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  • Editor: Christian Seassal
  • Vol. 21, Iss. S6 — Nov. 4, 2013
  • pp: A997–A1006
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Resonant circuit model for efficient metamaterial absorber

Alexandre Sellier, Tatiana V. Teperik, and André de Lustrac  »View Author Affiliations


Optics Express, Vol. 21, Issue S6, pp. A997-A1006 (2013)
http://dx.doi.org/10.1364/OE.21.00A997


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Abstract

The resonant absorption in a planar metamaterial is studied theoretically. We present a simple physical model describing this phenomenon in terms of equivalent resonant circuit. We discuss the role of radiative and dissipative damping of resonant mode supported by a metamaterial in the formation of absorption spectra. We show that the results of rigorous calculations of Maxwell equations can be fully retrieved with simple model describing the system in terms of equivalent resonant circuit. This simple model allows us to explain the total absorption effect observed in the system on a common physical ground by referring it to the impedance matching condition at the resonance.

© 2013 OSA

1. Introduction

A large variety of metallic and semiconductor metamaterials have been recently found to exhibit total absorption (TA) of electromagnetic radiation. This effect has been reported in broad frequency range including microwave [1

1. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008). [CrossRef] [PubMed]

4

4. 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, 9401–9407 (2011). [CrossRef] [PubMed]

], THz [5

5. T. V. Teperik, F. J. García de Abajo, V. V. Popov, and M. S. Shur, “Strong terahertz absorption bands in a scaled plasmonic crystal,” Appl. Phys. Lett. 90, 251910 (2007). [CrossRef]

8

8. L. Huang, D. R. Chowdhury, S. Ramani, M. T. Reiten, S.-N. Luo, A. J. Taylor, and Hou-Tong, “Experimental demonstration of terahertz metamaterial absorbers with a broad and flat high absorption band,” Optics Lett. 37, 154–156 (2012). [CrossRef]

], NIR [9

9. S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Efficient light absorption in metalsemiconductormetal nanostructures,” Appl. Phys. Lett. 85, 194 (2004). [CrossRef]

12

12. K. B. Alici, A. B. Turhan, C. M. Soukoulis, and E. Ozbay, “Optically thin composite resonant absorber at the near-infrared band: a polarization independent and spectrally broadband configuration,” Opt. Express 19, 14260–14267 (2011). [CrossRef] [PubMed]

], MIR [13

13. M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79, 033101 (2009). [CrossRef]

16

16. G. Dayal and S. A. Ramakrishna, “Metamaterial saturable absorber mirror,” Opt. Lett. 38, 272–274 (2013). [CrossRef] [PubMed]

] and visible [17

17. T. V. Teperik, F. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299–301 (2008). [CrossRef]

19

19. 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). [CrossRef] [PubMed]

] regions. A lot of diverse applications have been already proposed. Among them radar [20

20. J. Yang and Z. Shen, “A thin and broadband absorber using double-square loops,” IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 6, 388–391 (2007). [CrossRef]

23

23. H. Oraizi, A. Abdolali, and N. Vaseghi, “Application of double zero metamaterials as radar absorbing materials for the reduction of radar cross section,” Prog. Electromagn. Res. 101, 323–337 (2010). [CrossRef]

], electromagnetic compatibility [24

24. R. F. Huang, Z. W. Li, L. B. Kong, L. Liu, and S. Matitsine, “Analysis and design of an ultra-thin metamaterial absorber,” Prog. Electromagn. Res. B 14, 407–429 (2009). [CrossRef]

], photovoltaics [25

25. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010). [CrossRef] [PubMed]

], biosensing [11

11. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010). [CrossRef] [PubMed]

], thermal source emission [13

13. M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79, 033101 (2009). [CrossRef]

, 26

26. J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61 (2002). [CrossRef] [PubMed]

], and thermal bolometer [15

15. T. Maier and H. Brueckl, “Multispectral microbolometers for the midinfrared,” Opt. Lett. 35, 3766–3768 (2010). [CrossRef] [PubMed]

].

Although the structures that exhibit total absorption might differ considerably, they possess some common characteristics: the energy transmission through entire structure is forbidden, the structure possess an intrinsic resonance, and total absorption is achieved at a specific condition imposed on the geometry of the structure or on the material properties.

In this paper along with rigorous electromagnetic calculations we present a simple physical model describing the properties of planar metallic metamaterial in terms of equivalent oscillating-current resonant circuit. In this analytical approach we describe the absorptive layer squeezed between the periodic arrangement of metallic patches and ground plane by an effective load impedance. This allows us to go beyond the geometry and to find the universal ruler for TA effect to be achieved.

The paper is organized as follows. We start from the simplest geometry of a square patch in order to tackle the problem and understand the physics behind. In Sec. II we show the results of the rigorous electromagnetic calculations performed with use of the commercial software COMSOL Multiphysics [34] based on the finite element method. In Sec. III we present a simple physical model that describes the resonant absorption in terms of equivalent resonant circuit. In Sec. IV we develop the condition for the perfect absorber and discuss the role of radiative and dissipative damping of resonant mode supported by a metamaterial in the formation of absorption spectra. Finally, we tested our model with the planar metamaterials with arbitrary patch geometry.

2. Resonant absorption by a planar metamaterial

In Fig. 1 we present the structure under consideration (metasurface): it is a periodic arrangement of square metallic patches of length l located above a ground plane at a distance sλ (λ is the wavelength). Between the patch and the ground plane we include an absorptive layer with a weak loss tangent (tanδ = ε″/ε′ ≪ 1, where ε′ and ε″ are the real and imaginary part of dielectric function). We assume at the beginning that the ground plane as well as a patch are perfect metals.

Fig. 1 Schematic of planar metamaterial with lattice of metallic patches separated from the ground plane by absorptive layer.

In general, a structure presented in Fig. 1 poorly absorbs the electromagnetic energy. However, if one could match the free-space impedance (purely resistive), Z0 = 120π Ω, to the impedance of the metasurface, the incident energy would be completely transformed into Ohmic losses inside the absorptive layer and the total absorption effect would be achieved. If we consider that the electric current induced in absorptive layer by an incident plane wave is oscillating along the patch side, the electronic resistance R of the absorptive layer is inversely proportional to the layer thickness s and, therefore, extremely large compared to the free-space impedance Z0. The problem of the impedance matching may be solved by using an intrinsic resonance. At the resonance the real part of the effective impedance (i.e. the effective electric resistance) can be drastically decreased, while the inductive reactance inherent to the resonance may be canceled by an capacitive one, thus, leaving the effective impedance purely resistive. The absorptive layer squeezed between the patches and ground plane supports a transverse magnetic (TM) mode with a dispersion that can be easily obtained by imposing the zero electric field conditions above and below the absorptive layer:
k=ωε/c.
(1)
Here ω is a frequency, ε = ε′(1 + itanδ) is the complex dielectric function of absorptive layer, and c is the speed of light. The resonance frequencies of the structure in Fig. 1 can be obtained by quantization of the TM mode (Eq. (1)) by the cavity formed between the patch and ground plane. The metallic patches play the role of a Fabry-Perot resonator for the cavity TM standing wave squeezed between the patch and the ground plane, propagating along the absorptive layer and reflected at the terminations of the patch. Assuming that the modes are strongly localized under the patch and the field does not undergo the fringing at the patch edges, we can obtain the mode dispersion by considering rectangular cavity (l × l × s) with zero tangential electric field at the metallic walls and zero magnetic field at the other four walls of the cavity. Since sl and analysis presented in this paper concerns only the lower frequency modes for 2D case we have
knm=ωmnε/c=πln2+m2,
(2)
where fmn=ωmn/2π=cn2+m2/2lε are actually the resonant frequencies of classical square patch antenna [35

35. C. A. Balanis, Antenna Theory: Analysis and Designs (John Wiley & Sons, Inc., NY, 1997).

], n, m = 0, 1, 2,... are integer and n2 + m2 ≠ 0.

Fig. 2 (a) Absorption spectra for different patch length l: 12.2 mm (red curve), 13.2 mm (blue curve), and 15.2 mm (green curve). The period of the structure is l + Δl with patch-to-patch separation Δl = 2 mm and absorptive layer thickness s = 0.3 mm. (b) Near-field distribution Ez in the first and third resonant modes calculated along the line z = 0 and y = 0. (c) Resonant frequency as a function of patch-to-patch separation Δl for the first and second resonance of the spectra in Fig. 2(a), l = 15.2 mm. The points are connected by black dashed lines for eyes guidance. Blue dotted curves are obtained from Eq. (2)

The near field distributions Ez in absorptive layer (see Fig. 2(b)) calculated along the line z = 0 and y = 0 at frequencies A and B of the spectra shows the field oscillations that are typical for classical patch antenna [35

35. C. A. Balanis, Antenna Theory: Analysis and Designs (John Wiley & Sons, Inc., NY, 1997).

]. Note that the field variations along the height of the absorptive layer are nearly constant since for a given resonance wavelength the phase varies only slightly with |z| < s/2 ≪ λ. We have checked the z-dependence numerically (results not shown here). One can also notice the effect of field fringing at the edges of the patch. It is rather weak due to the small layer thickness. Therefore, the modes are strongly localized under the patch and the coupling between patches are extremely weak. That is why the resonant frequencies in spectra are approximately defined by Eq. (2) and independent from patch to patch distance within the studied range of Δl as one can perceive from Fig. 2(c).

3. Equivalent resonant circuit model

In order to provide a general view on the effect of total absorption regardless the particular geometry of the patch we apply RLC circuit model. In RLC model a structured surface is considered as a load impedance at the end of the transmission line modeling the free space. Similar model has been successfully applied to explain the total light absorption effect exhibited by the nanostructured metal inherent the plasmon resonance in visible [36

36. T. V. Teperik, V. V. Popov, and F. J. García de Abajo, “Void plasmons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71, 085408 (2005). [CrossRef]

].

Let us first introduce the effective surface impedance Zeff of the metasurface. In this case the reflection from metasurface can be described on a common basis independently of type of structuring. We describe the resonance of TM mode excited by a normally incident plane wave and squeezed between the patch and ground plane in terms of its equivalent resonant RLC circuit. In Fig. 3(b) we present the equivalent RLC circuit of the TM mode for the metasurface of Fig. 3(a). This circuit describes the main physical features of the resonant structures and contains (i) the total resistance R that determines the amount of power absorbed due to Ohmic losses, (ii) the total inductance L created by the finite electric currents oscillating in metallic patch and ground plane, and (iii) the total capacitance C that describes the charge accumulation induced by the external field. Note that inline with discussion above and results of Fig. 2(b) and 2(c) we did not take into account the patch-to-patch mode coupling. Elsewhere, an addition capacitance responsible for these coupling should be connected in series to the circuit presented in Fig. 3 (see, for example, Ref. [29

29. 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, 17413–17420 (2011). [CrossRef] [PubMed]

]).

Fig. 3 (a) Schematically charge distribution in TM mode induced by normally incident plane wave. (b) Resonant RLC equivalent circuit

The equivalent impedance of the circuit can be written as
Z=R+iωL1ω2LC+iωRC.
(3)
Equivalently, Eq. (3) can be cast in the form
Z=1C(2ν+iω)(ω02ω2+2iων),
(4)
where the dissipative mode damping ν = R/2L and ω0=1/LC. The resonant frequency can be derived by Im(Z) = 0 as ωres2=ω2(R/L)2=ω4ν2ω02. In the vicinity of the resonance ωω0 assuming that 2νω0 (i.e. high quality resonance) we obtain
Z=12Ci(ω0ω+iν),
(5)
The total frequency-dependent equivalent impedance of the metasurface can be expressed as
Zeff=|β|22Ci(ω0ω+iν),
(6)
where we introduce the coefficient |β|2 < 1 responsible for the coupling of the incident field with the resonant mode. The coupling coefficient |β|2 depends both: on the mode number and geometry of the structure (namely patch-to-patch distance).

Now let us calculate the absorption by a thin layer characterized by an effective impedance Zeff. Since there is no transmission through the structure we apply the impedance boundary condition [37

37. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

] and obtain a complex-valued reflection coefficient for the normal incidence in the form
r=ZeffZ0Zeff+Z0.
(7)
Then, the reflectance and absorbance of the electromagnetic energy in the vicinity of a given trapped mode resonance can be expressed as
=|r|2=(ω0ω)2+(νγ)2(ω0ω)2+(ν+γ)2,
(8)
𝒜=1=4νγ(ω0ω)2+(ν+γ)2,
(9)
Here we introduce
γ=|β|2/2CZ0
(10)
as the radiative damping of the mode that depends through the capacitance C on the geometry of the structure and dielectric function of absorptive layer. Note, that the absorption resonance described by Eq. (9) has Lorentzian lineshape with full width at half maximum FWHM = 2Γ = 2(ν + γ).

4. General condition for the perfect absorber

Having introduced the radiative and dissipative damping of the resonant TM modes, we now discuss their contribution to the shape of absorption spectra. From Eqs. (8) and (9) one finds at resonance (ω = ω0)
=(νγ)2(ν+γ)2,
(11)
𝒜=4νγ(ν+γ)2,
(12)
from where one can readily see that resonant total absorption (𝒜res = 1) occurs when
ν=γ
(13)
or
R2L=|β|22CZ0.
(14)
Obviously, for 𝒜res = 1 reflectance drops to zero (res = 0).

Note that if we ignores ohmic losses in the absorbing layer (R = 0, hence ν = 0), the resonance with entire linewidth given by 2γ disappears since in this case reflectance reaches unity and absorbance drops to zero. Therefore, the resonance mode sustains the radiative and dissipative damping simultaneously. In order to distinguish the radiative and dissipative contribution to the resonance linewidth we calculate numerically the absorbtion spectra at the first resonant mode for different ohmic losses in absorptive layer (see color curves in Fig. 4(a)). For this purpose we multiplied the originally used imaginary part of dielectric function ε″ = 0.088 (green curve in Fig. 2) by factor 0.125 and 2. This results in the narrowing and broadening of the resonant curve, respectively. The absorption is reduced in both cases indicating that ε″ = 0.088 is the optimal value. In the inset we plot Γ = ν + γ extracted from the spectra of Fig. 4(a) as a function of ε″. As we expect we observe the linear dependence of the resonant width Γ on ε″. Thus, by extrapolating the curve in the inset of Fig. 4(a) to ε″ = 0 (i.e. ν = 0) we can extract the radiative damping of the mode γ = 2.83 × 108s−1. Now with this result we find that the condition for total absorption ν = γ is satisfied at ε″ = 0.088. In this case the half width of the resonance is Γ = 2γ = 5.66×108s−1. In Fig. 4(a) the absorption spectra calculated numerically for γ = ν at ε″ = 0.088 (blue line) exhibits the total absorption of electromagnetic radiation at resonant frequency.

Fig. 4 (a) Absorption spectra of the first TM mode (n = 1, m = 0) and (b) next higher order TM mode (n = 3, m = 0) for different values of ohmic losses in absorptive layer introduced through ε″. Inset: half width of the resonance Γ as a function of imaginary part of dielectric function ε″ of absorptive layer. Green points correspond to the value of radiative damping γ extracted at ε″ = 0 and the total decay rate Γ at the optimal ε″, respectively. l = 15.2 mm and s = 0.3 mm.

Above we have considered in detail the properties of the first resonant mode. The resonant circuit model can be equally applied to achieve the TA effect when higher order TM mode is excited. For this purpose, we repeated the procedure discussed above. In Fig. 4(b) we plot the absorption spectra calculated for different ohmic losses in absorptive layer for the third TM mode (n = 3, m = 0). We observe the narrowing and broadening of the absorption resonance, while none of them exhibits the TA effect. In the inset of Fig. 4(b) we plot the width of the resonance extracted from resonant absorption curves as a function of ε″. The extrapolation of the curve gives us the radiative damping γ = 3.14 × 108s−1. Now the TA condition ν = γ is satisfied at ε″ = 0.0347. In Fig. 4(b) we present the absorption spectra for optimal ε″ by black line.

The radiative damping γ also depends on the particular geometry of the structure. To illustrate this effect we study in Fig. 5 the dependence of the radiative damping on the geometrical parameters of our metasurface. We extracted the value of γ from the absorption spectra calculations performed for different patch length l and absorptive layer thickness s. In Fig. 5 additionally to radiative damping γ we plot the half width of the resonance Γ for the sake of comparison. Evidently, that the dissipative damping ν can be obtained from the difference between the total decay rate Γ and radiative decay rate γ. One can observe that the radiative damping γ proportional to the absorptive layer thickness s and deviates only slightly from the inverse proportionality to l2 for large l. This dependance results from the inverse dependence of γ from the effective total capacitance C (see Eq. 10). Analyzing the near field distribution of the resonant mode under the patch in Fig. 2(b) one can perceive that it is characteristic of the series of parallel-plate capacitors with total capacitance Cε0εl2/s. The slight deviation from dependence 1/l2 for large l is explained by the fact that even for l ≫ Δl a small opening between patches ensures the residual coupling ξ of incident wave to TM resonant mode trapped under the patches. We can estimate this residual coupling by fitting γ. We obtained that γB/l2 +ξ (B = 4.5 × 1010, ξ = 0.13 × 1010). Analyzing the evolution of total mode decay rate Γ and radiative mode damping γ one can observe that there is a particular regime for s and l when Γ ≃ 2γ (i.e. γ = ν). This regime marked in the plot by grey/rose domains characterized by absorption higher than 95%. A weak sensitivity of absorption intensity to the patch length l within rose domain (cf. also the absorption spectra of the first resonant mode in Fig. 2(a)) is explained by inverse dependence of dissipative damping ν from the effective inductance L, that, in turn, is proportional to the length of a conducting layer l. Therefore, in this regime, the increase of radiative damping for larger l is accompanied by an increase of dissipative damping ν ensuring the condition of Eq. (13) being nearly accomplished within rather broad region of parameter l.

Fig. 5 Radiative damping γ (dashed curves) and total damping Γ (solid curves) of the first resonant TM mode as a function of patch length l (top axis) and absorptive layer thickness s (bottom axis). The points are connected by dashed lines for eyes guidance. Black curves: l = 15.2, Δl = 2 mm. Red curves: s = 0.3 mm, Δl = 2 mm. The grey/rose domains are characterized by absorption higher than 95%.

Fig. 6 Absorption spectra obtained from RLC model (green solid line) and numerical (black dashed line) calculations for (a) the first and (b) the next higher order TM mode. Inset: real (red curve) and imaginary (blue curve) parts of the effective impedance of the metasurface Zeff as a function of frequency.

Finally, the TA effect is not the exceptional property of the square patch metasurface. One can obtain TA for other geometry by applying the procedure discussed above. In Fig. 7 we plot the absorption spectra for some examples of planar metamaterials. We have checked that regardless the different geometry of the metasurface the TA absorption effect can be achieved once the radiative and dissipative damping of the mode squeezed between metal parts of the structure are equal. We also performed the exact calculations taking into account the Ohmic losses of cooper instead of model of the perfect metal (not shown here). We found that that neither resonant frequency nor absorption intensity changes. Only the distribution of absorbed energy is influenced. For example, the amount of energy absorbed by the metal patch in the absorption spectra presented by black curve in Fig. 7 is about 2% while less then 0.1% is absorbed by the ground plan.

Fig. 7 Absorption spectra of absorptive layer with ε = 4.4 + i0.088 squeezed under the periodic arrangement of patches of different geometry: square patch with l = 15.2 mm, s = 0.3 mm, Δl = 2 mm (black curve), circular patch with diameter d = 14.8 mm and s = 0.3 mm, and patch-to-patch separation 2 mm (red curve), square hole with side size l = 12 mm, s = 3 mm, and period 16.6 mm (blue curve), circular hole with diameter d = 16 mm, s = 3 mm, and period 19 mm (green curve).

5. Conclusion

In conclusion, we have investigated the resonant absorption phenomenon in planar metamaterials. Along with rigorous electromagnetic calculations we present a simple resonant circuit model that describes the resonant absorption in terms of impedance matching and radiative/dissipative damping of the resonant mode. We show that in spite of evident simplicity of the model it fully reproduces the rigorous calculations. We distinguished the radiative and dissipative contributions to the resonance linewidth and discussed the role of radiative and dissipative trapped mode decay rates in formation of the absorption spectra. In particular, we found that the square patch based metasurface can exhibits the effect of total absorption once the radiative and dissipative damping of modes are equal. Finally, we have shown that this condition of total absorption is universal and can be satisfied for metasurface of arbitrary geometry providing the effect of total absorption in a large frequency range.

Acknowledgments

The authors are grateful to the Direction Gnrale de lArmement (DGA) for the financial support of the REI project Novel Metamaterial-based Radar Absorbing Structures under Contract No. 2009-34-0030. The authors also thank Sylvain Gransart, Prof. Vyacheslav V. Popov and Prof. Andrey G. Borisov for fruitful discussions.

References and links

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N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008). [CrossRef] [PubMed]

2.

B. Wang, T. Koschny, and C. M. Soukoulis, “Wide-angle and polarization-independent chiral metamaterial absorber,” Phys. Rev. B 80, 033108 (2009). [CrossRef]

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Y. Cheng, H. Yang, Z. Cheng, and B. Xiao, “A planar polarization-insensitive metamaterial absorber,” Photonics and Nanostructures Fundamentals and Applications 9, 8–14 (2011). [CrossRef]

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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, 9401–9407 (2011). [CrossRef] [PubMed]

5.

T. V. Teperik, F. J. García de Abajo, V. V. Popov, and M. S. Shur, “Strong terahertz absorption bands in a scaled plasmonic crystal,” Appl. Phys. Lett. 90, 251910 (2007). [CrossRef]

6.

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, 7181–7188 (2008). [CrossRef] [PubMed]

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L. Huang, D. R. Chowdhury, S. Ramani, M. T. Reiten, S.-N. Luo, A. J. Taylor, and Hou-Tong, “Experimental demonstration of terahertz metamaterial absorbers with a broad and flat high absorption band,” Optics Lett. 37, 154–156 (2012). [CrossRef]

9.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Efficient light absorption in metalsemiconductormetal nanostructures,” Appl. Phys. Lett. 85, 194 (2004). [CrossRef]

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J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96, 251104 (2010). [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, 2342–2348 (2010). [CrossRef] [PubMed]

12.

K. B. Alici, A. B. Turhan, C. M. Soukoulis, and E. Ozbay, “Optically thin composite resonant absorber at the near-infrared band: a polarization independent and spectrally broadband configuration,” Opt. Express 19, 14260–14267 (2011). [CrossRef] [PubMed]

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M. Diem, T. Koschny, and C. M. Soukoulis, “Wide-angle perfect absorber/thermal emitter in the terahertz regime,” Phys. Rev. B 79, 033101 (2009). [CrossRef]

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G. Dayal and S. A. Ramakrishna, “Metamaterial saturable absorber mirror,” Opt. Lett. 38, 272–274 (2013). [CrossRef] [PubMed]

17.

T. V. Teperik, F. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299–301 (2008). [CrossRef]

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H. Oraizi, A. Abdolali, and N. Vaseghi, “Application of double zero metamaterials as radar absorbing materials for the reduction of radar cross section,” Prog. Electromagn. Res. 101, 323–337 (2010). [CrossRef]

24.

R. F. Huang, Z. W. Li, L. B. Kong, L. Liu, and S. Matitsine, “Analysis and design of an ultra-thin metamaterial absorber,” Prog. Electromagn. Res. B 14, 407–429 (2009). [CrossRef]

25.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010). [CrossRef] [PubMed]

26.

J.-J. Greffet, R. Carminati, K. Joulain, J.-P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61 (2002). [CrossRef] [PubMed]

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J. Hao, L. Zhou, and M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83, 165107 (2011). [CrossRef]

28.

P. Bouchon, C. Koechlin, F. Pardo, R. Hadar, and J.-L. Pelouard, “Wideband omnidirectional infrared absorber with a patchwork of plasmonic nanoantennas,” Opt. Lett. 37, 1038–1040 (2012). [CrossRef] [PubMed]

29.

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, 17413–17420 (2011). [CrossRef] [PubMed]

30.

H. Wakatsuchi, S. Greedy, C. Christopoulos, and J. Paul, “Customised broadband metamaterial absorbers for arbitrary polarisation,” Opt. Express 18, 22187–22198 (2010). [CrossRef] [PubMed]

31.

W. Zhu, X. Zhao, B. Gong, L. Liu, and B. Su, “Optical metamaterial absorber based on leaf-shaped cells,” Appl. Phys. A 102, 147–151 (2011). [CrossRef]

32.

W. Zhu and X. Zhao, “Metamaterial absorber with dendritic cells at infrared frequencies,” J. Opt. Soc. Am. B 26, 2382–2385 (2009). [CrossRef]

33.

P. V. Tuong, V. D. Lam, J. W. Park, E. H. Choi, S. A. Nikitov, and Y. P. Lee, “Perfect-absorber metamaterial based on flower-shaped structure,” Photonics and Nanostructures - Fundamentals and Applications 11, 89–94 (2013). [CrossRef]

34.

http://www.comsol.com.

35.

C. A. Balanis, Antenna Theory: Analysis and Designs (John Wiley & Sons, Inc., NY, 1997).

36.

T. V. Teperik, V. V. Popov, and F. J. García de Abajo, “Void plasmons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71, 085408 (2005). [CrossRef]

37.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

OCIS Codes
(260.5740) Physical optics : Resonance
(300.1030) Spectroscopy : Absorption
(160.3918) Materials : Metamaterials

ToC Category:
Subwavelength Structures, nanostructures

History
Original Manuscript: July 17, 2013
Revised Manuscript: September 26, 2013
Manuscript Accepted: September 26, 2013
Published: October 10, 2013

Citation
Alexandre Sellier, Tatiana V. Teperik, and André de Lustrac, "Resonant circuit model for efficient metamaterial absorber," Opt. Express 21, A997-A1006 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-S6-A997


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  29. 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. Express19, 17413–17420 (2011). [CrossRef] [PubMed]
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  37. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

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