Nanoscale. Realization of near-perfect absorption in the whole reststrahlen band of SiC COMMUNICATION. Introduction

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COMMUNICATION Cite this:, 2018, 10, 9450 Received 28th February 2018, Accepted 28th April 2018 DOI: 10.

1 COMMUNICATION Cite this:, 2018, 10, 9450 Received 28th February 2018, Accepted 28th April 2018 DOI: /c8nr01706a Realization of near-perfect absorption in the whole reststrahlen band of SiC Dongxue Chen, a Jianjie Dong, a Jianji Yang, b Yilei Hua, c Guixin Li, d Chuanfei Guo, d Changqing Xie, c Ming Liu c and Qian Liu * a,e rsc.li/nanoscale Materials used for outdoor radiative cooling technologies need not only be transparent in the solar spectral region, but also need to have a broadband perfect absorption in the infrared atmospheric transparency window (infrared-atw). Silicon carbide (SiC) has been thought to be a potential candidate for such materials. However, due to the near-perfect reflection of electromagnetic waves in the whole reststrahlen band (RB) of SiC, which is within the infrared-atw, perfect absorption in the whole RB remains a challenge. Here by constructing a cone pillar double-structure surface on SiC, a near-perfect absorption (>97%) of normally incident electromagnetic waves in the whole RB has been realized experimentally. Simulation results reveal that the dominant reason for the near-perfect absorption is the efficient coupling of incident electromagnetic waves into the bulk evanescent waves in the freespace wavelength range (10.33 μm, μm) and the efficient coupling of incident electromagnetic waves into the surface phonon polaritons in the free-space wavelength range (10.55 μm, 12.6 μm). Our findings open up an avenue to enhance the absorption performance of SiC in infrared-atw, and may lead to many new applications. Introduction Since different optical properties of a material have different applications in science and technology, it is very important to change and adjust the optical properties of a material. 1 6 A a CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing , China. liuq@nanoctr.cn b Department of Electrical Engineering, Stanford University, California 94305, USA c Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing , China d Department of Materials Science and Engineering, Southern University of Science and Technology, No Xueyuan Blvd, Shenzhen, Guangdong , China e Suzhou Institute of Nano-tech and Nano-bionics, Chinese Academy of Sciences, Suzhou , China Electronic supplementary information (ESI) available: Sample preparation, SEM characterization, measurement of the absorptivity, and numerical simulation. See DOI: /c8nr01706a These authors contributed equally. conventional method to modulate the optical properties of a material is to adjust its atomic composition or/and change its inherent microstructure. However, in many cases, we need some innate properties of materials and therefore cannot change their composition and inherent microstructure, resulting in a stupendous difficulty in modulation of the optical properties of materials. In recent years, the rapid development of nanofabrication has sparked the appearance of artificial structures, which have realized some unique optical properties in noble metals such as gold and silver while maintaining their composition and inherent structure For example, broadband high-performance absorption and antireflection have been realized in the visible and infrared spectral regions, respectively. 9,10 Although noble metal artificial structures can meet many requirements for applications, they are still limited in some technologies such as outdoor radiative cooling technology An ideal material for outdoor radiative cooling devices needs not only to be transparent in the solar spectral region, but also to have a broadband perfect absorption in the mid-infrared atmospheric transparency window (the free-space wavelength range from 8 μm to13μm) in order to provide perfect thermal radiation ability, which is equal to its absorption ability according to Kirchhoff s law of thermal radiation. 12 Obviously, the noble metal artificial structures cannot satisfy the transparent requirement in the solar spectral region, 14 although they may be able to achieve a broadband high-performance mid-infrared absorption. 15 SiC is a polar crystal with highly transparent properties in the solar spectral region, but it has a reststrahlen band (RB) with a near-perfect reflection within a mid-infrared region from μm to 12.6 μm. If we can change the reflection property of SiC in its RB with a surface with artificial structures while maintaining its composition and inherent structure, it will be a promising material for many mid-infrared applications. Recent studies have shown that SiC with a grating structure surface can achieve discrete wavelength near-perfect absorption in the RB However, near-perfect absorption in the whole RB, so far, has not been realized yet. 9450,2018,10, This journal is The Royal Society of Chemistry 2018

2 In this work, we propose a cone pillar double-structure surface (CPDSS) that is composed of a periodic array of micron-sized SiC pillars and a nonperiodic array of nano-sized SiC cones, and demonstrate numerically and experimentally that by using the CPDSS, near-perfect absorption of normally incident electromagnetic waves can be realized in the whole RB of SiC. Our findings open up an avenue to control the absorption and reflection properties of SiC in its RB, and make it very promising for applications in outdoor radiative cooling, broadband mid-infrared generation, 14 stealth technology, 19 and mid-infrared detection. 20,21 Results and discussion The interaction between incident electromagnetic waves and lattice vibrations of SiC can be described by Huang s equations as 22,23 d 2 W * dt 2 ¼ b 11W * þ b 12 E * ; ð1þ P * ¼ b 21 W * þ b 22 E * ; ð2þ where W * is the displacement of the effective positive ion relative to the effective negative ion, P * is the dielectric polarization, and E * is the electric field. b 11, b 12, b 21 and b 22 are expressed as b 11 = ω 2 p TO, b 12 ¼ b 21 ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðω LO2 ω TO2 Þε 1 ε 0 and b 22 =(ε 1)ε 0, where ε, ε 0, ω TO and ω LO are the high frequency dielectric constant, the vacuum dielectric constant, the transverse optical (TO) phonon angular frequency and the longitudinal optical (LO) phonon angular frequency, respectively. The angular frequency ω can be expressed as ω =2πc 0 /λ 0, where c 0 and λ 0 are the speed and the wavelength of electromagnetic waves in vacuum, respectively. The dispersion relation of electromagnetic waves in SiC based on eqn (1) and (2) is shown in Fig. 1a. It can be found that there is no electromagnetic wave whose wave vector is larger than zero in the RB (the region between the two red dashed lines in Fig. 1a) of SiC. In other words, the incident electromagnetic waves in the RB cannot propagate in SiC. This is the physical origin of the near-perfect reflection property of a bulk SiC (see the black solid curve in Fig. 1b). In order to investigate modes of electromagnetic waves that can propagate in the RB of SiC, the real part Re(ε) of its dielectric constant ε is plotted in Fig. 1c (the black solid curve). Clearly, Re(ε) is smaller than zero in the RB. Therefore, the electromagnetic p wave that can be expressed as a 0 exp½ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ReðεÞk 0 ðn * r * ÞŠ when Im(ε) = 0 (i.e., the vibration damping loss is neglected) can propagate in the RB of SiC. Here a 0, k 0, n * k and * r are the initial amplitude, the wave vector of the electromagnetic wave in vacuum, the unit of the wave vector, and the position vector, respectively. Obviously, this electromagnetic wave decays rapidly with the propagation distance and thus can be called the bulk evanescent wave (BEW). The electromagnetic energy of the BEW can be converted into Fig. 1 Dispersion relation, reflectivity and absorptivity of a bulk SiC. (a) Dispersion relation of electromagnetic waves in SiC. (b) Simulated reflectivity R and absorptivity A of a SiC sample with planar surfaces. (c) Real part Re(ε) and imaginary part Im(ε) of the dielectric constant of SiC. The region between two red dashed lines is the RB. the thermal energy of SiC when Im(ε) = 0 (the blue solid curve in Fig. 1c). This indicates that a part of the incident electromagnetic waves can be converted into BEWs of a bulk SiC with planar surfaces, and its absorptivity A is larger than zero in the RB (see the blue solid curve in Fig. 1b). However, A is very small because the refractive index has a large mutation in the air/sic interface in most areas of the RB. In the range from λ 0 = μm toλ 0 = 12.6 μm, Re(ε) < 1 and hence surface phonon polaritons (SPhPs) can exist on the surfaces of SiC, which are surface electromagnetic waves coupled with phonons. The SPhPs also decay rapidly with the propagation distance, and can be absorbed by SiC due to the collisions of the coupled phonons. However, SPhPs, whose wave vector k SPhP on pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a planar surface can be expressed by k SPhP ¼ k 0 ε=ðε þ 1Þ, cannot be directly excited by the incident electromagnetic wave because its wave vector is larger than that of the incident electromagnetic wave at the same frequency. 24 This implies that it is necessary to add some structures on the surfaces of SiC for solving the wave vector mismatching problem. In order to realize the absorption of incident electromagnetic waves in the whole RB, we propose the CPDSS whose structure is schematically shown in Fig. 2a. Firstly, the nanosized cones of the CPDSS can gradually change the refractive index near the air/sic interface in the RB; so the coupling efficiency between incident electromagnetic waves and BEWs can be significantly improved in the range from λ 0 = μm to λ 0 = μm due to the relatively large value of the skin This journal is The Royal Society of Chemistry 2018, 2018, 10,

vector in the direction perpendicular to E * and the direction Fig. 2 Surfaces and absorptivity of different SiC samples. (a) Schematic of the CPDSS. (b) Sizes of different cones.

3 vector in the direction perpendicular to E * and the direction Fig. 2 Surfaces and absorptivity of different SiC samples. (a) Schematic of the CPDSS. (b) Sizes of different cones. (c) Simulated absorptivity A of a SiC sample with the CPDSS at different polarization angles α. (d) A SiC surface with only pillars. (e) A SiC surface with only cones. (f) Simulated absorptivity A of a SiC whose surface has only cones (or only pillars) at α = 0. The region between two red dashed lines in (c, f) is the RB. depth (Fig. S1 ). However, this coupling efficiency cannot be significantly improved in the range from λ 0 = μm toλ 0 = 12.6 μm due to the very small value of the skin depth. Secondly, SPhPs can be efficiently excited by using the tips of cones and the sharp edges of pillars in the range from λ 0 = μm toλ 0 = 12.6 μm, resulting in the efficient coupling of incident electromagnetic waves to SPhPs in this range. The corresponding physical origin is explained as follows. The tip size of each cone (or the size of the sharp edge of each pillar) of the CPDSS can be denoted by 2δ, and the diffracted waves of the normally incident electromagnetic waves at the tip of each cone (or the sharp edge of each pillar) can be approximately expressed as a d f 1 ðzþf 2 ðr? Þ X þ1 k k E *¼ 1 c kk E * expðik k E *r k Þ, where a d is a constant amplitude, f 1 (z) and f 2 (r ) are functions of z and r, respectively, k ke * is a component of the wave vector in the direction parallel to E *, r and r k are components of the position parallel to E *, respectively, and c kk E * / sinðδk ke *=2Þ=ðδk ke *=2Þ.25 The k * component of the diffracted waves has a relatively ke large amplitude when k * is located in the range 2π ke δ ; 2π. δ Because δ λ 0, there is a component of the diffracted waves whose k * can meet k * ¼ k SPhP in the range 2π ke ke δ ; 2π.In δ other words, SPhPs can be effectively excited by the diffracted waves from the tips of cones and the sharp edges of pillars of the CPDSS. Considering both the possibility of the fabrication and the absorptivity of SiC samples (Fig. S2 ), a set of optimized geometrical parameters of the CPDSS is chosen as follows: the width of the unit cell including a pillar is 8 μm in both the x and y directions; the diameter and height of pillars are D = 6 μm and H = 8.3 μm, respectively; the number of cones in the unit cell is 258 and their sizes are shown in Fig. 2b. The cones with the same size are approximately uniformly distributed on the top surface of pillars and the substrate. Fig. 2c shows the simulated absorptivity A of a SiC sample with the CPDSS at different polarization angles α. It can be seen that the simulated A is larger than 0.91 in the whole RB for different polarization angles and the difference among the absorptivity curves of different polarization angles in the RB is very small. These results indicate that the near-perfect absorption property of a SiC sample with CPDSS is almost independent of the polarization direction of the incident linearly polarized electromagnetic wave. This is mainly because the structural units (i.e., the pillar and the cone) of CPDSS are axisymmetric and the direction of the incident magnetic field is parallel to the xy plane. This result is also valid for a normally incident complex electromagnetic wave, which can be decomposed as a linear superposition of a series of linearly polarized electromagnetic waves. To understand the role of pillars and that of cones in absorbing the incident electromagnetic waves, the simulated A for a SiC surface with only pillars (Fig. 2d) and that with only cones (Fig. 2e) in the RB is given in Fig. 2f. It can be found that for a SiC surface with only pillars, the simulated A has a large value near two sides of the RB but has a relatively small value near the center of the RB. Although the simulated A of a SiC sample whose surface has only cones has a value of about 1 in a wide area near the center of the RB, its value is located in the range from 0.5 to 0.9 near two edges of the RB. Therefore, the CPDSS uses the complementary effect of pillars and cones to realize the near-perfect absorption in the whole RB. In order to deeply understand the mechanism of the nearperfect absorption, the normalized electric field intensity distributions in an observation plane passing through the central axes of transverse pillars at various free-space wavelengths are plotted in Fig. 3a f (see Fig. S3 for more details). It can be found that in the range (λ 0 = μm, λ 0 = 12.6 μm), the elec- 9452, 2018, 10, This journal is The Royal Society of Chemistry 2018

Fig. 3 Simulation results of electric field intensity. (a f) The normalized electric field intensity distributions at (a) λ 0 = 12.6 μm, (b) λ 0 = 12.2 μm, (c) λ 0 = 11.7 μm, (d) λ 0 = 11.

Inset: SEM image of the cross section of a pillar. (b) SEM image of the cross section of the fabricated CPDSS obtained by milling the sample along the direction shown in (a) (pink dashed line).

4 Fig. 3 Simulation results of electric field intensity. (a f) The normalized electric field intensity distributions at (a) λ 0 = 12.6 μm, (b) λ 0 = 12.2 μm, (c) λ 0 = 11.7 μm, (d) λ 0 = 11.1 μm, (e) λ 0 = 10.7 μm and (f) λ 0 = 10.4 μm. Fig. 4 Experimental results of reflectivity and absorptivity of SiC samples. (a) SEM image of the fabricated CPDSS taken at a 30 tilt angle. Inset: SEM image of the cross section of a pillar. (b) SEM image of the cross section of the fabricated CPDSS obtained by milling the sample along the direction shown in (a) (pink dashed line). (c) Measured reflectivity R and absorptivity A of a SiC sample with a planar incident surface. (d) Measured absorptivity A (the solid line with dots) of a SiC sample with the fabricated CPDSS. (e) Measured reflectivity R and absorptivity A of SiC samples whose surface has only cones or pillars. The region between two red dashed lines in (c, d) is the RB. tric field is strongly confined on the surfaces of cones and within the gaps (with width G =2μm) among pillars (Fig. 3a e), demonstrating that SPhPs on the surfaces of cones and that within the gaps are efficiently excited. These results suggest that in the range (λ 0 = μm, λ 0 = 12.6 μm), where Re(ε) < 1, the near-perfect absorption of incident electromagnetic waves is mainly due to the excitation of SPhPs. In the range (λ 0 = μm, λ 0 = μm), the electric field is mainly confined inside cones and pillars, reflecting that the incident electromagnetic wave can be effectively converted into the BEW. When the BEW propagates back and forth in pillars, it can be completely absorbed by them. Therefore, the main reason for the near-perfect absorption in the range (λ 0 = μm, λ 0 = μm) is that the incident electromagnetic waves are effectively converted into BEWs. To further verify the above analyses, the Poynting vectors at various free-space wavelengths, whose direction represents the direction of energy flow, are given in Fig. S4a w. Clearly, the electromagnetic energy flows to the surfaces of cones and pillars in the range (λ 0 = μm, λ 0 = 12.6 μm) (Fig. S4a u ), but it mainly flows into cones and pillars (a small part of it circulates between the pillars and the gaps) in the range (λ 0 = μm, λ 0 = μm) (Fig. S4v w ). These results support the above analyses. To further illustrate the performance of the CPDSS, we carried out a series of experiments. The fabrication process of the CPDSS is shown in Fig. S5 S8. Scanning electron microscope (SEM) images of the CPDSS fabricated on a SiC sample are shown in Fig. 4a and b. For the fabricated CPDSS, the pillar parameters are G 2 μm, D 6 μm and H 8.3 μm, and the sizes of most of the cones approximate their corresponding design values. In the case of the SiC sample with only a planar incident surface, the measured R is relatively large and the measured A is relatively small for normally incident electromagnetic waves in the whole RB, as shown in Fig. 4c. In the case of the SiC sample with the CPDSS, the measured A is larger than 0.97 for normally incident electromagnetic waves in the whole RB, as shown in Fig. 4d. Obviously, these experimental results agree well with their corresponding simulation results in Fig. 1b and 2c. It is worth noting that in some areas of the RB, the measured A of the SiC sample with the CPDSS is slightly larger than the simulated A, which is mainly due to the existence of some small grooves and ridges on the sidewalls of the fabricated pillars (Fig. 4b and S9 ). The main trend of measured A is consistent with that of the corresponding simulated A both for the case of the SiC sample with only cones (Fig. S10a ) and for the case of the SiC sample with only pillars (Fig. S10b ), as shown in Fig. 4e. These experimental results support the analyses on the roles of pillars and cones. The differences between the experimental result in Fig. 4e and their corresponding simulation results in Fig. 2f are caused by fabrication errors. It s worth pointing out that although our research focuses on the case of the normal incidence of electromagnetic waves, the near-perfect absorption in the whole RB can also be realized at small incident angles (Fig. S11 ). This journal is The Royal Society of Chemistry 2018, 2018, 10,

5 Conclusions In summary, we have proposed the CPDSS, which is composed of a periodic array of micron-sized SiC pillars and a nonperiodic array of nano-sized SiC cones, and have demonstrated that using the CPDSS, near-perfect absorption of normally incident electromagnetic waves can be realized in the whole RB of SiC. Furthermore, we have demonstrated that the dominant reason for the near-perfect absorption is the efficient coupling of incident electromagnetic waves into the BEWs in the free-space wavelength range (10.33 μm, μm) and the efficient coupling of incident electromagnetic waves into the SPhPs in the free-space wavelength range (10.55 μm, 12.6 μm). Our work can lead to new applications in outdoor radiative cooling devices, broadband thermal mid-infrared emitters for medical diagnostics and biological analysis, stealth devices, and mid-infrared detectors. Conflicts of interest The authors declare no conflict of interest. Acknowledgements We would like to thank Prof. Jingsong Wei for his help in infrared measurement. This work was supported by the National Key Research and Development Program of China (2016YFA ), the CAS Strategy Pilot Program (XDA ), the National Natural Science Foundation of China ( , ), and the Eu-FP7 Project (No ). References 1 N. Yu and Z. Gaburro, Science, 2011, 334, Y. Shen, M. Soljacic, J. Joannopoulos and S. Johnson, Science, 2014, 343, X. Ni, Z. J. Wong, M. Mrejen, Y. Wang and X. Zhang, Science, 2015, 349, A. Moreau, C. Ciraci1, J. J. Mock1, R. T. Hill, Q. Wang, B. J. Wiley, A. Chilkoti and D. R. Smith, Nature, 2012, 492, F. Cheng, J. Gao, T. S. Luk and X. Yang, Sci. Rep., 2015, 5, T. Xu, Y. K. Wu, X. Luo and L. J. Guo, Nat. Commun., 2010, 1, T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov and X. Zhang, Science, 2004, 303, G. Kang, Y. Fang, I. Vartiainen, Q. Tan and Y. Wang, Appl. Phys. Lett., 2012, 101, V. G. Kravets, F. Schedin and A. N. Grigorenko, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 78, P. Fan, B. Bai, J. Long, D. Jiang, G. n. Jin, H. Zhang and M. Zhong, Nano Lett., 2015, 15, E. Rephaeli, A. Raman and S. Fan, Nano Lett., 2013, 13, A. P. Raman, M. A. Anoma, L. Zhu, E. Rephaeli and S. Fan, Nature, 2014, 515, L. Zhu, A. P. Ramanb and S. Fan, Proc. Natl. Acad. Sci. U. S. A., 2015, 112, Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He and N. X. Fang, Nano Lett., 2012, 12, M. M. Hossain, B. Jia and M. Gu, Adv. Opt. Mater., 2015, 3, R. C. J. Greffet, K. Joulain, J. Mulet, S. Mainguy and Y. Chen, Nature, 2002, 416, C. Arnold, F. Marquier, M. Garin, F. Pardo, S. Collin, N. Bardou, J. Pelouard and J. Greffet, Phys. Rev. B: Condens. Matter Mater. Phys., 2012, 86, Y. Chen, Y. Francescato, J. D. Caldwell, V. Giannini, T. W. W. Ma, O. J. Glembocki, F. J. Bezares, T. Taubner, R. Kasica, M. Hong and S. A. Maier, ACS Photonics, 2014, 1, R. A. Stonier, SAMPE J., 1991, 27, M. P. Touse, G. Karunasiri and K. R. Lantz, Appl. Phys. Lett., 2005, 86, A. D. Stiff, S. Krishna, P. Bhattacharya and S. W. Kennerly, IEEE J. Quantum Electron., 2001, 37, K. Huang, Nature, 1951, 167, K. Huang, Proc. R. Soc. London, Ser. A, 1951, 208, D. N. Basov, M. M. Fogler and G. D. A. Fj, Science, 2016, 354, J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, ,2018,10, This journal is The Royal Society of Chemistry 2018

PHYSICAL REVIEW B 71,

PHYSICAL REVIEW B 71, Coupling of electromagnetic waves and superlattice vibrations in a piezomagnetic superlattice: Creation of a polariton through the piezomagnetic effect H. Liu, S. N. Zhu, Z. G. Dong, Y. Y. Zhu, Y. F. Chen,