1. Introduction

For ordinary thermal radiation, the emission band is broad and the peak wavelength and total radiated amount only depend on the temperature. The radiation energy of natural objects at room temperature mainly locates in the long-wavelength infrared. The thermal control, such as radiation cooling and thermophotovoltaic power generation, is vital and beneficial to humans. The control strategy with micro/nano size constructed materials [1–7] has attracted growing attention due to its excellent capability and flexibility to manipulate the thermal radiation within thin thickness. For example, wearable radiative heating textile is proposed to warm up human body by nanoporous metallized polyethylene textile. It has been indicated that the metallized structure possesses low infrared radiation emissivity on the textile outer surface and high infrared radiation reflectivity on the inner surface [1]. In addition, radiative cooling materials for solar absorbers that rely on high emissivity in the infrared band to cool the absorbers which have high absorption efficiency in visible are also presented [2]. Infrared thermal radiation can be transferred to specific bands by artificial controlling the emissivity of the material in each band [8–13]. Frequency-selective perfect absorbers [14–20] are used as the surface coating to adjust the infrared radiation band of the targets to the non-atmospheric windows (non-AW), which ensures the targets invisible to the infrared detectors [19–23]. Resonances based multiband perfect absorbers [19–20] are designed to transfer the radiation to non-AW and realize multi-spectral stealth, but the absorption peak is narrow and the average absorption rate in atmospheric windows (AW) is still high. Metal based multilayer emitters [8,21–22] exhibit higher radiative cooling efficiency in vacuum and practical environments, but such a metal based infrared stealth coating will shield microwave signals which is pivotal to the microwave communication. All dielectric based absorbers [23–24] are proposed to achieve prefect absorption in a broadband of wavelength which are capable of manipulating terahertz radiation. The fabricated structures mentioned above are mainly based on nanolithography, and thus lead to time consumption and energy cost. Distributed Bragg reflector (DBR) is a kind of reflection structure composed of high and low refractive index dielectric layers with optical thickness of 1/4 wavelength. DBRs own mature production process and have many applications in spectral sensing and imaging in a wide range of wavelength [25–28]. Despite one-dimensional photonic crystal (1D-PC) [29–30] based absorbers can realize perfect absorption through introducing the defect states, the absorptance is sensitive to incident angle and absorption band is limited. Besides, the metamaterial based absorbers [15,19–20] are either limited by the bandwidth or the simultaneous control over non-atmospheric windows (6.3-7.5µm) and atmospheric windows (8-14µm). Thus, absorbers that can be manipulated to selectively control the thermal radiation in the long wave infrared with no dependence on the polarization are desired.

In this paper, an all dielectric frequency-selective absorber has been proposed to control the thermal radiation characteristics in long-wavelength infrared. The structure is constructed with two spectral regions: the selective transparent part where high transmission in 5-8 µm and high reflectance in 8-14 µm, and the absorption part which absorbs the transmitted waves in the non-AW [5-8 µm]. The bandwidth of absorbance and polarization dependence are both demonstrated. The ideal absorption properties make it a perfect coating for suppressing the thermal emission of LWIR. Our work may find applications in wearable radiative heating textile design or thermal-protective coatings

2. Theoretical analysis and structure design

According to Kirchhoff’s law, a body’s radiation absorptivity and thermal emissivity are identical for a given frequency, direction, and polarization. The radiation of black body follows the Planck’s Law. However, the LWIR thermal radiation suppression imposes the emission spectrum to be rectangular which means the emission rates are uniformly high in non-AW and low enough in AW. The principle of our absorber design is based on the Kirchhoff's law of thermal radiation, the emittance of an object is equal to its absorption rate under the condition of thermal balance. Therefore, the emissivity of the multilayer metamaterials can be characterized through controlling the absorption [14,21]. In other words, the demand on LWIR AW suppression turns to achieving both high absorption in the non-AW and low absorption in the AW.

The bulk materials with loss in MWIR non-AW and transparent in LWIR AW are rare in nature. Therefore, the composite structure is necessary to realize the above mentioned LWIR thermal radiation suppression. Among choices, the strategy shown in Figs. 1(a)–1(c) that two materials of optical quarter-wave thickness with high and low refractive indexes alternatively stacked, is most suitable to achieve broadband total reflection in LWIR. As shown in Fig. 1(d), the incident light normally illuminates the multilayer structure, the eigenmatrix of the composite structures which contains the multilayer film and substrate can be expressed as:

The absorption (A) spectrum of the structure is obtained by A = 1-R-T.

 

Fig. 1. Schematic of frequency-selective absorber. (a) Selective transmission part which consists of alternately placed Ge and ZnSe has high transmission in 5-8 µm and high reflectance in 8-14 µm. (b) Absorption part constructed of PbS and ZnSe layers that can absorb most of electromagnetic waves in 5-14 µm. (c) Frequency-selective absorber is optimized by the combination of two parts. (d) Diagram of a multilayer dielectric film with plane wave excitation. dj and nj represents the thickness and index of each layer, respectively. ${\theta _0}$ is the incident angle and ${\theta _{k + 1}}$ is the angle of emergence (e) Real(n) and imaginary(k) part of refractive index of PbS in LWIR. PbS owns high index around 4 in LWIR and exhibits loss among 6-10µm and 12-14 µm.

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The design principle of DBR is employed to from the initial structure of reflection part. With selected high and low refractive index materials, the reflection amplitude and phase of each layer can be tuned to achieve the desired reflection curve by adjusting the thickness of each layer. As shown in Fig. 1(a), the selective transparent part is designed where the non-AW waves are allowed to transmit while the AW waves are almost totally reflected. The lossless materials with refractive index difference are selected to design this part. The selective transparent part is designed with germanium (Ge) and zinc selenide (ZnSe), whose refractive index is around 4.02 and 2.43 in LWIR [31]. Alternately arranged multilayers with Ge on the top are optimized to reach maximum reflectance in LWIR AW.

Then the broadband absorption part is designed to absorb the transmitted non-AW infrared wave ranging from 5-8 µm. The real(n) and imaginary(k) part of the refractive index of lead sulfide (PbS) is plotted in Fig. 1(e) [31] and piecewise cubic spline interpolation is adopted to fit the curves. As shown in Fig. 1(b), the combined multilayers of PbS with ZnSe result in uniformly broadband absorption. Figure 1(c) illustrates the schematic geometry of the whole structure, where the absorption part is below selective transparent part. The substrate is calcium fluoride (CaF₂) with refractive index around 1.35.

With the combination of two parts, an initial structure with limited spectral response is proposed which still needs further structural parameters optimization. Several target absorptances in LWIR are defined to form the ideal absorption curve which have high absorptance in non-AW and low absorptance in AW. A merit function, representing the difference between the absorption curve of the initial structure and ideal curve, is defined as:

3. Simulation results and discussion

With the above strategy, a frequency-selective absorber that is capable of controlling the thermal radiation is achieved. The material and thickness of each layer are listed in Table 1 marked as Structure 1(Struct. 1). Struct. 1 has 20 layers composed of Ge, ZnSe and PbS with a whole thickness of 9.5µm. The simulation is carried out using FEM method under normal incidence with x-polarization. As shown in Fig. 2(a), Struct. 1 exhibits perfect rectangular absorption up to 95% within a bandwidth of 1.2µm in non-AW, while the average absorption is below 2% in LWIR AW. The calculated results are also demonstrated in Fig. 2(a), which coincide perfectly with simulated curves. To clearly demonstrate the physics behind the reflection and transmission spectra, the FEM method is adopted to illustrate the electric field and energy distributions at different wavelengths. It can be seen from the reflection that the selective transmission region has not totally reflect the LWIR AW waves, but the absorption rate of the whole structure is very low in 8-12 µm. This is due to the lossless PbS in the range of 10-12 µm. The normalized electric field distributions of Struct. 1 at wavelengths 5µm, 7µm and 9µm are shown in Figs. 2(b)–2(d), respectively. At wavelength of 7 µm, the electromagnetic wave transmits through the top selective transparent part and is absorbed by the absorption part. For wavelengths at 5µm and 9µm, most of the electromagnetic waves are reflected back, only a small portion transmitted but not absorbed by the bottom part.

 

Fig. 2. (a) Simulated and calculated transmission (T), reflection (R) and absorption (A) spectra of Struct. 1 versus normal incidence with x-polarization. The normalized electric field profile distributions of Struct. 1 at (b) 5µm, (c) 7µm and (d) 9µm. The structure is marked with red line.

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Table 1. The material and thickness of each layer in the all-dielectric multilayer structures.

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As illustrate in Fig. 1(e), PbS exhibits lossy property at wavelengths between 12-14 µm. In order to ensure the low emissivity in the whole AW, the selective transparent part should be designed to totally reflect back the incidence in the lossy bands of PbS. As shown in Fig. 3(a), Struct. 2 with low infrared emissivity within a broader band is optimized and it exhibits rectangular absorption with the average absorption rate 90% in 6.2-7.8 µm. The average absorption rate is below 3% in 8-14 µm. The calculated results are also coincide perfectly with simulated curves. The normalized electric field distributions of the Struct. 2 is similar to those in Struct. 1. As shown in Fig. 3(a), the structure reflects most of the electromagnetic waves in the common bands (8-10 µm and 12-14 µm) of AW. The lossy bands of PbS in AW also remain low absorption. The normalized electric field profile shown in Fig. 3(d) further proves that the selective transparent part reflects most of the infrared waves.

 

Fig. 3. (a) Simulated and calculated transmission (T), reflection (R) and absorption (A) spectra of Struct. 2 versus normal incidence of x-polarization waves. The normalized electric field profile distributions of the Struct. 2 at wavelengths (b) 5µm, (c) 7µm, (d) 9µm and (e)11µm. The structure is marked with red line. For wavelength of 5µm, 7µm and 9µm, the intensity of transmitted electric field is very weak because of the strong reflection in 5µm and 9µm, and high absorption in 7µm. At wavelength of 11µm, most of the electromagnetic waves are transmitted through the structure.

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Due to the rotational symmetry, the designed frequency-selective absorbers are insensitive to the polarization of the normal incidence. To investigate the influence of incident angles on the absorption for different polarizations, the absorption as function of different polarization as indicated in Figs. 4(a) and 4(d) is simulated. The spectral absorptivity of Struct. 1 for incident angles within 60 degrees are presented in Figs. 4(b) and 4(e). As the incident angle increases, the absorption for both polarizations gradually decrease. However, the average absorption for x and y-polarization remains more than 89% and 85%, respectively, within the band from 6.3µm to 7.5µm for incidence angles up to 40 degree. Similar figure for Struct. 2 is depicted in Figs. 4(c) and 4(f). Compared with Struct. 1, the absorption bandwidth is wider and the average absorption rate decreases more slowly as the angle increases. The average absorption within 6.3-7.5 µm is more than 91% for incidence angles less than 40 degree for x-polarizations, and more than 92% for y-polarization with the incidence angles up to 55 degree. Thus, it can be concluded that the high efficiency frequency-selective absorbers which are insensitive to the incident angle and polarization states are obtained. Based on Kirchhoff’s law, the structures designed above can control the thermal radiation and have emissivity peaks within 5-7um instead of the LWIR AW. Taking advantages of the suppression of thermal radiation in AW and the propagation obstacles in non-AW, the designed structure is valuable for the design of thermal-protective coatings.

 

Fig. 4. Diagram of oblique incidence with electric field of (a) x-polarization and (d) y-polarization. Simulated absorption spectra versus incident angle for x polarization of (b) Struct. 1 and (c) Struct. 2. Simulated absorption spectra versus incident angle for y-polarization of (e) Struct. 1 and (f) Struct. 2. The two structures, for both polarizations, maintain a good rectangular absorptivity curve even with large oblique incidence angle at 45 degrees.

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4. Conclusion

In summary, we propose an all-dielectric multilayer absorber to control the thermal radiation in LWIR. The structures exhibit excellent absorption up to 95% within a bandwidth of 1.2µm in non-AW, and remains low absorption in AW with normal incidence. High absorption is maintained with a large incident angle and the absorber is almost insensitive to the polarization states of the incident waves. In other words, the structures can suppress the thermal emission of LWIR and keep high emissivity at a wide range of emission angles in non-AW. With the excellent performance, our designed broadband absorber for thermal radiation control in long-wavelength infrared can be valuable in many applications such as infrared sensing, thermal imaging and thermal-protective coatings.