Metasurface for Multiwavelength Coherent Perfect ... - IEEE Xplore

Open Access

Metasurface for Multiwavelength Coherent Perfect Absorption Volume 9, Number 1, February 2017 Dong Xiao Keyu Tao Qiong Wang Yuexia Ai Zhengbiao Ouyang

DOI: 10.1109/JPHOT.2016.2636019 1943-0655 © 2016 IEEE

IEEE Photonics Journal

Metasurface for Multiwavelength Coherent

Metasurface for Multiwavelength Coherent Perfect Absorption Dong Xiao,1 Keyu Tao,1 Qiong Wang,1 Yuexia Ai,2 and Zhengbiao Ouyang1 1 THz

Technical Research Center, Shenzhen Key Laboratory of Micro-Nano Photonic Information Technology, College of Electronic Science and Technology, Shenzhen University, Shenzhen 518060, China 2 Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Opto-Electronic Engineering, Shenzhen University, Shenzhen 518060, China

DOI:10.1109/JPHOT.2016.2636019 C 2016 IEEE. Translations and content mining are permitted for academic research only. 1943-0655 Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Manuscript received September 21, 2016; accepted November 30, 2016. Date of publication December 7, 2016; date of current version December 20, 2016. This work was supported in part by the National Natural Science Foundation of China under Grant 61275043, Grant 60877034, Grant 61307048, Grant 61107049, and Grant 61171006 and in part by the Shenzhen Science Bureau under Grant 200805 and Grant CXB201105050064A. Corresponding author: Z. Ouyang (e-mail: [email protected]).

Abstract: We design and investigate a metasurface for achieving multiband coherent perfect absorption (CPA) in the mid-infrared region. The operating wavelengths and bandwidth of CPA for the metasurface can be precisely tailored through structure design. The coherent absorption of each operating wavelength can be independently modulated by adjusting the phase difference between two coherent waves. Meanwhile, the coherent absorption performance is insensitive to polarized and oblique incident angles. The scalability of our proposed metasurface design can also be extended to other technical wavelength ranges, such as the optical and terahertz regions, and may find a variety of application areas. Index Terms: Plasmonics, metamaterial, nanostructures, spatial coherence and absorption.

1. Introduction Metasurfaces are artificially engineered planar metamaterials, which have exotic optical properties that are unattainable in natural materials [1]. Metasurfaces are able to mold the flow of light by dramatically changing its amplitude, phase and polarization in deep subwavelength scale, thus, paving the way for vast applications including light manipulation [2]–[4], light absorption [5], nonlinear optics [6], and hyper-spectral imaging [7]. In particular, light absorption plays a key role in a variety of applications such as solar energy to electricity converting, bio-sensing, and thermal emitting. In fact, metamaterial absorbers with the advantages of perfect light absorption, easy-tunable resonance and subwavelength scale have been intensively investigated and designed covering all technical wavelength range [8]–[11]. However, the operating wavelength and absorption intensity of metamaterial absorbers are determined by their structure. Both of them are hard to actively control, which greatly hampers their further applications such as optical switching and modulation. Recently, the emerging of coherent perfect absorption (CPA) provides a new method to realize tunability of light absorption. The CPA refers to complete light absorption in a lossy material due to the interference of two counter-propagating coherent waves. This is also interpreted as a time-reverse process of a laser [12]. Actually the CPA has been experimentally and theoretically demonstrated

Vol. 9, No. 1, February 2017

6800108



Fig. 1. (a) Schematic of the proposed metasurface in association with two counter-propagating coherent incident waves. (b) Side view of the unit cell of the metasurface where a ZnS slab with thickness d = 0.3 μm is coated with identical pattern silver film with thickness m = 60 nm on both sides. (c) Top view of the unit cell of the metasurface where four square patches with width l1 = 2.2 μm, l2 = 2.3 μm, l3 = 2.4 μm, and l4 = 2.55 μm are labeled in the figure.

in many nano-structure systems such as grating, metamaterial and metasurface [13]–[17] and it is regarded as a versatile platform to realize coherently controlled light absorption/transparency [18], optical activity [19], and selected mode excitation [20]. Nevertheless, just like a laser, CPA is typically featured with single operating wavelength and is hard to extend to broad- or multi-band operation. So far, burgeoning efforts have been devoted to achieve multiband or broadband CPA, for example, multilayered split rings [20] or resistive sheet with specific impedance [21] for microwave region, doped silicon film for terahertz [22], or multilayer doped ITO [23] for infrared region. However, realizable schemes are still limited, especially for infrared and optical region. Furthermore, although the CPA using resistive sheet has very broad operating wave band, when it is used for CPAs in required bands it cannot keeping other bands transparent to light. In addition, fewer previous studies have focused on planer structures. In this work, we demonstrate that a metasurface is able to support multiband CPA, showing many advantages compared with previous works. The optical response, intrinsic loss, and operating wave bands of the metasurface could be easily tuned by changing the structure parameters of each meta-atom, and therefore, it is possible to meet the requirement and condition of CPAs at any specified wavelength and to precisely control the operating bandwidth. The property cannot be found in none resonance structure such as that using resistive film. It also shows good polarization-independent property. Furthermore, it can eliminate additional phase shift that occurs in multilayered structures and remain ultrathin in scale. As an example, we propose a metasurface operating in the region of 10–14 μm, which is known as atmospheric transparency window and is exploited for a variety of applications such as thermal imaging. The CPA occurs at four separated wavelengths and can be dynamically controlled from 0 to nearly 100% by phase modulation independently. The absorption by the metasurface under the illumination of oblique coherent light is further investigated, which shows good angle-insensitive property. The scalability of our metasurface design enables their deployment in the wide wavelength range from optical to terahertz spectra and may be beneficial for many potential applications.

2. Structure Design and Method The configuration of metasurface is shown in Fig. 1, where a thin zinc sulfide (ZnS) slab with thickness d = 0.3 μm is coated with identical patterned silver film with thickness m = 60 nm on both sides. The period of metasurface’s unit cell is = 6.5 μm. The silver film in each unit cell is etched into four square patches with widths l1 = 2.2 μm, l2 = 2.3 μm, l3 = 2.4 μm, and l4 = 2.55 μm, respectively. Therefore, the metasurface is formed by four different periodically arranged meta-atoms, in which each meta-atom is composed by up- and down- patches separated by a dielectric layer.


6800108



As demonstrated in the following, each meta-atom forms a current loop, leading to surface plasmon resonance, namely magnetic resonance. There are four magnetic resonances in the unit cell of the metasurface. The four magnetic resonances can be assumed to be independent and have no coupling effects between any of them. First, we consider the case of two normal counter-propagating coherent waves, named a + and a − , where ± refers to propagating towards z + and z − , respectively. The optical response of the metasurface can be treated as linear superposition of that of each meta-atom. When the metasurface is set at z = 0, the forward and backward complex scattering coefficients of a single meta-atom b i + and b i − can be expressed as bi + a t r a+ = Si + = i i (1) bi − a− r i ti a− where Si (i = 1−4) denotes the scattering matrix of each single meta-atom. Since the two-port system satisfies spatial symmetry and reciprocity, the transmission and reflection complex scattering coefficients of each meta-atom are identical for a ± and denoted as t i , r i . Then, the forward and backward complex scattering coefficients (b ± ) of the whole metasurface can be expressed as 4 b+ bi + = . (2) b− bi − i =1

Due to the deep subwavelength scale feature, the optical response of the meta-atom can be regarded as being dominated by a dipolar resonance described by Lorentzian oscillators, as long as the wavelength is close to intrinsic wavelength λ0 . The dipole resonance could be electric resonance as depicted in [24] or magnetic resonance as shown in our case, and Si can be expressed as [24], [25] λ0i − λ − i di i si Si =

i si

λ0i − λ − i di

λ0i − λ − i si − i di

(3)

where λ0i , di and si refer to the intrinsic resonant wavelength, characteristic length of dissipation loss, and characteristic length of scattering loss of the i-th meta-atom, respectively. It is worth noting that in our proposed structure, the intrinsic wavelength λ0i can be tuned by the patch length li , and the transmittance, reflectance and absorption intensity could be modified by changing the slab thickness d, indicating that dissipation loss di and scattering loss si can be tuned to meet the requirement and condition of specific CPAs. In mathematics, CPA occurs when the eigenvalue of Si is zero at a real wavelength [12]. For symmetric incident coherent waves, the eigenvector is ( a + a − ) = ( 1 1 ) and the eigenvalue s of each meta-atom’s scattering matrix is si . (4) si = (t i + r i ) = 1 + 2i λ0i − λ − i (si + di ) Because of the independence of each meta-atom, four null points can be instantly obtained at resonant wavelengths λ0i (i = 1−4) on the condition that si = di , from which the critical condition of CPA can be obtained as |t i | = |r i | = 0. Thus, multi-wavelength CPA is achieved in our metasurface. In contrast, for anti- symmetric incident coherent waves, the eigenvector is ( a + a − ) = ( 1 −1 ); the eigenvalue is a constant s = 1; the absorption becomes zero, and the metasurface is transparency for both incident waves. The commercial solver Comsol Multiphysics based on full-vector finite-element method is employed to calculate the absorption and field distribution of the metasurface. In the simulation, the optical constant of ZnS is set as n = 2.2 and can be regarded as lossless in mid-infrared region [26]. The silver is described by a Drude model εs = ε∞ − f p2 /(f 2 + i γ f ), where f p = 1.38 × 1016 Hz, γ = 2.73 × 1013 Hz and ε∞ = 3.7 [27]. In the simulation, the periodic boundary is employed in the x- and y- directions and perfect matched layer (PML) in the z direction. The normalized coherent


6800108



Fig. 2. (a) Coherent absorption spectra for single meta-atom with patch length varying from 2 to 2.8 μm, where the inset depicts the schematic of the proposed meta-atom. (b) Linear relationship between wavelength of CPA and patch length. (c) Amplitude spectra of simulated and analytical coherent absorptions, and forward and backward amplitudes of scattered waves for the metasurface in Fig. 1. Four nearly-perfect CPAs occur at λ01 = 10.92 μm, λ02 = 11.38 μm, λ03 = 11.88 μm, and λ04 = 12.57 μm with absorption intensities of 95.4%, 97.2%, 100%, and 100%, respectively. The red dotted line represents the analytical CPA. (d) Coherent absorption spectra changing with polarization angle θ from 0° (electric filed along the x axis) to 90° (electric filed along the y axis).

absorption A c is defined as A c = 1 − (|b + |2 + |b − |2 )/(|a + |2 + |a − |2 ). For simplification, in the simulation the intensity of the two normal counter-propagating coherent waves is set as |a+ |2 = |a− |2 = 0.5, and we assume that the electric field of the two coherent waves is polarized along the x axis. The forward and backward scattering coefficients are calculated by their far-fields using S parameters at z = ±20 μm.

3. Results and Discussion For integrity, we first calculate a metasurface with one identical meta-atom in a unit cell shown in the inset of Fig. 2(a) and with the period of its meta-atom set as 3 μm. The thickness of the dielectric layer is tuned to d = 0.22 μm to satisfy the condition of CPA, and the patch length varies from 2 to 2.8 μm. When illuminated by two coherent waves with phase difference ϕ = 0◦ , the coherent absorption spectra is shown in Fig. 2(a). It’s clearly seen that the CPA wavelength occurs at the resonant peak and is changed along with the patch length. As the patch length increases, the CPA wavelength has a redshift. Fig. 2(b) further indicates that the relationship between the CPA wavelength and the patch length is linear, which is useful for designing CPAs at particular wavelengths. Now we turn to investigate the metasurface with four different meta-atoms in a unit cell as shown in Fig. 1. Its absorption and scattering spectra are shown in Fig. 2(c). The intensity of the scattered waves |b+ |2 and |b− |2 in the region from 10 to 14 μm is exactly equal, which also means |t i | = |r i | (i = 1−4). Four distinct resonant wavelengths are found at λ01 = 10.92 μm, λ02 = 11.38 μm, λ03 = 11.88 μm and λ04 = 12.57 μm, where the transmission and reflection coefficients are equal and almost null (|t i | = |r i | = 0) and nearly perfect coherent absorption occurs accordingly as shown in solid line. The numerical result demonstrates that a metasurface for broadband or multi-band CPA can be achieved by designing different meta-atoms. Furthermore, according to (1)–(3),


6800108



Fig. 3. (a) Coherent absorption of the metasurface versus. wavelength and phase difference ϕ. The white dash line refers to the contour lines of absorption. (b) Phase modulation of absorption at λ = 12.57 μm. The absorption coefficient varies from maximum 1 to minimum 0 as ϕ changing from 0° to 180°. The red circle dotted line is the result of the analytical CPA.

the resonance behavior of the metasurface is the superposition of the dipole resonance of each meta-atom. The theoretical coherent absorption of the metasurface can be expressed as

A ca =

4

m i 2di

i =1

(λ − λ0i )2 + 2di

(5)

where m i is the absorption coefficient of the i-th meta-atom. If m i is set as 0.86, 0.81, 0.88 and 0.93 for i = 1 − 4 and the parameters in (2) are set as d 1 = s1 = 113 nm, d 2 = s2 = 124 nm, d 3 = s3 = 174 nm and d 4 = s4 = 197 nm, the result of analytical coherent absorption shown in dot line agrees well with that of numerical simulation. The absorption spectra of polarized coherent waves are also investigated. The polarized angle θ is defined as the angle between the plane of incidence and the electric field vector. In our study, the initial electric field of the coherent waves is parallel to the plane of incidence (along the x axis) and θ is zero (p-polarized). As θ varies from 0° to 90° (s-polarized), the absorption spectra almost keeps unchanged, as depicted in Fig. 2(d). The result shows that the proposed metasurface structure is insensitive to the polarized angle θ, which is required for many practical applications. It is interesting that although the unit cell with four different meta-atoms has no rotational symmetry, the whole structure is still polarization-independent. This property is actually originated from the fourfold rotational symmetry in the neighboring nine identical unit cells [28]. The phase modulation of coherent absorption is shown in Fig. 3(a), where the absorption of four resonances simultaneously varies from nearly 1 to 0 if the phase difference ϕ changes from 0 to 180°, demonstrating that the metasurface is highly efficient in manipulating multiband light absorption. The white dashed contour line plotted in Fig. 2(a) indicates that the change of coherent absorption at the four different resonant wavelengths follows the same pattern. Actually, the eigenvector of scattering matrix can be depicted as (1 ei ϕ ); according to (1) and (2), there is |b+ | = |b− | = sin2 (ϕ/2) at the four resonant wavelengths, and the theoretical coherent absorption can be obtained as A ca = cos2 (ϕ/2). For clarify, Fig. 3(b) shows the phase modulation at 12.57 μm, in which the coherent absorption A c is modulated from 1 to 0 and back to 1 if the phase difference ϕ varies form 0° to 360°, which agrees well with the theoretical expression of A ca . To better understand the underlying physical mechanism, field distributions for the corresponding resonant wavelengths at z = 0 are calculated. When the metasurface is illuminated by two counterpropagating coherent waves, the currents in the up and down metallic patches at a specific position for a specific wavelength flow in opposite directions and form a current loop. And this generates a strong magnetic dipole moment, which couples to the magnetic field of the incident light, and the coupling leads to strong light absorption in the metallic patches. Such a resonance is also known as magnetic dipole resonance. As shown in Fig. 4, when the coherent waves is symmetric (ϕ = 0°), the resonance is further enhanced by the interference of two coherent waves. At the same time, the intensity of magnetic field is greatly strengthened in the dielectric layer of each


6800108



Fig. 4. Magnetic field distribution |H y |2 in the dielectric slab (z = 0) at each resonant wavelength for phase difference ϕ = 0◦ . (a) λ01 = 10.92 μm, (b) λ02 = 11.38 μm, (c) λ03 = 11.88 μm, and (d) λ04 = 12.57 μm.

Fig. 5. (a) Configuration of the two incident counter-propagating waves with incident angle α; the dash line is the normal of the metasurface. (b) Coherent absorption under different oblique incident angles.

meta-atom at the corresponding wavelength. Thus, the two coherent waves are totally absorbed by the metasurface. On the contrary, if the coherent waves are anti-symmetric (ϕ = 180°), the resonance is completely restrained and the metasurface is transparency for the coherent waves. Therefore, the field distributions prove that the assumption and the aforementioned theory are valid. Thanks to the highly confinement effect of magnetic dipole resonance, each meta-atom works independently. This feature is quite impressive because multiband or broadband CPA can be easily achieved and precisely controlled regardless of additional phase shift. Meanwhile, the thickness of metasurface keeps ultrathin in scale. We mention that, although the size of single meta-atom is less than a quarter of a period in deep subwavelength scale, the meta-atoms keep in large densities within the space in one working wavelength, and therefore, the absorption efficiency still remains considerably high. We point out that the scalability of magnetic dipole resonance ensures that the application of our proposed metasurface can be extended to other wavelength ranges such as the optical and terahertz range [8], [29].


6800108



Angle-insensitive absorption is interesting in many applications. For this purpose, the absorption performance of the proposed bidirectional metasurface under oblique incidence of two coherent waves is further investigated. The configuration of oblique incidence is depicted in Fig. 5(a), two incident counter-propagating coherent waves with incidence angle α illuminate on the metasurface. The phase differenceϕ is fixed at 0° and α is varying form 0° to 60°. As shown in Fig. 5(b), the absorption intensity of the four wave bands slightly decreases as α increases. Even at large oblique incidence angle, for example, α = 60◦ , the absorption intensity at the four resonant wavelengths is still large than 80%. Fig. 5(b) suggests that the multi-wavelength metasurface can perform well in a wide range of incident angle. Meanwhile, the feature is highly flexible in designing optical devices such as switchers and modulators. One beam can act as a control light to modulate the absorption and reflection of another coherent light at oblique incidence. The angle-insensitive property of the metasurface originates from the magnetic dipole resonance in the structure because the incident angle has little influence on it in the meta-atoms [29].

4. Conclusion In conclusion, we theoretically and numerically demonstrated that a metasurface can achieve multiband CPA. The result of theoretical analysis agrees well with that of numerical simulation. Each meta-atom in the metasurface forms a magnetic dipole and its intrinsic optical resonance and dispassion loss can be easily tuned through structure design, enabling CPA at any specified wavelength. The coherent absorption at each operating wavelength can be independently modulated from 0 to nearly 1 by changing the phase differenceϕ between the two coherent waves. The coherent absorption is further investigated for oblique incident angles, revealing the angle-insensitive property of the metasurface and its potential applications. The scalability of magnetic dipole resonance enables our proposed metasurface operating from optical to terahertz range.

References [1] A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science, vol. 339, Mar. 2013, Art. no. 1232009. [2] C. H. Wu, A. B. Khanikaev, and G. Shvets, “Broadband slow light metamaterial based on a double-continuum fano resonance,” Phys. Rev. Lett., vol. 106, Mar. 2011, Art. no. 107403. [3] J. K. Gansel et al., “Gold helix photonic metamaterial as broadband circular polarizer,” Science, vol. 325, pp. 1513–1515, Sep. 2009. [4] N. F. Yu et al. “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science, vol. 334, pp. 333–337, Oct. 2011. [5] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett., vol. 100, May 2008, Art. no. 207402. [6] M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science, vol. 313, pp. 502–504, Jul. 2006. [7] X. L. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett., vol. 107, Jul. 2011, Art. no. 045901. [8] J. M. Hao, J. Wang, X. L. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett., vol. 96, Jun. 2010, Art. no. 251104. [9] X. L. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Appl. Phys. Lett., vol. 104, May 2010, Art. no. 207403. [10] Y. X. Cui et al., “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett., vol. 12, pp. 1443–1447, Mar. 2012. [11] F. Ding, Y. X. Cui, X. C. Ge, Y. Jin, and S. L. He, “Ultra-broadband microwave metamaterial absorber,” Appl. Phys. Lett., vol. 100, Mar. 2012, Art. no. 103506. [12] Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: Time-reversed lasers,” Phys. Rev. Lett., vol. 105, Jul. 2010, Art. no. 053901. [13] W. R. Zhu, F. J. Xiao, M. Kang, and M. Premaratne, “Coherent perfect absorption in an all-dielectric metasurface,” Appl. Phys. Lett., vol. 108, Mar. 2016, Art. no. 121901. [14] J. F. Zhang, K. F. MacDonald, and N. I. Zheludev, “Controlling light-with-light without nonlinearity,” Light-Sci. Appl., vol. 1, Jul. 2012, Art. no. e18. [15] M. Kang, Y. D. Chong, H. T. Wang, W. R. Zhu, and M. Premaratne, “Critical route for coherent perfect absorption in a Fano resonance plasmonic system,” Appl. Phys. Lett., vol. 105, Sep. 2014, Art. no. 131103. [16] X. Fang, M. L. Tseng, J. Y. Ou, K. F. MacDonald, D. P. Tsai, and N. I. Zheludev, “Ultrafast all-optical switching via coherent modulation of metamaterial absorption,” Appl. Phys. Lett., vol. 104, Apr. 2014, Art. no. 141102.


6800108



[17] A. L. Fannin, J. W. Yoon, B. R. Wenner, J. W. Allen, M. S. Allen, and R. Magnusson, “Experimental evidence for coherent perfect absorption in guided-mode resonant silicon films,” IEEE Photon. J., vol. 8, no. 3, Jun. 2016, Art. no. 6802307. [18] A. Gogyan and Y. Malakyan, “Coherent-state-induced transparency,” Phys. Rev. A, vol. 93, Apr. 2016, Art. no. 043801. [19] S. A. Mousavi, E. Plum, J. H. Shi, and N. I. Zheludev, “Coherent control of birefringence and optical activity,” Appl. Phys. Lett., vol. 105, Jul. 2014, Art. no. 011906. [20] G. Y. Nie, Q. C. Shi, Z. Zhu, and J. H. Shi, “Selective coherent perfect absorption in metamaterials,” Appl. Phys. Lett., vol. 105, Nov. 2014, Art. no. 201909. [21] S. C. Li et al. “Broadband perfect absorption of ultrathin conductive films with coherent illumination: Superabsorption of microwave radiation,” Phys. Rev. B, vol. 91, Jun. 11 2015, Art. no. 220301. [22] M. B. Pu et al., “Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination,” Opt. Exp.,, vol. 20, pp. 2246–2254, Jan. 2012. [23] T. Y. Kim, M. A. Badsha, J. Yoon, S. Y. Lee, Y. C. Jun, and C. K. Hwangbo, “General strategy for broadband coherent perfect absorption and multi-wavelength all-optical switching based on epsilon-near-zero multilayer films,” Sci. Rep., vol. 6, Mar. 2016, Art. no. 22941. [24] S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett., vol. 101, Jul. 2008, Art. no. 047401. [25] M. Kang, F. Liu, T. F. Li, Q. H. Guo, J. S. Li, and J. Chen, “Polarization-independent coherent perfect absorption by a dipole-like metasurface,” Opt. Lett., vol. 38, pp. 3086–3088, Aug. 2013. [26] E. D. Palik, Handbook of Optical Constants of Solids. New York, NY, USA: Academic, 1991. [27] X. S. Lin and X. G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett., vol. 33, pp. 2874–2876, Dec. 2008. [28] R. Feng, J. Qiu, L. H. Liu, W. Q. Ding, and L. X. Chen, “Parallel LC circuit model for multi-band absorption and preliminary design of radiative cooling,” Opt. Exp., vol. 22, pp. A1713–A1724, Dec. 2014. [29] Y. Todorov et al., “Optical properties of metal-dielectric-metal microcavities in the THz frequency range,” Opt. Exp., vol. 18, pp. 13886–13907, Jun. 2010.


6800108