Abstract

A broadband absorber in the infrared wavelength range from 1 μm up to 5 μm is designed and demonstrated with stacked double chromium ring resonators on a reflective chromium mirror. The near-perfect broadband absorption is realized by combining the multilayer impedance match in the short wavelength range and the double plasmonic resonances in the long wavelength range, which is illustrated with an equivalent circuit model for the impedance analysis. The broadband absorber is proved to be angle-insensitive and polarization-independent due to the geometrical symmetry. The thermal analysis for heat generation and temperature distributions inside the absorber structure is also investigated.

© 2017 Optical Society of America

1. Introduction

Broadband infrared absorbers have been widely studied recently [1,2] due to their crucial roles in various applications such as solar energy harvesting [3,4], thermophotovoltaic energy conversion [5–7], thermal emission [8,9], thermal imaging [10], and stealth devices [11]. Diverse methods have been considered to obtain broadband absorption based on different mechanisms including the combination of multiple resonances in metasurfaces [4,8,12], exciting interferences in metal-dielectric stacks [3,13–15], achieving impedance match in multilayers with free space [16,17], and the generation of slow light in tapered multilayer waveguides [18–21].

In this paper, a broadband infrared absorber made of stacked double chromium (Cr) ring resonators on a chromium mirror is designed based on the combination of multilayer impedance match in the short wavelength range and the double plasmonic resonances in the long wavelength range. The absorber structure is milled from two pairs of Cr-SiO2 layers with overall thickness of 360 nm on a reflective substrate. Different from combining multiple resonators in the same horizontal plane, the proposed absorber has double Cr ring resonators stacked in the vertical direction. At the same time, the stacked double ring structure can be effectively regarded as one-dimensional metal-dielectric multilayer lattice for satisfying impedance match conditions in the short wavelength range. An equivalent circuit (EC) model is developed to analyze and optimize the broadband absorber according to the transmission line theory for the multilayer impedance in the short wavelength range and the coupled lumped-element LC resonators [22–25] for the resonance impedance in the long wavelength range. The absorption spectra predicted by the EC model agree with both the simulated and measured absorption spectra and can explain the two absorption mechanisms thoroughly. Further investigations on the oblique incidence under different polarizations, resonant mode fields, heat generation and temperature increase are also performed.

2. Absorber design and equivalent circuit model

The designed infrared absorber is based on a multilayer stack consisting of two pairs of Cr-SiO2 layers with 30 nm thick Cr and 150 nm thick SiO2 in each pair deposited on top of a 200 nm thick Cr mirror coated on a silicon wafer. There is an additional 30 nm thick SiO2 protecting layer deposited on top of the multilayer stack to prevent the top Cr layer from oxidation. The multilayer stack is grown by RF sputtering. The Cr is grown in an Ar atmosphere at 5 mTorr pressure at a deposition rate of 0.5 Å/sec  and the SiO2 is grown in a 12:1 mixture of Ar:O2 at a rate of 0.14 Å/sec. Figure 1(a) shows a scanning electron microscope (SEM) image of the deposited Cr-SiO2 multilayer before milling where each layer can be clearly seen. The thick Cr mirror will block any transmission through the sample. At first, the absorption spectrum of the multilayer film is measured using Fourier transform infrared spectroscopy (FTIR). As shown in Fig. 1(b), the experimental absorption is below 50% in the range of 1~5 μm, which can be matched well with simulation (COMSOL Multiphysics software), by using the Cr permittivity of εCr=εCr'+iεCr" shown in Fig. 1(c) calculated according to the Brendel-Bormann model [26–28]. The SiO2 permittivity is equal to a constant εSiO2=2.25.

 figure: Fig. 1

Fig. 1 (a) SEM image of the Cr-SiO2 multilayer film before milling. (b) Absorption spectra of the multilayer film from both experiment (red curve) and simulation (blue curve). (c) The real (solid curve) and imaginary (dashed curve) parts of Cr permittivity.

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The schematic of the designed absorber with stacked double ring resonators is illustrated in Fig. 2(a). The absorber structure is fabricated using Focused Ion Beam (FIB) milling in two steps. First, the top pair of Cr-SiO2 layer is milled to form the top ring resonator; and then the bottom pair of Cr-SiO2 layer is milled to form the bottom ring resonator. During the FIB milling, a SiO2 layer with very thin thickness is remained on top of the second Cr layer to avoid oxidation. Due to the zero transmission from the absorber, the absorption A is merely determined by the reflection R and is equal to A=1R. The Cr layers have the thickness of tm=30 nm and the two SiO2 layers have the thickness of td=150 nm. In one unit cell, the period in x and y directions are both equal to P. For one design, when the period is P=700 nm, the top ring width is wt=350 nm and the bottom ring width is wb=600 nm. The inner hole size of the two rings is the same with wi=175 nm.

 figure: Fig. 2

Fig. 2 (a) Schematic of the designed broadband infrared absorber consisting of stacked double Cr ring resonators milled from two pairs of Cr-SiO2 layers on top of a reflective Cr mirror. (b) Equivalent circuit model of the total impedance for the double-ring absorber consisting of Zmul as a high-pass filter and Zres as a low-pass filter. (c) Transformation of two half-rings of width w and length l into two equal cut-wires of effective width w' and effective length l'. (d) Equivalent circuit for Zres based on the coupled lumped-element LC resonators.

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An equivalent circuit (EC) model is developed to evaluate the broadband absorption mechanism of the designed double-ring absorber by considering the combination of the multilayer impedance match in the short wavelength range and the double plasmonic resonances in the long wavelength range. The multilayer impedance Zmul can be regarded as a high-pass filter with no reflection at high frequencies and the resonance impedance Zres can be treated as a low-pass filter with no reflection at low frequencies. As shown in Fig. 2(b), the EC model is then built up by adding the two impedances together in series to estimate the total impedance of the absorber, Ztot=Zmul+Zres. And the absorption can be calculated as A=1((ZtotZ0)/(Ztot+Z0))2, where Z0 is the impedance of free space.

Zmul can be evaluated according to the transmission line theory by regarding the double-ring resonators as effective one-dimensional metal-dielectric multilayer lattice in the vertical direction [17,29,30],

Zmul=Z(1),andZ(j)=Zj(Z(j+1)iZjtanδj)ZjiZ(j+1)tanδj,j=1,2,...,6
where Z(1) represents the wave impedance of the whole multilayer structure seen from the top and can be calculated layer by layer starting from the bottom Cr mirror with the wave impedance of Z(6) up to the top SiO2 protecting layer with the wave impedance ofZ(1), by considering the phase shift δj and the characteristic impedance Zj for each layer j of the multilayer lattice. δj=fpjκ0Njtj in which κ0 is the wave vector of incident wave, Nj is the complex refractive index and tj is the layer thickness. Particularly, tj is modified by a factor fpj to represent the effective layer thickness due to the material milling.

Zres is estimated based on the coupled lumped-element LC resonators. As shown in Fig. 2(c), when the incident light has the field components of Ex and Hy, each ring resonator can be divided into two symmetric half-ring parts [31–33] of width w and length l by the central line and transformed into two cut-wires of effective width w' and effective length l'. Each cut-wire is a LC resonator consisting of three components: inductor  Lm, resistor Rm and capacitor Cm. The capacitor Ce due to the electric resonance between two neighboring rings is ignored to simplify the circuit since the magnetic resonance is dominant in this structure [34]. Here, Lm can be expressed as the capacitance between two parallel plates separated by a distance [35], Lm=amμ0ltd/w, where μ0 is the permeability of vacuum and am is a numerical factor considering the effective length l' of the cut-wire. Rm=crρl/(wtm) , where cr is a numerical factor, andρ1/σ=R'iωL'=1/(iωε0(εm 1) ) is defined as the combination of intrinsic resistivity R' and inductivity L' [23] of the metal (with relative permittivity of εm) since the contribution of the drifting electrons cannot be neglected at infrared frequencies [22,24,33]. Cm is formed between the half-ring and the Cr mirror due to the magnetic resonance and evaluated by the capacitance between two parallel plates separated by the dielectric spacer [32,35], Cm=bmε0εdw(0.5l)/td, where ε0 is the permittivity of vacuum, εd is the relative permittivity of the dielectric spacer, and bm is a numerical factor representing the effective capacitance area.

The equivalent circuit for Zres is shown in Fig. 2(d) consisting of two LC resonators. The first LC resonator includes Lm1 and Rm1 representing the top ring and Cm1 between the top-ring layer and the Cr mirror. The second LC resonator is similar to the first one but it is formed by the middle ring and the Cr mirror including circuit components of Lm2, Rm2 and Cm2. Meanwhile, when two ring resonators are placed closely, they are coupled through the capacitor  Cc=bcε0εdw1(0.5l1)/td between the two rings separated by the dielectric spacer [36,37]. Eventually, the calculated Zres can be expressed as:

Zres=Cc+Cm2iωCcCm2((2Cc+Cm2)(Cm1Cm2+Cc(Cm1+Cm2))Cc(Cm2(Cm1+Cm2)+Cc(Cm1+3Cm2))+Cc+Cm2iωCcCm2Rm1ω2CcCm2Lm1CcCm2(2+ω(Cc+Cm2)(iRm2+ωLm2)))

3. Demonstration of broadband infrared absorber

The broadband absorption response of the double-ring absorber can be evaluated by combing the two impedances of Zmul and Zres together. As an example, for the absorber with period of P=700 nm, Fig. 3(a) shows the absorption spectra calculated by the EC model and the simulation result (COMSOL Multiphysics software). In order to fit the simulated resonance peaks of two ring resonators and absorption amplitude, the coefficients used in the EC model for the double-ring absorber with P=700 nmare set as the following: fpj=0.8,  0.17,  0.8,  0.33,  0.97 for each effective layer of j=1,  2,  3,  4,  5 respectively; am1=1.0,  bm1=0.8, cr1=0.4 for the top ring resonator, am2=1.9, bm2=0.75, cr2=0.9 for the bottom ring resonator, and bc=3.2 for the coupling of two ring resonators. In the long wavelength range (2~5 μm), the absorption is majorly due to the double ring resonances, and in the short wavelength range (1~2 μm), the absorption is mainly due to the multilayer impedance match condition. To explain the combination of these two absorption mechanisms, Zmul, Zres and Ztot calculated by the EC model are plotted in Fig. 3(b). There are two peaks in the real part ofZres=Zres'+iZres'' located at about λ=2.1 μm and λ=3.7 μm representing the two Cr ring resonances in the long wavelength range. Correspondingly, two absorption peaks in the range of λ=2~5 μm can be observed in the EC model curve in Fig. 3(a). Additionally, the real part ofZmul=Zmul'+iZmul'' is close to Z0=1 at about λ=1.8 μm indicating that the multilayer impedance match condition can be achieved in the short wavelength range. The absorption peak of the theoretical absorption in the range of λ=1~2 μm is the intersection of Zmul and Zres resulting from the real part ofZtot=Ztot'+iZtot'' close to Z0=1.

 figure: Fig. 3

Fig. 3 (a) Comparison of the absorption spectra calculated from the EC model (dashed black curved) and the simulation (blue solid curve) for the double-ring absorber with P=700 nm. (b) The corresponding real parts (solid curves) and imaginary parts (dashed curves) of impedances for Zmul  (in red), Zres (in blue), and Ztot (in black).

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In order to show how the absorption spectrum change with the absorber structure size, three double-ring absorbers with different periods and ring sizes are fabricated. As shown in Figs. 4(a)-4(c), the solid curves are the measured absorption spectra for the double-ring absorbers with periods of P=600 nm (in magenta), P=700 nm (in blue) and P=800 nm (in red), respectively, while the ring dimensions keep the same ratios as Win=P/4, Wt=P/2, Wb=l=P100(nm) (the gap between two neighboring bottom rings is always 100 nm). The dashed curves are the simulated absorption spectra. The insert in each figure is the SEM image of the fabricated double-ring absorber. The absorption spectrum range is affected by the period P and the ring length l. When P = 600 nm (with ring dimensions of wb=500 nm, wt=300 nm and wi=150 nm), the absorption spectrum range with more than 80% absorption is λ=1~3.1 μm. As P is increased, the absorption spectrum range gets broader but the absorption becomes lower. For P = 800 nm (with ring dimensions of wb=700 nm, wt=400 nm and wi=200 nm), the absorption spectrum range can reach λ=1~4.8 μm for the absorption over 80%. The absorber with P=700 nm (with ring dimensions of wb=600 nm, wt=350 nm and wi=175 nm) is the optimized result by taking account of the trade-off between absorption spectrum range and absorption amount. Its absorption spectrum range can reach λ=1~3.75 μm with the absorption over 80%.

 figure: Fig. 4

Fig. 4 Experimental (solid curves) and simulated (dashed curves) absorption spectra for the double-ring absorber with (a) P=600 nm, (b) P=700 nm and (c) P=800 nm, respectively. The insert is the SEM image of the fabricated double-ring absorber structure.

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The double-ring structure will change into double-square structure if the center hole has the zero width, which can make the fabrication process simpler. Similar to the double-ring structure, the double-square structure can also be regarded as two coupled plasmonic resonators. As shown in Fig. 5, the double-square absorbers with the periods of P=600 nm, P=700 nm and P=800 nm can also achieve the broadband absorption spectra with absorption above 80% similar to the double-ring absorbers. The absorption spectrum of double-square absorber is not as flat as that of double-ring absorber, but it has a small absorption peak in the long wavelength range.

 figure: Fig. 5

Fig. 5 Experimental (solid curves) and simulated (dashed curves) absorption spectra for the double-square absorber with (a) P=600 nm, (b) P=700 nm and (c) P=800 nm, respectively. The insert is the SEM image of the fabricated double-square absorber structure.

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Oblique incidence is also considered to show if the designed absorber can work in different incident angles and collect more infrared light. Since the double-ring structure is symmetric, the absorption is the same for TE and TM polarizations (configurations as shown in Figs. 6(a) and 6(b)) under normal incidence. However, under oblique incidence, the absorption spectra varies differently for TE and TM polarizations when considering the incident angle from 0° to 85°, as shown in Figs. 6(c) and 6(d) for the absorber with  P=700 nm. It is shown that the absorption for TM polarization can be kept around 80% even at high incident angles, while the absorption for TE polarization is not as high as TM polarization but still remains around 70% at high incident angles. This is because the double ring resonances are magnetic resonances and the multilayer impedance match can be sustained better for TM polarization at oblique incidence. In consequence, the designed broadband infrared absorber is angle-insensitive and polarization-independent and thus it is practical for energy harvesting applications.

 figure: Fig. 6

Fig. 6 (a), (b) Configurations of TE polarization and TM polarization. (c), (d) Simulated absorption spectra of the double-ring absorber with P=700 nm under oblique incidence for TE polarization and TM polarization, respectively.

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To further explore the two plasmonic resonances of the stacked double Cr ring resonators, optical field distributions are analyzed at the resonant wavelengths using COMSOL Multiphysics software. As shown in Fig. 7(a), the two magnetic resonances can be illustrated with the normalized |Hy| field profiles in yz plane. At the first magnetic resonance of λ=2.15 μm dominated by the top ring, the magnetic field is mainly located between the two rings. At the second magnetic resonance of λ=3.75 μm dominated by the bottom ring, the magnetic field is mostly confined between the bottom ring layer and the Cr mirror.

 figure: Fig. 7

Fig. 7 (a) Normalized magnetic field distributions, (b) heat generation density distributions q and (c) temperature increase distributions T in yz plane from simulation at λ=2.15 μmand λ=3.75 μm, respectively, for the double-ring absorber with P=700 nm when the incident power is 20.4 μW/μm2(corresponding to 10 μW into one unit cell).

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Particularly in solar thermophotovoltaics (STPV) applications, the device working temperature is usually required to reach at least 800  [38–40] which approaches or even sometimes surpasses the melting points of bulk gold (1063 ) and silver (961 ) [41]. Chromium with a melting point of 1906  [17] utilized in infrared absorbers can stand high operating temperature. In addition, chromium is significantly cheaper than gold or silver, making chromium a reasonable choice for high-volume production of infrared absorbers. In the broadband absorber, incident light will be eventually converted into heat because of the resistive loss (Rm) of metal. In this way, the Cr ring resonators act as nanoscale heat sources resulting in the local temperature increase and eventually a thermal equilibrium will be reached since the heat is conducted away by air above the absorber structure and the Cr mirror below. To investigate the temperature distribution in the absorber, the heat transfer equation ·(kθ)=q is solved, where k is the thermal conductivity and q is the heat power density generated in the Cr layers, q(r)=(ω/2)Im[ε(ω)]ε0|E(r)|2. As shown in Fig. 7(b), when the incident single-wavelength plane wave at  λ=2.15 μm matching the top ring resonance is used with the incident power of 20.4 μW/μm2 (corresponding to 10 μW optical power into each unit cell), the maximum heat generation density is about 2.06×1015W/m3 located at the top ring. When the wavelength of incident plane wave is tuned to match the bottom ring resonance at λ=3.75 μm, the maximum heat generation density can reach 2.92×1015W/m3 located at the bottom ring. At thermal equilibrium, the temperature increase distribution is a result of the balance between the heat generation and the boundary conditions where heat is conducted away. In simulation, the top and bottom boundaries are set as the fixed temperature and the side boundaries are insulated since the structure is periodic. The temperature increase distributions are plotted in Fig. 7(c) at the two resonant wavelengths. According to the Fourier’s law where heat transfer rate is proportional to the thermal conductivity of material and the temperature gradient as well, the highest temperature 51.3  is located in the top-ring for λ=2.15 μm since heat is mostly generated in the top ring. However, for λ=3.75 μm, temperature increase in the top ring is still high (reaching to 72.7 ) although heat is mainly generated in the bottom ring. This is because the bottom ring is close to the Cr mirror with high thermal conductivity, while dielectric layer and air has a much lower thermal conductivity.

4. Conclusion

A broadband infrared absorber consisting of stacked double Cr ring resonators on a Cr mirror has been designed and demonstrated with an average absorption more than 80% in 1 ~5 μm spectrum range. It is made of the refractory metal Cr based on the combination of two absorption mechanisms: the multilayer impedance match in the short wavelength range and the double plasmonic resonances in the long wavelength range. An equivalent circuit model has been constructed to analyze the impedance of the absorber. The designed absorber is proved to be angle-insensitive and polarization-independent under oblique incidence so that more light can be collected under different situations. The demonstrated Cr based absorber can work in high temperature environments due to the high melting point of Cr. The demonstrated broadband Cr double-ring absorber in infrared wavelength range will advance the relevant applications such as thermophotovoltaics, solar thermophotovoltaics, thermal detection, and thermal imaging.

Funding

National Science Foundation (NSF) (DMR-1552871, ECCS-1653032); Office of Naval Research (ONR) (N00014-16-1-2408); U.S. Department of Energy, Office of Science, under Contract No. DE-AC02-06CH11357).

Acknowledgment

The authors acknowledge the facility support from the Materials Research Center at Missouri S&T. This work was performed, in part, at the Center for Nanoscale Materials, a U.S. Department of Energy Office of Science User Facility, and supported by the U.S. Department of Energy, Office of Science, under Contract No. DE-AC02-06CH11357.

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References

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  1. Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. He, “Plasmonic and metamaterial structures as electromagnetic absorbers,” Laser Photonics Rev. 8(4), 495–520 (2014).
  2. C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. 24(23), OP98–OP120(2012).
    [PubMed]
  3. N. P. Sergeant, O. Pincon, M. Agrawal, and P. Peumans, “Design of wide-angle solar-selective absorbers using aperiodic metal-dielectric stacks,” Opt. Express 17(25), 22800–22812 (2009).
    [PubMed]
  4. H. Wang and L. Wang, “Perfect selective metamaterial solar absorbers,” Opt. Express 21(Suppl 6), A1078–A1093 (2013).
    [PubMed]
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  7. H. Deng, T. Wang, J. Gao, and X. Yang, “Metamaterial thermal emitters based on nanowire cavities for high-efficiency thermophotovoltaics,” J. Opt. 16, 035102 (2014).
  8. 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).
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2015 (4)

H. Deng, Z. Li, L. Stan, D. Rosenmann, D. Czaplewski, J. Gao, and X. Yang, “Broadband perfect absorber based on one ultrathin layer of refractory metal,” Opt. Lett. 40(11), 2592–2595 (2015).
[PubMed]

Q. Zhang, L. Bai, Z. Bai, P. Hu, and C. Liu, “Theoretical analysis and design of a near-infrared broadband absorber based on EC model,” Opt. Express 23(7), 8910–8917 (2015).
[PubMed]

N. Moshonas, G. K. Pagiatakis, and N. A. Stathopoulos, “Application of the transmission line method for the study of highly nonlinear multilayer optical structures,” Opt. Eng. 53(11), 115106 (2015).

S. Ghosh and K. V. Srivastava, “An Equivalent Circuit Model of FSS-Based Metamaterial Absorber Using Coupled Line Theory,” IEEE Antennas Wirel. Propag. Lett. 14, 511–514 (2015).

2014 (10)

S. Bhattacharyya, S. Ghosh, and K. V. Srivastava, “Equivalent circuit model of an ultra-thin polarization-independent triple band metamaterial absorber,” AIP Adv. 4, 097127 (2014).

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory Plasmonics with Titanium Nitride: Broadband Metamaterial Absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[PubMed]

D. Barchiesi and T. Grosges, “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 083097 (2014).

D. Zhu, M. Bosman, and J. K. W. Yang, “A circuit model for plasmonic resonators,” Opt. Express 22(8), 9809–9819 (2014).
[PubMed]

Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. He, “Plasmonic and metamaterial structures as electromagnetic absorbers,” Laser Photonics Rev. 8(4), 495–520 (2014).

H. Deng, T. Wang, J. Gao, and X. Yang, “Metamaterial thermal emitters based on nanowire cavities for high-efficiency thermophotovoltaics,” J. Opt. 16, 035102 (2014).

W. Wang, Y. Cui, Y. He, Y. Hao, Y. Lin, X. Tian, T. Ji, and S. He, “Efficient multiband absorber based on one-dimensional periodic metal-dielectric photonic crystal with a reflective substrate,” Opt. Lett. 39(2), 331–334 (2014).
[PubMed]

D. Fei, J. Yi, C. Hao, L. Mo, F. Ding, Y. Jin, B. Li, H. Cheng, L. Mo, and S. He, “Ultrabroadband strong light absorption based on thin multilayered metamaterials,” Laser Photonics Rev. 8(6), 946–953 (2014).

J. Zhou, A. F. Kaplan, L. Chen, and L. J. Guo, “Experiment and theory of the broadband absorption by a tapered hyperbolic metamaterial array,” ACS Photonics 1(7), 618–624 (2014).

D. Ji, H. Song, X. Zeng, H. Hu, K. Liu, N. Zhang, and Q. Gan, “Broadband absorption engineering of hyperbolic metafilm patterns,” Sci. Rep. 4, 4498 (2014).
[PubMed]

2013 (5)

N. Mattiucci, M. J. Bloemer, N. Aközbek, and G. D’Aguanno, “Impedance matched thin metamaterials make metals absorbing,” Sci. Rep. 3, 3203 (2013).
[PubMed]

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[PubMed]

H. Wang and L. Wang, “Perfect selective metamaterial solar absorbers,” Opt. Express 21(Suppl 6), A1078–A1093 (2013).
[PubMed]

S. Molesky, C. J. Dewalt, and Z. Jacob, “High temperature epsilon-near-zero and epsilon-near-pole metamaterial emitters for thermophotovoltaics,” Opt. Express 21(Suppl 1), A96–A110 (2013).
[PubMed]

Y. Pang, H. Cheng, Y. Zhou, and J. Wang, “Analysis and design of wired-based metamaterial absorbers using equivalent circuit approach,” J. Appl. Phys. 113, 114902 (2013).

2012 (6)

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” Phot. Nano. Fund. Appl. 10(1), 166–176 (2012).

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
[PubMed]

D. Cheng, J. Xie, P. Zhou, H. Zhang, N. Zhang, and L. Deng, “Numerical study of a new negative index material in mid-infrared spectrum,” Opt. Express 20(23), 25744–25751 (2012).
[PubMed]

W. Chihhui, N. Burton, J. Jeremy, M. Andrew, Z. Byron, S. Steve, and S. Gennady, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14, 024005 (2012).

C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. 24(23), OP98–OP120(2012).
[PubMed]

Y. Sun, B. Edwards, A. Alù, and N. Engheta, “Experimental realization of optical lumped nanocircuits at infrared wavelengths,” Nat. Mater. 11(3), 208–212 (2012).
[PubMed]

2011 (2)

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, 517 (2011).
[PubMed]

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).
[PubMed]

2009 (3)

2008 (1)

P. Nagpal, S. E. Han, A. Stein, and D. J. Norris, “Efficient low-temperature thermophotovoltaic emitters from metallic photonic crystals,” Nano Lett. 8(10), 3238–3243 (2008).
[PubMed]

2006 (5)

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006).

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006).
[PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[PubMed]

J. W. Dong, G. Q. Liang, Y. H. Chen, and H. Z. Wang, “Robust absorption broadband in one-dimensional metallic-dielectric quasi-periodic structure,” Opt. Express 14(5), 2014–2020 (2006).
[PubMed]

B. J. Lee and Z. M. Zhang, “Design and fabrication of planar multilayer structures with coherent thermal emission characteristics,” J. Appl. Phys. 100, 063529 (2006).

2003 (1)

A. Narayanaswamy and G. Chen, “Surface modes for near field thermophotovoltaics,” Appl. Phys. Lett. 82, 3544–3546 (2003).

1998 (1)

Abelson, J. R.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[PubMed]

Agrawal, M.

Aközbek, N.

N. Mattiucci, M. J. Bloemer, N. Aközbek, and G. D’Aguanno, “Impedance matched thin metamaterials make metals absorbing,” Sci. Rep. 3, 3203 (2013).
[PubMed]

Alù, A.

Y. Sun, B. Edwards, A. Alù, and N. Engheta, “Experimental realization of optical lumped nanocircuits at infrared wavelengths,” Nat. Mater. 11(3), 208–212 (2012).
[PubMed]

Andrew, M.

W. Chihhui, N. Burton, J. Jeremy, M. Andrew, Z. Byron, S. Steve, and S. Gennady, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14, 024005 (2012).

Arpin, K. A.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[PubMed]

Atwater, H. A.

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, 517 (2011).
[PubMed]

Aydin, K.

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, 517 (2011).
[PubMed]

Bai, L.

Bai, Z.

Barchiesi, D.

D. Barchiesi and T. Grosges, “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 083097 (2014).

Bhattacharyya, S.

S. Bhattacharyya, S. Ghosh, and K. V. Srivastava, “Equivalent circuit model of an ultra-thin polarization-independent triple band metamaterial absorber,” AIP Adv. 4, 097127 (2014).

Bingham, C. M.

N. I. Landy, C. M. Bingham, T. Tyler, N. Jokerst, D. R. Smith, and W. J. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79, 125104 (2009).

Bloemer, M. J.

N. Mattiucci, M. J. Bloemer, N. Aközbek, and G. D’Aguanno, “Impedance matched thin metamaterials make metals absorbing,” Sci. Rep. 3, 3203 (2013).
[PubMed]

Boltasseva, A.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory Plasmonics with Titanium Nitride: Broadband Metamaterial Absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[PubMed]

Bosman, M.

Braun, P. V.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[PubMed]

Briggs, R. M.

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, 517 (2011).
[PubMed]

Burton, N.

W. Chihhui, N. Burton, J. Jeremy, M. Andrew, Z. Byron, S. Steve, and S. Gennady, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14, 024005 (2012).

Byron, Z.

W. Chihhui, N. Burton, J. Jeremy, M. Andrew, Z. Byron, S. Steve, and S. Gennady, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14, 024005 (2012).

Chen, G.

A. Narayanaswamy and G. Chen, “Surface modes for near field thermophotovoltaics,” Appl. Phys. Lett. 82, 3544–3546 (2003).

Chen, L.

J. Zhou, A. F. Kaplan, L. Chen, and L. J. Guo, “Experiment and theory of the broadband absorption by a tapered hyperbolic metamaterial array,” ACS Photonics 1(7), 618–624 (2014).

Chen, Y. H.

Cheng, D.

Cheng, H.

D. Fei, J. Yi, C. Hao, L. Mo, F. Ding, Y. Jin, B. Li, H. Cheng, L. Mo, and S. He, “Ultrabroadband strong light absorption based on thin multilayered metamaterials,” Laser Photonics Rev. 8(6), 946–953 (2014).

Y. Pang, H. Cheng, Y. Zhou, and J. Wang, “Analysis and design of wired-based metamaterial absorbers using equivalent circuit approach,” J. Appl. Phys. 113, 114902 (2013).

Chihhui, W.

W. Chihhui, N. Burton, J. Jeremy, M. Andrew, Z. Byron, S. Steve, and S. Gennady, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14, 024005 (2012).

Cloud, A. N.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[PubMed]

Conway, J.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” Phot. Nano. Fund. Appl. 10(1), 166–176 (2012).

Cui, Y.

W. Wang, Y. Cui, Y. He, Y. Hao, Y. Lin, X. Tian, T. Ji, and S. He, “Efficient multiband absorber based on one-dimensional periodic metal-dielectric photonic crystal with a reflective substrate,” Opt. Lett. 39(2), 331–334 (2014).
[PubMed]

Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. He, “Plasmonic and metamaterial structures as electromagnetic absorbers,” Laser Photonics Rev. 8(4), 495–520 (2014).

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
[PubMed]

Czaplewski, D.

D’Aguanno, G.

N. Mattiucci, M. J. Bloemer, N. Aközbek, and G. D’Aguanno, “Impedance matched thin metamaterials make metals absorbing,” Sci. Rep. 3, 3203 (2013).
[PubMed]

Deng, H.

H. Deng, Z. Li, L. Stan, D. Rosenmann, D. Czaplewski, J. Gao, and X. Yang, “Broadband perfect absorber based on one ultrathin layer of refractory metal,” Opt. Lett. 40(11), 2592–2595 (2015).
[PubMed]

H. Deng, T. Wang, J. Gao, and X. Yang, “Metamaterial thermal emitters based on nanowire cavities for high-efficiency thermophotovoltaics,” J. Opt. 16, 035102 (2014).

Deng, L.

Dewalt, C. J.

Ding, F.

Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. He, “Plasmonic and metamaterial structures as electromagnetic absorbers,” Laser Photonics Rev. 8(4), 495–520 (2014).

D. Fei, J. Yi, C. Hao, L. Mo, F. Ding, Y. Jin, B. Li, H. Cheng, L. Mo, and S. He, “Ultrabroadband strong light absorption based on thin multilayered metamaterials,” Laser Photonics Rev. 8(6), 946–953 (2014).

Djurišic, A. B.

Dong, J. W.

Economon, E. N.

Edwards, B.

Y. Sun, B. Edwards, A. Alù, and N. Engheta, “Experimental realization of optical lumped nanocircuits at infrared wavelengths,” Nat. Mater. 11(3), 208–212 (2012).
[PubMed]

Elazar, J. M.

Engheta, N.

Y. Sun, B. Edwards, A. Alù, and N. Engheta, “Experimental realization of optical lumped nanocircuits at infrared wavelengths,” Nat. Mater. 11(3), 208–212 (2012).
[PubMed]

Fan, S.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[PubMed]

E. Rephaeli and S. Fan, “Absorber and emitter for solar thermo-photovoltaic systems to achieve efficiency exceeding the Shockley-Queisser limit,” Opt. Express 17(17), 15145–15159 (2009).
[PubMed]

Fang, N. X.

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
[PubMed]

Fei, D.

D. Fei, J. Yi, C. Hao, L. Mo, F. Ding, Y. Jin, B. Li, H. Cheng, L. Mo, and S. He, “Ultrabroadband strong light absorption based on thin multilayered metamaterials,” Laser Photonics Rev. 8(6), 946–953 (2014).

Ferry, V. E.

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, 517 (2011).
[PubMed]

Fung, K. H.

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
[PubMed]

Gan, Q.

D. Ji, H. Song, X. Zeng, H. Hu, K. Liu, N. Zhang, and Q. Gan, “Broadband absorption engineering of hyperbolic metafilm patterns,” Sci. Rep. 4, 4498 (2014).
[PubMed]

Gao, J.

H. Deng, Z. Li, L. Stan, D. Rosenmann, D. Czaplewski, J. Gao, and X. Yang, “Broadband perfect absorber based on one ultrathin layer of refractory metal,” Opt. Lett. 40(11), 2592–2595 (2015).
[PubMed]

H. Deng, T. Wang, J. Gao, and X. Yang, “Metamaterial thermal emitters based on nanowire cavities for high-efficiency thermophotovoltaics,” J. Opt. 16, 035102 (2014).

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W. Chihhui, N. Burton, J. Jeremy, M. Andrew, Z. Byron, S. Steve, and S. Gennady, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14, 024005 (2012).

Ghosh, S.

S. Ghosh and K. V. Srivastava, “An Equivalent Circuit Model of FSS-Based Metamaterial Absorber Using Coupled Line Theory,” IEEE Antennas Wirel. Propag. Lett. 14, 511–514 (2015).

S. Bhattacharyya, S. Ghosh, and K. V. Srivastava, “Equivalent circuit model of an ultra-thin polarization-independent triple band metamaterial absorber,” AIP Adv. 4, 097127 (2014).

Girolami, G. S.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
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W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory Plasmonics with Titanium Nitride: Broadband Metamaterial Absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[PubMed]

Guler, U.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory Plasmonics with Titanium Nitride: Broadband Metamaterial Absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[PubMed]

Guo, L. J.

J. Zhou, A. F. Kaplan, L. Chen, and L. J. Guo, “Experiment and theory of the broadband absorption by a tapered hyperbolic metamaterial array,” ACS Photonics 1(7), 618–624 (2014).

Han, S. E.

P. Nagpal, S. E. Han, A. Stein, and D. J. Norris, “Efficient low-temperature thermophotovoltaic emitters from metallic photonic crystals,” Nano Lett. 8(10), 3238–3243 (2008).
[PubMed]

Hao, C.

D. Fei, J. Yi, C. Hao, L. Mo, F. Ding, Y. Jin, B. Li, H. Cheng, L. Mo, and S. He, “Ultrabroadband strong light absorption based on thin multilayered metamaterials,” Laser Photonics Rev. 8(6), 946–953 (2014).

Hao, Y.

He, S.

W. Wang, Y. Cui, Y. He, Y. Hao, Y. Lin, X. Tian, T. Ji, and S. He, “Efficient multiband absorber based on one-dimensional periodic metal-dielectric photonic crystal with a reflective substrate,” Opt. Lett. 39(2), 331–334 (2014).
[PubMed]

D. Fei, J. Yi, C. Hao, L. Mo, F. Ding, Y. Jin, B. Li, H. Cheng, L. Mo, and S. He, “Ultrabroadband strong light absorption based on thin multilayered metamaterials,” Laser Photonics Rev. 8(6), 946–953 (2014).

Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. He, “Plasmonic and metamaterial structures as electromagnetic absorbers,” Laser Photonics Rev. 8(4), 495–520 (2014).

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
[PubMed]

He, Y.

Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. He, “Plasmonic and metamaterial structures as electromagnetic absorbers,” Laser Photonics Rev. 8(4), 495–520 (2014).

W. Wang, Y. Cui, Y. He, Y. Hao, Y. Lin, X. Tian, T. Ji, and S. He, “Efficient multiband absorber based on one-dimensional periodic metal-dielectric photonic crystal with a reflective substrate,” Opt. Lett. 39(2), 331–334 (2014).
[PubMed]

Hu, H.

D. Ji, H. Song, X. Zeng, H. Hu, K. Liu, N. Zhang, and Q. Gan, “Broadband absorption engineering of hyperbolic metafilm patterns,” Sci. Rep. 4, 4498 (2014).
[PubMed]

Hu, P.

Jacob, Z.

Jeremy, J.

W. Chihhui, N. Burton, J. Jeremy, M. Andrew, Z. Byron, S. Steve, and S. Gennady, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14, 024005 (2012).

Ji, D.

D. Ji, H. Song, X. Zeng, H. Hu, K. Liu, N. Zhang, and Q. Gan, “Broadband absorption engineering of hyperbolic metafilm patterns,” Sci. Rep. 4, 4498 (2014).
[PubMed]

Ji, T.

Jin, Y.

D. Fei, J. Yi, C. Hao, L. Mo, F. Ding, Y. Jin, B. Li, H. Cheng, L. Mo, and S. He, “Ultrabroadband strong light absorption based on thin multilayered metamaterials,” Laser Photonics Rev. 8(6), 946–953 (2014).

Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. He, “Plasmonic and metamaterial structures as electromagnetic absorbers,” Laser Photonics Rev. 8(4), 495–520 (2014).

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
[PubMed]

Jokerst, N.

N. I. Landy, C. M. Bingham, T. Tyler, N. Jokerst, D. R. Smith, and W. J. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79, 125104 (2009).

Jokerst, N. M.

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).
[PubMed]

Kalanyan, B.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[PubMed]

Kaplan, A. F.

J. Zhou, A. F. Kaplan, L. Chen, and L. J. Guo, “Experiment and theory of the broadband absorption by a tapered hyperbolic metamaterial array,” ACS Photonics 1(7), 618–624 (2014).

Kildishev, A. V.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory Plasmonics with Titanium Nitride: Broadband Metamaterial Absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[PubMed]

Kinsey, N.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory Plasmonics with Titanium Nitride: Broadband Metamaterial Absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[PubMed]

Koschny, T.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006).

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006).
[PubMed]

Landy, N. I.

N. I. Landy, C. M. Bingham, T. Tyler, N. Jokerst, D. R. Smith, and W. J. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79, 125104 (2009).

Lee, B. J.

B. J. Lee and Z. M. Zhang, “Design and fabrication of planar multilayer structures with coherent thermal emission characteristics,” J. Appl. Phys. 100, 063529 (2006).

Li, B.

D. Fei, J. Yi, C. Hao, L. Mo, F. Ding, Y. Jin, B. Li, H. Cheng, L. Mo, and S. He, “Ultrabroadband strong light absorption based on thin multilayered metamaterials,” Laser Photonics Rev. 8(6), 946–953 (2014).

Li, W.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory Plasmonics with Titanium Nitride: Broadband Metamaterial Absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[PubMed]

Li, Z.

Liang, G. Q.

Lin, Y.

W. Wang, Y. Cui, Y. He, Y. Hao, Y. Lin, X. Tian, T. Ji, and S. He, “Efficient multiband absorber based on one-dimensional periodic metal-dielectric photonic crystal with a reflective substrate,” Opt. Lett. 39(2), 331–334 (2014).
[PubMed]

Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. He, “Plasmonic and metamaterial structures as electromagnetic absorbers,” Laser Photonics Rev. 8(4), 495–520 (2014).

Liu, C.

Liu, K.

D. Ji, H. Song, X. Zeng, H. Hu, K. Liu, N. Zhang, and Q. Gan, “Broadband absorption engineering of hyperbolic metafilm patterns,” Sci. Rep. 4, 4498 (2014).
[PubMed]

Liu, X.

C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. 24(23), OP98–OP120(2012).
[PubMed]

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).
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K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[PubMed]

Ma, H.

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
[PubMed]

Majewski, M. L.

Mallek, J.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
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N. Mattiucci, M. J. Bloemer, N. Aközbek, and G. D’Aguanno, “Impedance matched thin metamaterials make metals absorbing,” Sci. Rep. 3, 3203 (2013).
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D. Fei, J. Yi, C. Hao, L. Mo, F. Ding, Y. Jin, B. Li, H. Cheng, L. Mo, and S. He, “Ultrabroadband strong light absorption based on thin multilayered metamaterials,” Laser Photonics Rev. 8(6), 946–953 (2014).

D. Fei, J. Yi, C. Hao, L. Mo, F. Ding, Y. Jin, B. Li, H. Cheng, L. Mo, and S. He, “Ultrabroadband strong light absorption based on thin multilayered metamaterials,” Laser Photonics Rev. 8(6), 946–953 (2014).

Molesky, S.

Moshonas, N.

N. Moshonas, G. K. Pagiatakis, and N. A. Stathopoulos, “Application of the transmission line method for the study of highly nonlinear multilayer optical structures,” Opt. Eng. 53(11), 115106 (2015).

Nagpal, P.

P. Nagpal, S. E. Han, A. Stein, and D. J. Norris, “Efficient low-temperature thermophotovoltaic emitters from metallic photonic crystals,” Nano Lett. 8(10), 3238–3243 (2008).
[PubMed]

Naik, G. V.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory Plasmonics with Titanium Nitride: Broadband Metamaterial Absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
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K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
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Norris, D. J.

P. Nagpal, S. E. Han, A. Stein, and D. J. Norris, “Efficient low-temperature thermophotovoltaic emitters from metallic photonic crystals,” Nano Lett. 8(10), 3238–3243 (2008).
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C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. 24(23), OP98–OP120(2012).
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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).
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N. I. Landy, C. M. Bingham, T. Tyler, N. Jokerst, D. R. Smith, and W. J. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79, 125104 (2009).

Pagiatakis, G. K.

N. Moshonas, G. K. Pagiatakis, and N. A. Stathopoulos, “Application of the transmission line method for the study of highly nonlinear multilayer optical structures,” Opt. Eng. 53(11), 115106 (2015).

Pang, Y.

Y. Pang, H. Cheng, Y. Zhou, and J. Wang, “Analysis and design of wired-based metamaterial absorbers using equivalent circuit approach,” J. Appl. Phys. 113, 114902 (2013).

Parsons, G. N.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
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J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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Pincon, O.

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Rephaeli, E.

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J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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Sergeant, N. P.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
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N. P. Sergeant, O. Pincon, M. Agrawal, and P. Peumans, “Design of wide-angle solar-selective absorbers using aperiodic metal-dielectric stacks,” Opt. Express 17(25), 22800–22812 (2009).
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W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory Plasmonics with Titanium Nitride: Broadband Metamaterial Absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
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Smith, D. R.

N. I. Landy, C. M. Bingham, T. Tyler, N. Jokerst, D. R. Smith, and W. J. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79, 125104 (2009).

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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Song, H.

D. Ji, H. Song, X. Zeng, H. Hu, K. Liu, N. Zhang, and Q. Gan, “Broadband absorption engineering of hyperbolic metafilm patterns,” Sci. Rep. 4, 4498 (2014).
[PubMed]

Soukoulis, C. M.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006).

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006).
[PubMed]

Srivastava, K. V.

S. Ghosh and K. V. Srivastava, “An Equivalent Circuit Model of FSS-Based Metamaterial Absorber Using Coupled Line Theory,” IEEE Antennas Wirel. Propag. Lett. 14, 511–514 (2015).

S. Bhattacharyya, S. Ghosh, and K. V. Srivastava, “Equivalent circuit model of an ultra-thin polarization-independent triple band metamaterial absorber,” AIP Adv. 4, 097127 (2014).

Staffaroni, M.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” Phot. Nano. Fund. Appl. 10(1), 166–176 (2012).

Stan, L.

Starr, A. F.

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).
[PubMed]

Starr, T.

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).
[PubMed]

Stathopoulos, N. A.

N. Moshonas, G. K. Pagiatakis, and N. A. Stathopoulos, “Application of the transmission line method for the study of highly nonlinear multilayer optical structures,” Opt. Eng. 53(11), 115106 (2015).

Stein, A.

P. Nagpal, S. E. Han, A. Stein, and D. J. Norris, “Efficient low-temperature thermophotovoltaic emitters from metallic photonic crystals,” Nano Lett. 8(10), 3238–3243 (2008).
[PubMed]

Steve, S.

W. Chihhui, N. Burton, J. Jeremy, M. Andrew, Z. Byron, S. Steve, and S. Gennady, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14, 024005 (2012).

Sun, Y.

Y. Sun, B. Edwards, A. Alù, and N. Engheta, “Experimental realization of optical lumped nanocircuits at infrared wavelengths,” Nat. Mater. 11(3), 208–212 (2012).
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M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” Phot. Nano. Fund. Appl. 10(1), 166–176 (2012).

Tian, X.

Tuttle, G.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006).

Tyler, T.

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).
[PubMed]

N. I. Landy, C. M. Bingham, T. Tyler, N. Jokerst, D. R. Smith, and W. J. Padilla, “Design, theory, and measurement of a polarization-insensitive absorber for terahertz imaging,” Phys. Rev. B 79, 125104 (2009).

Vedantam, S.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” Phot. Nano. Fund. Appl. 10(1), 166–176 (2012).

Wang, H.

Wang, H. Z.

Wang, J.

Y. Pang, H. Cheng, Y. Zhou, and J. Wang, “Analysis and design of wired-based metamaterial absorbers using equivalent circuit approach,” J. Appl. Phys. 113, 114902 (2013).

Wang, L.

Wang, T.

H. Deng, T. Wang, J. Gao, and X. Yang, “Metamaterial thermal emitters based on nanowire cavities for high-efficiency thermophotovoltaics,” J. Opt. 16, 035102 (2014).

Wang, W.

Watts, C. M.

C. M. Watts, X. Liu, and W. J. Padilla, “Metamaterial electromagnetic wave absorbers,” Adv. Mater. 24(23), OP98–OP120(2012).
[PubMed]

Xie, J.

Xu, J.

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12(3), 1443–1447 (2012).
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Yablonovitch, E.

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” Phot. Nano. Fund. Appl. 10(1), 166–176 (2012).

Yang, J. K. W.

Yang, L.

Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. He, “Plasmonic and metamaterial structures as electromagnetic absorbers,” Laser Photonics Rev. 8(4), 495–520 (2014).

Yang, X.

H. Deng, Z. Li, L. Stan, D. Rosenmann, D. Czaplewski, J. Gao, and X. Yang, “Broadband perfect absorber based on one ultrathin layer of refractory metal,” Opt. Lett. 40(11), 2592–2595 (2015).
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H. Deng, T. Wang, J. Gao, and X. Yang, “Metamaterial thermal emitters based on nanowire cavities for high-efficiency thermophotovoltaics,” J. Opt. 16, 035102 (2014).

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Y. Cui, Y. He, Y. Jin, F. Ding, L. Yang, Y. Ye, S. Zhong, Y. Lin, and S. He, “Plasmonic and metamaterial structures as electromagnetic absorbers,” Laser Photonics Rev. 8(4), 495–520 (2014).

Yi, J.

D. Fei, J. Yi, C. Hao, L. Mo, F. Ding, Y. Jin, B. Li, H. Cheng, L. Mo, and S. He, “Ultrabroadband strong light absorption based on thin multilayered metamaterials,” Laser Photonics Rev. 8(6), 946–953 (2014).

Yu, Z.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, G. S. Girolami, J. R. Abelson, S. Fan, and P. V. Braun, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[PubMed]

Zeng, X.

D. Ji, H. Song, X. Zeng, H. Hu, K. Liu, N. Zhang, and Q. Gan, “Broadband absorption engineering of hyperbolic metafilm patterns,” Sci. Rep. 4, 4498 (2014).
[PubMed]

Zhang, H.

Zhang, L.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006).

Zhang, N.

D. Ji, H. Song, X. Zeng, H. Hu, K. Liu, N. Zhang, and Q. Gan, “Broadband absorption engineering of hyperbolic metafilm patterns,” Sci. Rep. 4, 4498 (2014).
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Zhang, Z. M.

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Figures (7)

Fig. 1
Fig. 1 (a) SEM image of the Cr-SiO2 multilayer film before milling. (b) Absorption spectra of the multilayer film from both experiment (red curve) and simulation (blue curve). (c) The real (solid curve) and imaginary (dashed curve) parts of Cr permittivity.
Fig. 2
Fig. 2 (a) Schematic of the designed broadband infrared absorber consisting of stacked double Cr ring resonators milled from two pairs of Cr-SiO2 layers on top of a reflective Cr mirror. (b) Equivalent circuit model of the total impedance for the double-ring absorber consisting of Z mul as a high-pass filter and Z res as a low-pass filter. (c) Transformation of two half-rings of width w and length l into two equal cut-wires of effective width w' and effective length l'. (d) Equivalent circuit for Z res based on the coupled lumped-element LC resonators.
Fig. 3
Fig. 3 (a) Comparison of the absorption spectra calculated from the EC model (dashed black curved) and the simulation (blue solid curve) for the double-ring absorber with P=700 nm. (b) The corresponding real parts (solid curves) and imaginary parts (dashed curves) of impedances for Z mul   (in red), Z res (in blue), and Z tot (in black).
Fig. 4
Fig. 4 Experimental (solid curves) and simulated (dashed curves) absorption spectra for the double-ring absorber with (a) P=600 nm, (b) P=700 nm and (c) P=800 nm, respectively. The insert is the SEM image of the fabricated double-ring absorber structure.
Fig. 5
Fig. 5 Experimental (solid curves) and simulated (dashed curves) absorption spectra for the double-square absorber with (a) P=600 nm, (b) P=700 nm and (c) P=800 nm, respectively. The insert is the SEM image of the fabricated double-square absorber structure.
Fig. 6
Fig. 6 (a), (b) Configurations of TE polarization and TM polarization. (c), (d) Simulated absorption spectra of the double-ring absorber with P=700 nm under oblique incidence for TE polarization and TM polarization, respectively.
Fig. 7
Fig. 7 (a) Normalized magnetic field distributions, (b) heat generation density distributions q and (c) temperature increase distributions T in yz plane from simulation at λ=2.15 μmand λ=3.75 μm, respectively, for the double-ring absorber with P=700 nm when the incident power is 20.4  μW/μm 2 (corresponding to 10 μW into one unit cell).

Equations (2)

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Z mul =Z(1), and Z( j )= Z j ( Z( j+1 )i Z j tan δ j ) Z j iZ( j+1 )tan δ j ,j=1,2,...,6
Z res = C c + C m2 iω C c C m2 ( ( 2 C c + C m2 )( C m1 C m2 + C c ( C m1 + C m2 ) ) C c ( C m2 ( C m1 + C m2 )+ C c ( C m1 +3 C m2 ) ) + C c + C m2 iω C c C m2 R m1 ω 2 C c C m2 L m1 C c C m2 ( 2+ω( C c + C m2 )( i R m2 +ω L m2 ) ) )

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