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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 7 — Mar. 26, 2012
  • pp: 7165–7172
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Interference theory of metamaterial perfect absorbers

Hou-Tong Chen  »View Author Affiliations


Optics Express, Vol. 20, Issue 7, pp. 7165-7172 (2012)
http://dx.doi.org/10.1364/OE.20.007165


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Abstract

The impedance matching to free space in metamaterial perfect absorbers has been believed to involve and rely on magnetic resonant response, with direct evidence provided by the anti-parallel surface currents in the metal structures. Here I present a different theoretical interpretation based on interference, which shows that the two layers of metal structures in metamaterial absorbers are linked only by multiple reflections with negligible near-field interactions or magnetic resonances. This is further supported by the out-of-phase surface currents derived at the interfaces of resonator array and ground plane through multiple reflections and superpositions. The theory developed here explains all features observed in narrowband metamaterial absorbers and therefore provides a profound understanding of the underlying physics.

© 2012 OSA

1. Introduction

The demonstration of metamaterial perfect absorbers [1

1. A. Alù, F. Bilotti, N. Engheta, and L. Vegni, “A thin absorbing screen using metamaterial complementary pairs,” in Proceedings of the International Conference on Electromagnetics in Advanced Applications, (Turin, Italy, September 12–16, 2005), 75–78.

, 2

2. 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]

] represents one of the most important applications employing the astonishing properties found in metamaterials [3

3. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000). [CrossRef] [PubMed]

5

5. W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).

]. The original idea [2

2. 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]

] is that, in metamaterials with simultaneous electrical and magnetic resonances, both of the effective permittivity ε(ω) and permeability μ(ω) are highly dispersive and can be tailored independently. At certain frequencies the effective impedance, which is defined as Z(ω)=μ(ω)/ε(ω), matches to the free space impedance Z0, and therefore the reflection is minimized. If at the same time the metamaterial is also of high loss, which causes very low transmission, then near-unity absorption can occur within an ultra thin layer of material. Under such considerations, in a typical metamaterial absorber, the magnetic resonance from the bi-layered metal structure [6

6. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95, 137404 (2005). [CrossRef] [PubMed]

, 7

7. V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356–3358 (2005). [CrossRef]

] is essential, and each layer of metal structure also provides the electrical response. As a direct evidence of the magnetic resonance in metamaterial absorbers, the surface currents excited in the two metal layers are found to be anti-parallel [8

8. 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]

].

While all of the above arguments seem to be plausible and accepted by a majority of researchers [9

9. Y. Avitzour, Y. A. Urzhumov, and G. Shvets, “Wide-angle infrared absorber based on a negative-index plasmonic metamaterial,” Phys. Rev. B 79, 045131 (2009). [CrossRef]

11

11. 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]

], fundamental questions remain. In fact, such a metamaterial absorber can be equivalent to a single layer of atoms (or molecules), and it is strongly inhomogeneous in the wave propagating direction [12

12. J. Zhou, H.-T. Chen, T. Koschny, A. K. Azad, A. J. Taylor, C. M. Soukoulis, and J. F. O’Hara, “Application of metasurface description for multilayered metamaterials and an alternative theory for metamaterial perfect absorber,” http://arxiv.org/abs/1111.0343.

]. So it can hardly be considered as an effective bulk medium where the constitutive parameters ε(ω) and μ(ω) apply. Additionally, Fabry-Pérot resonance [12

12. J. Zhou, H.-T. Chen, T. Koschny, A. K. Azad, A. J. Taylor, C. M. Soukoulis, and J. F. O’Hara, “Application of metasurface description for multilayered metamaterials and an alternative theory for metamaterial perfect absorber,” http://arxiv.org/abs/1111.0343.

14

14. J. Sun, L. Liu, G. Dong, and J. Zhou, “An extremely broad band metamaterial absorber based on destructive interference,” Opt. Express 19, 21155–21162 (2011). [CrossRef] [PubMed]

], conventional transmission line [15

15. Q. Y. Wen, Y. S. Xie, H. W. Zhang, Q. H. Yang, Y. X. Li, and Y. L. Liu, “Transmission line model and fields analysis of metamaterial absorber in the terahertz band,” Opt. Express 17, 20256–20265 (2009). [CrossRef] [PubMed]

], and cavity resonance [16

16. D. Y. Shchegolkov, A. K. Azad, J. F. O’Hara, and E. I. Simakov, “Perfect subwavelength fishnetlike metamaterial-based film terahertz absorbers,” Phys. Rev. B 82, 205117 (2010). [CrossRef]

] models have been proposed to explain metamaterial absorbers or antireflection coatings, which also raise questions regarding the existence or involvement of the magnetic resonance in metamaterial absorbers.

2. Models in numerical simulations

2.1. Coupled system

Without losing generality, I use a simple and typical metamaterial absorber structure operating at terahertz frequencies as an example. It consists of a cross-resonator array and a ground plane separated by d = 10 μm thick polyimide dielectric spacer [17

17. H. Tao, C. M. Bingham, A. C. Strikwerda, D. Pilon, D. Shrekenhamer, N. I. Landy, K. Fan, X. Zhang, W. J. Padilla, and R. D. Averitt, “Highly flexible wide angle of incidence terahertz metamaterial absorber: Design, fabrication, and characterization,” Phys. Rev. B 78, 241103(R) (2008). [CrossRef]

19

19. X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104, 207403 (2010). [CrossRef] [PubMed]

]. The unit cell is shown in Fig. 1(a), where the periodicity is p = 100 μm, the length and width of cross wires are l = 90 μm and w = 10 μm, respectively, and the thickness of metal is t = 0.2 μm. Due to the presence of the ground plane, the substrate only provides mechanical support and the choice of material does not affect the performance of the metamaterial absorber. Numerical simulations have been carried out using CST Microwave Studio 2009 [20

20. CST Microwave Studio 2009, http://www.cst.com/.

]. A perfect electric conductor (PEC) is used to simulate the metal, while the ohmic loss is effectively put in the polyimide spacer with dielectric constant εspacer = 3.1 × (1+ 0.07i). Periodic boundary conditions are applied to the side walls parallel to z direction, and the ports are at the front and back surfaces of the unit cell. The simulated electric field reflection |S11| is shown by the solid red curve in Fig. 1(c), which reveals a nearly zero reflection at a frequency slightly below 1 THz. This also suggests that the incident light is almost completely absorbed by the metamaterial in this narrow frequency band, according to A(ω) = 1–R(ω) – T(ω), where R(ω) = |S11|2 is the reflectance, and T(ω) = |S21|2 = 0 is the zero transmittance due the presence of the ground plane. The surface currents in the cross-resonator array and the ground plane exhibit anti-parallel directions, as shown in Fig. 1(d).

Fig. 1 (a) Schematic structure of the metamaterial absorber unit cell, which repeats in the x and y directions forming a square array with periodicity p. (b) Unit cell used to obtain the reflection and transmission coefficients at the air-spacer interface with the cross-resonator array. (c) The solid red curve is the reflection |S11| from the metamaterial absorber shown in unit cell (a), and the dashed blue curve is the resonant transmission |S21| through the cross-resonator array shown in unit cell (b). (d) Surface currents of the metamaterial absorber at the peak absorption frequency. The current at the cross flows to left direction, while it flows to right direction at the ground plane.

2.2. Decoupled system

The above model treats the metamaterial absorber as a coupled system, i.e., the possible near-field interactions and magnetic resonance have been taken into account between the cross-resonator array and the ground plane. However, we may also consider the presence of the metal cross-resonator array resulting in an impedance-tuned air-spacer interface [21

21. C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two-dimensional equivalent of metamaterials,” Metamaterials 3, 100–112 (2009). [CrossRef]

] with dramatically modified complex reflection and transmission coefficients shown in Fig. 2. The ground plane, on the other hand, functions as a perfect reflector with reflection coefficient −1. In the interference model we decouple the metamaterial absorber into two tuned interfaces, with the cross-resonator array and ground plane located at the two sides of the spacer. They are only linked by multiple reflections, as shown in the inset to Fig. 2(a), while any near-field interaction or magnetic resonance has been neglected. In this model, we need to know the reflection/transmission coefficients at the air-spacer interface with the cross-resonator array. These are obtained from simulations using the unit cell shown in Fig. 1(b), where the ground plane and the substrate have been removed (the spacer stays!) from the unit cell shown in Fig. 1(a). That is, the cross-resonators are on the surface of a half dielectric space. The cross-resonator array reveals a dipole resonance as indicated by the deep transmission dip at about 1.1 THz, shown in the dashed blue curve in Fig. 1(c). Comparing the two curves, the feature of particular interest and worthy of mentioning is that near-zero reflection (or unity absorption) of the metamaterial absorber occurs at a frequency different from and lower than the resonance frequency of the cross-resonator array.

Fig. 2 (a) Amplitude and (b) phase of the reflection and transmission coefficients at the air-spacer interface with cross-resonator array, obtained by numerical simulations using the unit cell shown in Fig. 1(b). Inset: Multiple reflections and interference model of the metamaterial absorber, where the cross-resonator array is indicated by the dashed line at the air-spacer interface.

3. Interference theory

As shown in the inset to Fig. 2(a), at the air-spacer interface with cross-resonator array, the incident light is partially reflected back to air with a reflection coefficient 12 = r12e12 and partially transmitted into the spacer with a transmission coefficient 12 = t12eiθ12. The latter continues to propagate until it reaches the ground plane, with a complex propagation phase β˜=βr+iβi=ε˜spacerk0d, where k0 is the free space wavenumber, βr is the propagation phase, and βi represents the absorption in the spacer. After the reflection at the ground plane and addition of another propagation phase β̃, partial reflection and transmission occur again at the air-spacer interface with cross-resonators with coefficients 21 = r21e21 and 21 = t21eiθ21. Similar to the light propagation in a stratified media [22

22. M. Born and E. Wolf, Principles of optics (Pergamon, 1980), 6th ed.

], the overall reflection is then the superposition of the multiple reflections:
r˜=r˜12t˜12t˜21ei2β˜1+r˜21ei2β˜,
(1)
where the first term is the reflection directly from the cross-resonator array, and the second term, including the “–” sign, is the reflection resulting from superposition of the multiple reflections between the cross-resonator array and ground plane. The absorptance is then retrieved through A(ω) = 1 – |(ω)|2 since the transmission is zero.

3.1. Spacer thickness dependent absorption

Using the reflection and transmission coefficients shown in Fig. 2, the absorptance is calculated in the decoupled metamaterial absorber system and the results are shown in Fig. 3, where I have purposely varied the spacer thickness d from 4 μm to 16 μm. The spacer thickness dependent absorptance in the coupled metamaterial absorber is also simulated directly using the unit cell shown in Fig. 1(a) and the results are shown in the inset to Fig. 3, which is in excellent agreement with the results calculated in the decoupled metamaterial absorber using the interference model. With all of these spacer thicknesses, we observe an absorption peak which increases in the beginning and its frequency red-shifts as the spacer thickness increases. It reaches near-unity absorption at 1 THz when the spacer thickness is about 10 μm, and then the peak value decreases and its frequency continuously red-shifts when the spacer thickness increases further. Further numerical simulations and calculations reveal that, with any chosen spacer dielectric material, there is always an optimized spacer thickness where the reflection can reach zero, i.e. unity-absorption.

Fig. 3 Calculated absorptance in the decoupled metamaterial absorber using the interference model for various spacer thicknesses. Insets: The simulated absorptance when treating the whole metamaterial absorber as a coupled system.

The excellent agreement shown in Fig. 3 validates the interference model I have presented above. The physical explanation of a metamaterial absorber is then as follows. The multiple reflections in the metamaterial absorber, i.e. the second term in Eq. (1), constructively interfere as evidenced by the fact that near 1 THz the phase change of a round trip is 2βr +ϕ21 + 180° ≈ 360°. The superposition of the multiple reflections then destructively interferes with the direct reflection from the air-spacer interface with cross-resonators, i.e. the first term in Eq. (1). With an optimized spacer thickness and in a narrow frequency range, these two terms completely cancel each other out resulting in zero reflection. For other spacer thicknesses or frequencies the amplitude and phase do not match and these two terms only partially cancel out or may even constructively add each other, resulting in: i) a reduced absorption peak and ii) corresponding frequency shift of the absorption peak when the spacer thickness deviates from the optimized value, and iii) dramatically reduced absorption when the frequency goes away from the center frequency. Obviously, this explanation does not involve any near-field interaction or magnetic resonance between the two metal layers in the metamaterial absorber. That is, the resonator array and ground plane in the “coupled” metamaterial absorber system can be indeed decoupled.

3.2. Anti-parallel surface currents

The remaining question is then why we observe the anti-parallel directions of the excited surface currents as shown in Fig. 1(d), which has been used as the evidence of a magnetic resonant response [8

8. 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]

] similar to fish-net metamaterials [6

6. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95, 137404 (2005). [CrossRef] [PubMed]

, 7

7. V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356–3358 (2005). [CrossRef]

]. In order to elucidate this mystic observation, by considering the boundary conditions at the interfaces I derive the excited effective surface currents based on interference and superposition. When the incident light with electric field Ecix^ is first reflected and transmitted at the air-spacer interface with cross-resonator array, according to the boundary condition requirements [23

23. J. D. Jackson, Classical Electrodynamics (Wiley, 1998), 3rd ed.

], it excites an effective surface current Jc=[(1r˜12)/Z0t˜12/Zs]Ecix^, where Z0 and Zs are impedances of the free space and spacer, respectively. The transmitted light continues to propagate and is reflected by the ground plane which excites a surface current at the ground plane Jg=2t˜12eiβ˜Eci/Zsx^. The reflection from the ground plane propagates back to the air-spacer interface with the cross-resonator array, where partial reflection and transmission occur which excites a surface current Jc=[(1r˜21)/Zst˜21/Z0]t˜12ei2β˜(1)Ecix^. This procedure continues and the overall surface currents at the cross-resonator array and ground plane are then superpositions of multiple excitations:
Jctotal={(1r˜12Z0t˜12Zs)(1r˜21Zst˜21Z0)t˜12ei2β˜1+r˜21ei2β˜}Ecix^,
(2)
Jgtotal=2t˜12eiβ˜1+r˜21ei2β˜1ZsEcix^.
(3)

With a spacer thickness of d = 10 μm, the phase and magnitude of surface currents in Eqs. (2) and (3) are shown in Fig. 4(a) and its inset, respectively, which reveal a phase difference of Δψ = ψcψg = 192° and comparable surface current magnitude at 1 THz. That is, they are almost out-of-phase, directly resulting from the interference rather than the magnetic resonance. We further use the obtained surface currents to calculate the overall backward radiation field (i.e. reflection) by ErJctotal+Jgtotaleiβ0 for different spacer thicknesses. The results shown in Fig. 4(b) reveal a reflection dip, in which the spacer thickness dependence of the reflection minimum and its frequency is again consistent with the absorption results shown in Fig. 2. We also notice that, in the calculated results shown in Fig. 4(a), although at frequencies below 1 THz the surface currents are out of phase (Δψ ∼180°), the difference of surface current magnitudes rapidly increases with decreasing frequency, which results in incomplete cancellation in backward radiation, i.e., high reflection and low absorption. On the other hand, at the higher frequency side, although the surface current magnitudes are relatively low, they are in phase (Δψ ∼ 3600°), which also results in high reflection and low absorption. These are in excellent agreement with the results in numerical simulations when treating the whole metamaterial absorber as a “coupled” system.

Fig. 4 (a) Phase spectra of the excited surface currents at the air-spacer interface with cross-resonator array (ψc) and at the ground plane (ψg), as well as their difference (ψcψg), calculated through multiple reflections and superposition based on the interference model. The corresponding magnitude of the surface currents are shown in the inset. (b) Backward radiation field (reflection) calculated through ErJctotal+Jgtotaleiβ0 for various spacer thicknesses.

4. Conclusion

I have shown that it is not required in a metamaterial absorber to have simultaneous electric and magnetic responses, which has previously been considered as the foundation of metamaterial absorbers. I explicitly demonstrate that the assumed magnetic resonance plays a negligible role in the impedance matching of metamaterial absorbers to free space. In contrast, it is the destructive interference between the direct reflection and the following multiple reflections that effectively traps light in the metamaterial absorbers and eventually causes the high absorption. Based on such an interference model, I derive the surface currents through multiple excitations and superposition, which clearly show the anti-parallel directions of surface currents in the resonator array and ground plane. This profound understanding of the underlying physics will undoubtedly provide valuable guidance in the future developments of more advanced metamaterial absorber based devices for microwave and photonic applications.

Acknowledgments

The author acknowledges the fruitful discussions with J. Zhou, Y. Zeng, L. Huang, A. K. Azad, J. F. O’Hara, W. J. Padilla, R. D. Averitt, and A. J. Taylor. I acknowledge support in part from the Los Alamos National Laboratory LDRD Program. This work was performed, in part, at the Center for Integrated Nanotechnologies, a US Department of Energy, Office of Basic Energy Sciences Nanoscale Science Research Center operated jointly by Los Alamos and Sandia National Laboratories. Los Alamos National Laboratory, an affirmative action/equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the US Department of Energy under contract DE-AC52-06NA25396.

References and links

1.

A. Alù, F. Bilotti, N. Engheta, and L. Vegni, “A thin absorbing screen using metamaterial complementary pairs,” in Proceedings of the International Conference on Electromagnetics in Advanced Applications, (Turin, Italy, September 12–16, 2005), 75–78.

2.

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]

3.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000). [CrossRef] [PubMed]

4.

H.-T. Chen, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “Manipulation of terahertz radiation using metamaterials,” Laser Photon. Rev. 5, 513–533 (2011). [CrossRef]

5.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).

6.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95, 137404 (2005). [CrossRef] [PubMed]

7.

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356–3358 (2005). [CrossRef]

8.

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]

9.

Y. Avitzour, Y. A. Urzhumov, and G. Shvets, “Wide-angle infrared absorber based on a negative-index plasmonic metamaterial,” Phys. Rev. B 79, 045131 (2009). [CrossRef]

10.

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]

11.

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]

12.

J. Zhou, H.-T. Chen, T. Koschny, A. K. Azad, A. J. Taylor, C. M. Soukoulis, and J. F. O’Hara, “Application of metasurface description for multilayered metamaterials and an alternative theory for metamaterial perfect absorber,” http://arxiv.org/abs/1111.0343.

13.

H.-T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010). [CrossRef] [PubMed]

14.

J. Sun, L. Liu, G. Dong, and J. Zhou, “An extremely broad band metamaterial absorber based on destructive interference,” Opt. Express 19, 21155–21162 (2011). [CrossRef] [PubMed]

15.

Q. Y. Wen, Y. S. Xie, H. W. Zhang, Q. H. Yang, Y. X. Li, and Y. L. Liu, “Transmission line model and fields analysis of metamaterial absorber in the terahertz band,” Opt. Express 17, 20256–20265 (2009). [CrossRef] [PubMed]

16.

D. Y. Shchegolkov, A. K. Azad, J. F. O’Hara, and E. I. Simakov, “Perfect subwavelength fishnetlike metamaterial-based film terahertz absorbers,” Phys. Rev. B 82, 205117 (2010). [CrossRef]

17.

H. Tao, C. M. Bingham, A. C. Strikwerda, D. Pilon, D. Shrekenhamer, N. I. Landy, K. Fan, X. Zhang, W. J. Padilla, and R. D. Averitt, “Highly flexible wide angle of incidence terahertz metamaterial absorber: Design, fabrication, and characterization,” Phys. Rev. B 78, 241103(R) (2008). [CrossRef]

18.

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]

19.

X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104, 207403 (2010). [CrossRef] [PubMed]

20.

CST Microwave Studio 2009, http://www.cst.com/.

21.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two-dimensional equivalent of metamaterials,” Metamaterials 3, 100–112 (2009). [CrossRef]

22.

M. Born and E. Wolf, Principles of optics (Pergamon, 1980), 6th ed.

23.

J. D. Jackson, Classical Electrodynamics (Wiley, 1998), 3rd ed.

OCIS Codes
(230.5750) Optical devices : Resonators
(310.1620) Thin films : Interference coatings
(160.3918) Materials : Metamaterials
(310.6805) Thin films : Theory and design

ToC Category:
Metamaterials

History
Original Manuscript: December 21, 2011
Revised Manuscript: February 24, 2012
Manuscript Accepted: February 26, 2012
Published: March 14, 2012

Citation
Hou-Tong Chen, "Interference theory of metamaterial perfect absorbers," Opt. Express 20, 7165-7172 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-7165


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References

  1. A. Alù, F. Bilotti, N. Engheta, L. Vegni, “A thin absorbing screen using metamaterial complementary pairs,” in Proceedings of the International Conference on Electromagnetics in Advanced Applications, (Turin, Italy, September 12–16, 2005), 75–78.
  2. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008). [CrossRef] [PubMed]
  3. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000). [CrossRef] [PubMed]
  4. H.-T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, “Manipulation of terahertz radiation using metamaterials,” Laser Photon. Rev. 5, 513–533 (2011). [CrossRef]
  5. W. Cai, V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).
  6. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95, 137404 (2005). [CrossRef] [PubMed]
  7. V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356–3358 (2005). [CrossRef]
  8. H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, W. J. Padilla, “A metamaterial absorber for the terahertz regime: Design, fabrication and characterization,” Opt. Express 16, 7181–7188 (2008). [CrossRef] [PubMed]
  9. Y. Avitzour, Y. A. Urzhumov, G. Shvets, “Wide-angle infrared absorber based on a negative-index plasmonic metamaterial,” Phys. Rev. B 79, 045131 (2009). [CrossRef]
  10. N. Liu, M. Mesch, T. Weiss, M. Hentschel, H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010). [CrossRef] [PubMed]
  11. J. Hao, L. Zhou, M. Qiu, “Nearly total absorption of light and heat generation by plasmonic metamaterials,” Phys. Rev. B 83, 165107 (2011). [CrossRef]
  12. J. Zhou, H.-T. Chen, T. Koschny, A. K. Azad, A. J. Taylor, C. M. Soukoulis, J. F. O’Hara, “Application of metasurface description for multilayered metamaterials and an alternative theory for metamaterial perfect absorber,” http://arxiv.org/abs/1111.0343 .
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