RTP has led to the use of millisecond-duration heating cycle, which is too short for thermal diffusion to even-out the temperature distribution. The feature size is already below 100 nm and is smaller than the wavelength (200-1000 nm) of the flash-lamp radiation. A number of researchers have modeled the radiative properties of different patterned structures on wafers and obtained reasonable agreement with experimental results. Erofeev et al. [88] modeled the radiation interaction with 2-D patterned wafers by solving the Maxwell equations using a finite element method coupled with the boundary integral equation. Hebb et al. [89] measured the reflectance of a memory die, logic die, and the backside of various multilayered wafers to assess the effectiveness of thin-film optics in providing approximations for the properties of patterned wafers. Tada et al. [90] evaluated the effects of thin SiO₂ film patterns on a Si wafer through the combination of coherent and incoherent approaches and compared the calculated results with experimental measurements. Liu et al. [91] predicted the radiative properties of patterned Si wafers through models based on FDTD and finite-volume time-domain (FVTD). The patterned structures were Si gratings, SiO₂ film on top of flat Si wafers, and SiO₂ films on top of Si gratings. These investigations are for relatively simple patterns with features in the order of micrometers. Chen et al. [41] and Fu et al. [43] recently performed a systematic numerical study of the radiative properties of selected patterns that may be found in device structures in advanced CMOS technology. The smallest feature size is 30 nm and the spectral region is between 200 nm to 1000 nm, which is the emission band from the flash-lamp used for millisecond processing. The effects of different temperatures, dielectric functions, patterns, polarization, angle of incidence, and wavelengths were explored. The limitation and usefulness of EMT were also addressed.

Enhancement and suppression of transmission

Transmission enhancement through subwavelength hole arrays in a metal film has stimulated numerous studies about controlling light transmission in nanometer scales using subwavelength apertures [92]. Similarly, one-dimensional (1D) metallic slit arrays have drawn much attention because the transmittance can also be significantly enhanced for transverse magnetic (TM) waves. A large number of studies have been conducted to investigate the physical origins of transmission enhancement through metallic slit arrays in the spectral range from ultraviolet to near-infrared [93-96]. The transmission enhancement is generally attributed to the combined effects of surface plasmon excitation and cavity resonance, as well as the dynamic diffraction of light [95]. Following the mathematic rules discussed in Ref. [97], Lee et al. [42] further improved the grating formulation for arbitrary incidence angle and polarization and showed that, depending on the spectral region, the enhanced transmission can be attributed to Wood’s anomaly, cavity resonance, and the effective-medium behavior.

Very large transmission enhancement and strong field localization can be achieved from nanoscale metallic slit arrays for mid-infrared radiation. The calculated energy density and Poynting vector distributions, as shown in Fig. 13, reveal that the EM fields are localized in the near field around the slit exit and inlet [98]. The result suggests that infrared radiation could be confined, at least in one dimension, to a length scale as small as 1/1000 wavelength, with 10-fold increase in the energy flux near the slit exits compared to that of the incident wave. This finding may enable construction of infrared nanoscale heating sources, which hold promise in applications such as the nanothermal patterning on polymers and nanoscale ablation of biomaterials.

Submicron metallic slit arrays with different geometry were designed and fabricated on silicon substrates [99]. The normal transmittance of three fabricated gold slit arrays was measured with an FTIR spectrometer at wavelengths between 2 and 15 μm. The experimental results were compared with those calculated from RCWA, as shown in Fig. 14 for the normal transmittance for both TE and TM waves. It is noted that the infrared transmittance is strongly polarization dependent. The agreement between the measurement and RCWA modeling results demonstrates the feasibility of quantitative tuning of the radiative properties by employing periodic micro/nanostructures.

One-dimensional photonic crystals

Photonic crystals (PCs) can also be used to tune thermal emission characteristics. Lin et al. [7] fabricated 3D tungsten PCs with enhanced absorption/emission at wavelengths from 1.5 to 1.9 μm. Chan et al. [100] performed a direct calculation of thermal emission from 3D PC. A TPV radiator can also be made of 1D PCs, whose unit cell consists of a 10-nm-thick tungsten and a 60-nm-thick alumina [101]. Metal-dielectric PCs with alternating layers of Zn, Se and Au can enhance the thermal emission in the mid-IR region [102]. PCs have also been suggested for use as thermal barrier coatings [103].

Because of the existence of an effective evanescent wave, a metallic thin film deposited on a semi-infinite 1D PC can support surface waves coupled with propagating waves in air [104]. Lee, Fu and Zhang [105] proposed a concept of constructing coherent thermal emission source using a multilayer structure, which is made of a polar material and a one-dimensional photonic crystal (1D PC) in the half plane, as shown in Fig. 15(a). The unit cell of a 1D PC is a binary layer consisting of a dielectric (type a) on both sides of a dielectric (type b) with a total thickness (lattice constant) of \mathrm{\Lambda }= d_a + d_b, where d_a = a₁ + a₂. SiC was chosen as the polar material to have coherent emission in the mid-infrared region. The surface termination is determined by the thickness of the dielectric (a₁) located at the surface of the PC. The key to tuning thermal emission is the excitation of the surface wave between the SiC and the PC because an effective evanescent wave exists in the PC’s stop band. Very high emission peaks were predicted at certain wavelengths in well confined directions, as illustrated in Fig. 15(b) for TE waves. The two bands correspond to the excitation of cavity modes and surface waves, respectively [106].

The concept has been extended and experimentally demonstrated with a truncated SiO₂/Si₃N₄ binary PC on Ag/Ti films deposited on a silicon substrate, as shown in Fig. 16(a). The thicknesses were obtained from fitting the reflectance dip wavelengths as d₁ = d₂ = 153 nm and the thickness of the surface termination layer is d_t = 100 nm [107]. The dispersion relation for surface waves at the interface between homogenous media is not applicable to PCs. Nevertheless, the surface-wave dispersion relation for 1D PCs can be obtained using the supercell method. The dispersion relation obtained by solving the eigenvalue equation for the supercell structure is shown in Fig. 16(b) for the TE wave. The measured dispersion relation based on reflectance dips lies on the dispersion curve of the PC-on-Ag structure in the stop band of the photonic crystal. The measured data agree well with the dispersion relation [108,109]. The results demonstrate the feasibility of constructing coherent emission sources based on truncated 1D PC.

An ab initio method was used to design coherent thermal emission sources with multilayered structures [110]. Thermal emission control can also be achieved with 2D PC structures [111,112]. PCs can also be coupled with gratings to achieve unique emission characteristics [113]. Surface wave resonance conditions are very sensitive to temperature changes [114]. Accurate measurements of thermal emission from microstructures remain a daunting task due to the lack of understanding of the optical properties at high temperatures.

Future directions and challenges

Because of the important applications to energy transport and conversion, the study of engineered surfaces with desired thermal radiative characteristics using controlled micro/nanostructures has emerged as a new frontier in thermophysics research. Future directions include the development of high-temperature coherent emission sources as well as complex multidimensional nanostructures with both electric and magnetic responses. Though many different methods have been proposed for obtaining novel optical and thermal radiative properties with metamaterials and other nanostructured materials, significant challenges still remain in the practical development of these materials for applications in the visible to infrared spectral range and at high temperatures.

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