Abstract

We have engineered numerically perfect absorbers based on a square ring pattern. The mono- and the multiband perfect absorption were presented in the whole midinfrared region. The characteristic dimension of the single square ring absorber (SSRA), i.e., lattice constant a, can be smaller than 0.1 times the operating wavelength so that the absorber could be viewed as continuous medium. This should be attributed to the high reactance of the patterns, as depicted in an extended equivalent circuit model of our structure. The model can accurately make a prediction of the operating wavelength of the SSRA, and the relative errors can be less than 5%. A crude numerical model of effective permeability was also deduced to account for the magnetic property of the absorbers in the optical spectrum. The multiband perfect absorber exhibited a good stability of polarization, incident angle, and azimuth.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011 (3)

2010 (3)

2009 (3)

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103, 213902 (2009).
[CrossRef]

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

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

2008 (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]

B. J. Lee, L. P. Wang, and Z. M. Zhang, “Coherent thermal emission by excitation of magnetic polaritons between periodic strips and a metallic film,” Opt. Express 16, 11328 (2008).
[CrossRef]

2007 (1)

2006 (1)

2005 (2)

T. Koschny, L. Zhang, and C. M. Soukoulis, “Isotropic three-dimensional left-handed metamaterials,” Phys. Rev. B 71, 121103 (2005).
[CrossRef]

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

2004 (2)

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[CrossRef]

2002 (1)

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

1983 (1)

Alexander, R. W.

Bell, R. J.

Bell, R. R.

Bell, S. E.

Chen, Q.

Chen, S.

Chen, X.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Cui, T. J.

Cumming, D. R. S.

Economon, E. N.

Economou, E. N.

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[CrossRef]

Frimmer, M.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103, 213902 (2009).
[CrossRef]

Grant, J.

Grzegorczyk, T. M.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Hao, Q.

He, S.

Huang, T. J.

Hubert, B.

Jiang, W. X.

Jin, Y.

Khalid, A.

Khoo, I. C.

Kim, J. B.

Kiraly, B.

Koenderink, A. F.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103, 213902 (2009).
[CrossRef]

Kong, J. A.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Koschny, T.

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

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

T. Koschny, L. Zhang, and C. M. Soukoulis, “Isotropic three-dimensional left-handed metamaterials,” Phys. Rev. B 71, 121103 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[CrossRef]

Lam, V. D.

Landau, L. D.

L. D. Landau, E. M. Liftshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, 1984).

Landy, N. I.

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]

Lee, B. J.

Lee, S. J.

Lee, Y. P.

Li, H.

Liftshitz, E. M.

L. D. Landau, E. M. Liftshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, 1984).

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[CrossRef]

Liu, X. L.

X. L. 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]

Long, L. L.

Ma, H. F.

Ma, Y.

Marcus, D.

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

Markos, P.

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Mock, J. J.

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]

Ordal, M. A.

Pacheco, J.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Padilla, W. J.

X. L. 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]

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]

Pitaevskii, L. P.

L. D. Landau, E. M. Liftshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, 1984).

Saha, S. C.

Sajuyigbe, S.

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]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Sersic, I.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103, 213902 (2009).
[CrossRef]

Shen, X. P.

Smith, D. R.

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]

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Soukoulis, C. M.

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

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

T. Koschny, L. Zhang, and C. M. Soukoulis, “Isotropic three-dimensional left-handed metamaterials,” Phys. Rev. B 71, 121103 (2005).
[CrossRef]

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Starr, A. F.

X. L. 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]

Starr, T.

X. L. 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]

Thomas, K.

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

Thomas, M.

Verhagen, E.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103, 213902 (2009).
[CrossRef]

Vier, D. C.

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

Wang, L. P.

Ward, C. A.

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[CrossRef]

Wu, B. I.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Ye, Y. Q.

Zhang, B.

Zhang, L.

T. Koschny, L. Zhang, and C. M. Soukoulis, “Isotropic three-dimensional left-handed metamaterials,” Phys. Rev. B 71, 121103 (2005).
[CrossRef]

Zhang, Z. M.

Zhao, J. M.

Zhao, Y.

Zhou, J.

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

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. B (2)

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. B (4)

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

T. Koschny, L. Zhang, and C. M. Soukoulis, “Isotropic three-dimensional left-handed metamaterials,” Phys. Rev. B 71, 121103 (2005).
[CrossRef]

T. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, “Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials,” Phys. Rev. B 71, 245105 (2005).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Phys. Rev. E (1)

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).
[CrossRef]

Phys. Rev. Lett. (3)

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103, 213902 (2009).
[CrossRef]

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]

X. L. 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]

Science (1)

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[CrossRef]

Other (1)

L. D. Landau, E. M. Liftshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, 1984).

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Figures (9)

Fig. 1.
Fig. 1.

Sketches of unit cell of the two absorbers in the calculation of the scattering parameters. (a) SSRA, (b) DSRA, and (c) the polarization and propagation direction of the incident wave.

Fig. 2.
Fig. 2.

Absorption spectra of SSRAs with different optimized parameter values given in Table 1.

Fig. 3.
Fig. 3.

(a) Calculated effective optical constants of the SSRA 4. The permittivity is scaled by a factor of 1/50. (b) The calculated effective impedance of the SSRA 4.

Fig. 4.
Fig. 4.

Monitored field distribution and magnetic energy density in two absorbers. (a) The current density distribution on the bottom of the square ring in SSRA 4 structure at a wavelength of 8.45 μm, (b) the side elevation of the current density distribution, (c) the electric field distribution in dielectric spacer view in x direction, (d) the sketch of the distribution of charges with opposite signs on the bottom of square ring. The contour represents the z component of electric field magnitude on a logarithmic scale. (e) The electric field distribution in between nearest unit cells, (f) the magnetic energy density in SSRA 4 at a wavelength of 8.45 μm, (g) and (h) representing the magnetic energy density of the DSRA 1 at wavelengths of 8.73 μm and 4.17 μm, respectively.

Fig. 5.
Fig. 5.

Schematic drawing of the extended equivalent circuit for one unit cell of the absorbers.

Fig. 6.
Fig. 6.

(a) Comparison between the predicted resonance wavelength and results obtained from the full-wave simulation for different side length values of the first five square rings in Table 1, apart from the thickness of spacer was held constant of 0.16 μm. The corresponding relative errors were calculated. (b) Dependence of resonance wavelength on the width w of the square ring, when a=1.9μm, l=1.7μm, d=0.16μm. (c) Dependence of resonance wavelength on the period a when l=1.7μm, w=0.4μm, d=0.16μm.

Fig. 7.
Fig. 7.

Calculated effective magnetic permeability for the first five SSRAs in Table 1.

Fig. 8.
Fig. 8.

Absorption spectra of DSRAs with different optimized parameter values given in Table 1.

Fig. 9.
Fig. 9.

Simulated absorption efficiencies as a function of incident angle θ for (a) TE polarization and (b) TM polarization, when azimuth ϕ=0. The absorptivity as a function of azimuth ϕ for (c) TE polarization and (d) TM polarization, when incident angle θ=60°.

Tables (1)

Tables Icon

Table 1. Optimized Geometrical Parameters of Two Kinds of Absorbers (in Micrometers)

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

Lm=μ0leffd/(2w),
Cm=ε0εrσeff/d,
σeff=w[0.5l+c1(l2w)],
Cg=0.5πε0l/ln(g/t).
Cg=0.5ε0lt/g
Ztot=iωLm1ω2LmCg+2iωCm+iωLm,
ωr=Cm+Cg(Cm2+Cg2)1/2LmCmCg.
LmdIdt+2CmIdt+Ug=dΦdt
CgdUgdt+1LmUgdt=I,
Ug=(Lm1LmCgω2)dIdt.
I=μ0SCm(ω2LmCgω4)22Lm(Cm+Cg)ω2+Lm2CmCgω4H.
μeff(ω)=1+2μ0S2Cm(ω2LmCgω4)a2(t+d)[22Lm(Cm+Cg)ω2+Lm2CmCgω4].

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