Open Access
Add to BibSonomy
Abstract
Metamaterial absorbers open a new door for the design of optical harvesting devices ranging from the microwave to optical regimes. The top resonator in these structures is critical for the function of metamaterial absorbers. The resonant frequency, bandwidth, and maximum absorption mainly depend on the choice of material, shape, and size of the top resonator. The maximum absorption is generally impaired as the size of the resonator changes, due to the high sensitivity of impedance matching with the medium. In this paper, we experimentally demonstrate a metamaterial perfect absorber with unabated absorption as its resonator’s size changes. The perfect absorber is based on an array of metal squares inscribed with a hollow square. The absorption maxima stay above 98% as the size changes from 600 to 1500 nm in the mid-infrared region, agreeing with simulated results yielding an absorption of ~100%. The unabated absorption properties can be interpreted by the equivalent circuit theory. Moreover, the experimental absorption remains above 91% for incident angles change up to 50°, both for TE and TM polarization. Our work offers a method for achieving stable perfect absorption in sensing, filtering, and selective thermal emission.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials are artificial composite materials that function by manipulating the complex effective parameters of the system, i.e. electric permittivity and magnetic permeability of metamaterials. This unique property permits to achieve new optical devices that require a negative, zero refractive index with extremely low absorption loss [1, 2]. One of their particular application, electromagnetic metamaterial perfect absorbers (MMPA), have attracted much attention since selective absorption can be obtained by exciting plasmonic resonances at specific wavelengths [3–5]. The basic concept in the design of a MMPA is to minimize the reflectance through impedance matching with the medium in a system that includes a continuous layer of metal to eliminate the transmittance. Since the first demonstration of MMPA, this field has spawned an extensive list of systems for applications on thermal imaging [6, 7], solar cells [8–10] and sensing [7, 11, 12]. Existing MMPA devices not only demonstrate narrow single band [4], dual-band [13–15], or multi-band absorption [16–18], but they can also maintain broadband absorption [19–21], with resonant frequencies in the GHz [4, 15, 22, 23], THz [6, 7, 12, 20, 24, 25], infrared [11, 14, 26] and optical ranges [8, 9, 27].
Narrow band MMPAs are critical in sensing [11], absorption filtering [28] and selective thermal emission [5, 29]. In a sandwiched metal-dielectric-metal structure, the first layer of the metallic resonator plays a key role in engineering impedance matching of MMPAs [4]. The size, material and shape of the resonator determine its resonant frequency and the absorptance of a narrow band MMPA [14, 30–32]. For example, a dual-band MMPA with a maximum absorption of 94% is experimentally accomplished by breaking the symmetry of a cross structure [33]. Circular patterns, rings, squares and H-shaped top resonators have demonstrated tunability on both resonant frequencies and absorptance [14, 30–32]. Although the resonant frequencies of a MMPA can be governed by modifying the size of the resonators, their absorptance is impaired as the size changes due to the high sensitivity of the impedance matching requirement [14, 30, 33, 34]. Based on an equivalent circuit theory, we propose a geometry that reduces the sensitivity of impedance matching between mediums as the size of a MMPA changes— using a metal square inscribed with a hollow square (MSIHS) that shows nearly perfect absorption in the infrared region as the size changes, extending the capabilities of other impedance matching designs in the literature [35, 36]. We experimentally studied the absorption of the MMPAs which is in agreement with our simulation.
2. Method
The proposed MMPA is a sandwiched structure and consists of two gold elements: a gold square resonator with an inscribed hollow square and a gold ground plane separated by a dielectric Ge film, as schematically shown in Fig. 1(a), 1(b) and 1(c). To investigate the proposed structure, we perform computational simulations by employing a finite difference time domain (FDTD) numerical method from Lumerical. The wavelength dependent variables A(λ), R(λ) and T(λ) are absorptance, reflectance and transmittance, respectively. The A(λ) depends on the other two as 1−R(λ)−T(λ). The bottom metallic film is thicker than the skin depth of light in the IR region and thus impedes transmission: i.e., T(λ) = 0 and the A(λ) can be simply determined by A(λ) = 1−R(λ). The refractive indexes of Au, Ge and Si are modelled using fitted optical data from Refs [37–39], respectively. The background refractive index is set to be 1. We simulate one unit cell of a given pattern using periodic boundary conditions (BC) in the x and y boundaries and perfectly matched layer BC in the propagation direction z. For the oblique incidence simulations, Bloch boundary condition is adopted. We decrease the mesh size until the results converge.
Fig. 1 Geometry of the MMPA structure: (a) 3D schematic view; (b) Top view; (c) Side view. SEM image with fake color of periodically patterned array (d) and single unit cell (e). The periodic ax = ay = 2 μm. The thickness of the resonator is 50 nm and the bottom of the blocking gold film is fixed at 150 nm separated by Ge with td = 120 nm. The scale bars in (d) and (e) are 2 μm and 500 nm, respectively.
The Au and Ge films are deposited sequentially by electron beam evaporation. The top resonators (l = 1 μm) are patterned by electron beam lithography and a lift-off process. The patterns are periodically distributed in both x and y directions forming a 2D lattice with a periodicity of 2 μm, as in the scanning electron microscope (SEM) images show in Fig. 1(d). The symmetric MSIHS unit enables totally polarization independent absorption at a normal illumination (not shown here). Figure 1(e) shows a fabricated single resonator in which the practical size is very close to the designed value with a ± 4 nm error. The corner of the pattern is not ideal right-angled and becomes rounded with a radius of 2 nm because of the fabrication technique limitation.
The normalized R(λ) was characterized within the infrared region by using a Fourier-transform infrared (FTIR) spectrometer equipped with a mercury cadmium telluride detector cooled with liquid nitrogen. Oblique incidence measurements were conducted by mounting the sample on a variable-angle specular reflection accessory to collect the angle-resolved reflectivity data up to 50°. The 300 μm × 300 μm sample was tested by focusing the beam into a spot of approximately 200 μm in diameter.
3. Results and discussion
To understand the strong optical absorption behaviour of the MMPA, we analysed the energy dissipation in the multilayers and field distribution in the resonator. For a non-magnetic material, the absorbed electromagnetic power can be defined by the formula:
where is the angular frequency, is the imaginary part of the permittivity and the is the total electric field confined in the material. As can be seen from Fig. 2, the majority of the energy is dissipated as ohmic loss within the Au resonator, which is ten orders of magnitude greater than that of the loss in dielectric and bottom gold film. This is due to the localized surface plasmon resonances in the gold resonator, as the electric field profile shows in Fig. 3(a).Fig. 2 Typical energy dissipation (logarithmic scale) in the MMPA at a wavelength of ~3500 nm: resonator (z = 295 nm), dielectric (z = 210 nm) and bottom gold film (z = 75 nm), respectively.
Fig. 3 (a) Near-field intensity of MMPA (logarithmic scale); (b) Dependence of the maximum absorption and resonant wavelength with the Ge thickness td. The resonator size l is fixed at 1000 nm; (c) The absorption spectra of MMPA with increased size from 800 to 1200 nm with td = 120 nm; (d) Relationship of peak absorption and resonant wavelength with resonator size l.
Figure 3(a) demonstrates the electric filed intensity profile in the x-y plane at the interface between resonator and dielectric at the resonant wavelength of ~3500 nm, indicating that the surface plasmons are excited. If the MMPA is used for specific applications, the tunability is critical in the MIR region. Its tunability is illustrated in Fig. 3(b)–3(d). The top resonator and bottom film allow the antiparallel currents between the two metallic layers to couple to the magnetic field, as illustrated in Fig. 4(a) and 4(b). Since the magnetic field is coupled to the antiparallel currents, the magnetic response can be tailored by changing the distance between the metal layers (dielectric layer). The critical role of the spacer thickness, which controls the strength of coupling, is demonstrated in Fig. 3(b). When td = 120 nm, nearly 100% absorption (0% reflectance) is achieved, and as the dielectric layer thickness td increases or decreases the coupling strength is reduced, leading to a reduced absorption. For the td = 120 nm case, the impedance of free space matches that of the MMPA i.e. Z(λ) = (μeff/εeff)1/2, and a perfect absorption can be obtained. Figure 3(c) and 3(d) present the absorption spectra of MMPA for various sizes of the resonator. As the size increases, the maximum absorption has no distinct drop, maintaining ~100%, while the resonant wavelength increases linearly as the size increases. These phenomena can be interpreted by an equivalent circuit theory, as shown in Fig. 4(c) [35]. As the size of resonator increases, the resistance (R) increases, the Q-factor decreases and thus leads to broadening of full width at half maximum (FWHM) [3]. For comparison, we also analyze the square patch (same size with MSIHS) based on the equivalent circuit theory, as shown in Fig. 4(b).
Fig. 4 (a) Schematic charge distribution in TM mode: square resonator (left), MSIHS (right); RLC equivalent circuit of square resonator MMPA (b) and MSIHS resonator MMPA (c); (d) Simulated charge density distribution (logarithmic scale) of MSIHS resonator MMPA at a wavelength of ~3500 nm.
As shown in Fig. 4(b) and 4(c), the equivalent impedance of the circuits Z1 and Z2 can be expressed as:
where ω is the radiation frequency, the total resistance R, inductance L and capacitance C are determined by the amount of power absorbed due to ohmic losses, the finite electric currents oscillating in the metallic resonator and the ground plane, and the charge accumulation induced by the external field, respectively. Where R’ = 8R, L’ = L/4 and C’ = C/8, respectively. As shown in Fig. 2, the main loss occurs in the metallic resonator and thus we only consider the ohmic losses from the resonator. In Eq. (2), L, R, C can be defined as:Where, d is dielectric thickness, N is the number of turns of an equivalent solenoid, μ0 is the magnetic constant, ρ is electrical resistivity, ε is absolute dielectric constant. Given that the impedance of each individual subcomponent scales with size just through changes on the dielectric thickness d, at the resonant frequency, ω0 = 1/, Z1 and Z2 can be further expressed according to Eq. (2) and (3) as a function of l:
where A and B are constants. As can be concluded from Eq. (4), the impedance matching of MSIHS is less sensitive to l, and thus the as l changes, its maximum absorption shows a smaller change than the square resonator.The proposed MMPA is totally polarization insensitive due to the symmetry of its top resonator. The fourfold rotational symmetry of the resonator atop ensures the absorption at normal incidence to be transverse electric (TE) and transverse magnetic (TM) polarization-independent, meaning that it has an appreciable efficiency and versatility, desirable to operate in different conditions and in various environments. Figure 5(a) plots the angular dependence of absorption at resonance wavelength under TE and TM illumination, as the left and right panel shows, respectively. The experimental results are in good agreement with the FDTD simulations until θ = 50°. The absorption for TE and TM polarization decreases with the increases of the incident angle. It remains above 91% (FDTD: 93%) for TE polarization up to 50°; it remains above 92% (FDTD: 96%) for TM polarization up to 50°.
Fig. 5 (a) Simulated and experimental directional absorptance of MMPA as a function of θ at λ = ~3500 nm. td = 120 nm; l = 1000 nm. (b) Simulated (solid lines) and experimental (dashed lines) absorption of MMPAs with different values of l (left to right: 800, 900, 1000, 1100, 1200 nm).
To verify the unabated absorption of MSIHS structure, we measure the reflection spectra of MMPA as its size changes (l = 800, 900, 1000, 1200 nm). As shown in Fig. 5(b), it is clear that the measured absorption spectra agree with the simulated ones. The maximum absorption remains unabated (~98%) as l changes, while in a typical MMPA design, as the size changes the maximum absorption will be impaired, especially at nanoscale sizes [14, 30, 33, 34, 40]. The perfect absorption range of MSIHS is from 600 (lower limit)-1500 (upper limit) nm. Although an obvious absorption decrease starts from l = 1600 nm, the maximum absorption is ~96%, while at the same point, that of the square patch is ~74% (see Appendix A, Fig. 6). We ascribe the unabated absorption to the lower sensitivity of the MSIHS to size changes, as explained through our equivalent circuit model. As shown in Eq. (4), the impedance-matching degree of MSIHS is less sensitive to l. In contrast to the absorption properties of MSIHS, the absorption strength of a full square is significantly lowered as the resonator size changes (see Appendix B, Fig. 7) [34]. It is worth noting that there are discrepancies between experiments and simulations—we conjecture that they are mainly due to the tolerances in the fabrication and the imperfection in measurements.
In conclusion, we proposed a MMPA with a resonator based on a metal square inscribed with a hollow square with nearly perfect absorption—the experimentally measured absorption is ~98% and the simulated value is ~100%. It still maintains a high absorption of 92% when the incident angles raises up to 50°. It is polarization insensitive for both TE and TM illumination, due to the symmetric properties of MSIHS. Moreover, the MSIHS structure provides a salient property in that its absorption is unabated as the resonator size changes, because it is less susceptible to size parameters based on the equivalent circuit theory. Our method provides a pathway to fabricate a perfect absorber with unabated absorption with respect to size change.
Appendix A
Appendix B
Funding
National Natural Science Foundation of China 51272038 and 61474015; National Program on Key Basic Research Project (973 Program) 2013CB933301; L.V.B. was supported by China Postdoctoral Science Foundation (2017M622992).
References
1. S. Tretyakov, A. Urbas, and N. Zheludev, “The century of metamaterials,” J. Opt. 19(8), 080404 (2017). [CrossRef]
2. I. B. Vendik and O. G. Vendik, “Metamaterials and their application in microwaves: A review,” Tech. Phys. 58(1), 1–24 (2013). [CrossRef]
3. S. Gu, J. Barrett, T. Hand, B.-I. Popa, and S. Cummer, “A broadband low-reflection metamaterial absorber,” J. Appl. Phys. 108(6), 064913 (2010). [CrossRef]
4. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef] [PubMed]
5. X. 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. 107(4), 045901 (2011). [CrossRef] [PubMed]
6. N. Landy, C. Bingham, T. Tyler, N. Jokerst, D. Smith, and W. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79(12), 125104 (2009). [CrossRef]
7. P. Kung and S. Kim, “Terahertz metamaterial absorbers for sensing and imaging,” in Proceedings of Progress in Electromagnetics Research Symposium, 2013), 232–235.
8. Y. Wang, T. Sun, T. Paudel, Y. Zhang, Z. Ren, and K. Kempa, “Metamaterial-plasmonic absorber structure for high efficiency amorphous silicon solar cells,” Nano Lett. 12(1), 440–445 (2012). [CrossRef] [PubMed]
9. K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2(1), 517 (2011). [CrossRef] [PubMed]
10. Y. Peng, Z. Fanlu, L. Ziyuan, Z. Zhiqin, G. Alexander, F. Lan, T. Hoe, J. Chennupati, and W. Zhiming, “Giant optical pathlength enhancement in plasmonic thin film solar cells using core-shell nanoparticles,” J. Phys. D Appl. Phys. 51(29), 295106 (2018). [CrossRef]
11. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010). [CrossRef] [PubMed]
12. F. Alves, D. Grbovic, B. Kearney, and G. Karunasiri, “Microelectromechanical systems bimaterial terahertz sensor with integrated metamaterial absorber,” Opt. Lett. 37(11), 1886–1888 (2012). [CrossRef] [PubMed]
13. M. Li, H.-L. Yang, X.-W. Hou, Y. Tian, and D.-Y. Hou, “Perfect metamaterial absorber with dual bands,” Prog. Electromagnetics Res. 108, 37–49 (2010). [CrossRef]
14. P. Yu, J. Wu, E. Ashalley, A. Govorov, and Z. Wang, “Dual-band absorber for multispectral plasmon-enhanced infrared photodetection,” J. Phys. D Appl. Phys. 49(36), 365101 (2016). [CrossRef]
15. H. Li, L. H. Yuan, B. Zhou, X. P. Shen, Q. Cheng, and T. J. Cui, “Ultrathin multiband gigahertz metamaterial absorbers,” J. Appl. Phys. 110(1), 014909 (2011). [CrossRef]
16. X. Shen, T. J. Cui, J. Zhao, H. F. Ma, W. X. Jiang, and H. Li, “Polarization-independent wide-angle triple-band metamaterial absorber,” Opt. Express 19(10), 9401–9407 (2011). [CrossRef] [PubMed]
17. L. Huang and H. Chen, “Multi-band and polarization insensitive metamaterial absorber,” Prog. Electromagnetics Res. 113, 103–110 (2011). [CrossRef]
18. J. W. Park, P. V. Tuong, J. Y. Rhee, K. W. Kim, W. H. Jang, E. H. Choi, L. Y. Chen, and Y. Lee, “Multi-band metamaterial absorber based on the arrangement of donut-type resonators,” Opt. Express 21(8), 9691–9702 (2013). [CrossRef] [PubMed]
19. J. A. Bossard, L. Lin, S. Yun, L. Liu, D. H. Werner, and T. S. Mayer, “Near-ideal optical metamaterial absorbers with super-octave bandwidth,” ACS Nano 8(2), 1517–1524 (2014). [CrossRef] [PubMed]
20. L. Huang, D. R. Chowdhury, S. Ramani, M. T. Reiten, S.-N. Luo, A. J. Taylor, and H.-T. Chen, “Experimental demonstration of terahertz metamaterial absorbers with a broad and flat high absorption band,” Opt. Lett. 37(2), 154–156 (2012). [CrossRef] [PubMed]
21. K. Chaudhuri, M. Alhabeb, Z. Wang, V. M. Shalaev, Y. Gogotsi, and A. Boltasseva, “Highly Broadband Absorber Using Plasmonic Titanium Carbide (MXene),” ACS Photonics 5(3), 1115–1122 (2018). [CrossRef]
22. Y. Huang, G. Wen, W. Zhu, J. Li, L.-M. Si, and M. Premaratne, “Experimental demonstration of a magnetically tunable ferrite based metamaterial absorber,” Opt. Express 22(13), 16408–16417 (2014). [CrossRef] [PubMed]
23. Y. Huang, L. Yang, J. Li, Y. Wang, and G. Wen, “Polarization conversion of metasurface for the application of wide band low-profile circular polarization slot antenna,” Appl. Phys. Lett. 109(5), 054101 (2016). [CrossRef]
24. H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: Design, fabrication and characterization,” Opt. Express 16(10), 7181–7188 (2008). [CrossRef] [PubMed]
25. Q. Xie, G. Dong, B.-X. Wang, and W.-Q. Huang, “Design of Quad-Band Terahertz Metamaterial Absorber Using a Perforated Rectangular Resonator for Sensing Applications,” Nanoscale Res. Lett. 13(1), 137 (2018). [CrossRef] [PubMed]
26. X.-T. Kong, L. Khosravi Khorashad, Z. Wang, and A. O. Govorov, “Photothermal Circular Dichroism Induced by Plasmon Resonances in Chiral Metamaterial Absorbers and Bolometers,” Nano Lett. 18(3), 2001–2008 (2018). [PubMed]
27. M. K. Hedayati, F. Faupel, and M. Elbahri, “Tunable broadband plasmonic perfect absorber at visible frequency,” Appl. Phys. A. 109(4), 769–773 (2012). [CrossRef]
28. J.-B. Brückner, J. Le Rouzo, L. Escoubas, G. Berginc, O. Calvo-Perez, N. Vukadinovic, and F. Flory, “Metamaterial filters at optical-infrared frequencies,” Opt. Express 21(14), 16992–17006 (2013). [CrossRef] [PubMed]
29. J. A. Mason, S. Smith, and D. Wasserman, “Strong absorption and selective thermal emission from a midinfrared metamaterial,” Appl. Phys. Lett. 98(24), 241105 (2011). [CrossRef]
30. N. Zhang, P. Zhou, D. Cheng, X. Weng, J. Xie, and L. Deng, “Dual-band absorption of mid-infrared metamaterial absorber based on distinct dielectric spacing layers,” Opt. Lett. 38(7), 1125–1127 (2013). [CrossRef] [PubMed]
31. B. Zhang, J. Hendrickson, and J. Guo, “Multispectral near-perfect metamaterial absorbers using spatially multiplexed plasmon resonance metal square structures,” J. Opt. Soc. Am. B 30(3), 656–662 (2013). [CrossRef]
32. Z. H. Jiang, S. Yun, F. Toor, D. H. Werner, and T. S. Mayer, “Conformal dual-band near-perfectly absorbing mid-infrared metamaterial coating,” ACS Nano 5(6), 4641–4647 (2011). [CrossRef] [PubMed]
33. K. Chen, R. Adato, and H. Altug, “Dual-band perfect absorber for multispectral plasmon-enhanced infrared spectroscopy,” ACS Nano 6(9), 7998–8006 (2012). [CrossRef] [PubMed]
34. B. T. Kearney, F. Alves, D. Grbovic, and G. Karunasiri, “Al/SiOx/Al single and multiband metamaterial absorbers for terahertz sensor applications,” Opt. Eng. 52(1), 013801 (2013). [CrossRef]
35. A. Sellier, T. V. Teperik, and A. de Lustrac, “Resonant circuit model for efficient metamaterial absorber,” Opt. Express 21(S6), A997–A1006 (2013). [CrossRef] [PubMed]
36. M. Pu, C. Hu, M. Wang, C. Huang, Z. Zhao, C. Wang, Q. Feng, and X. Luo, “Design principles for infrared wide-angle perfect absorber based on plasmonic structure,” Opt. Express 19(18), 17413–17420 (2011). [CrossRef] [PubMed]
37. R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86(23), 235147 (2012). [CrossRef]
38. H. H. Li, “Refractive index of silicon and germanium and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 9(3), 561–658 (1980). [CrossRef]
39. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998), Vol. 3.
40. P. Pitchappa, C. P. Ho, P. Kropelnicki, N. Singh, D.-L. Kwong, and C. Lee, “Dual band complementary metamaterial absorber in near infrared region,” J. Appl. Phys. 115(19), 193109 (2014). [CrossRef]
