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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 11 — May. 21, 2012
  • pp: 12515–12520

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Ultrathin and broadband high impedance surface absorbers based on metamaterial substrates

Yongqiang Pang, Haifeng Cheng, Yongjiang Zhou, Zenggnag Li, and Jun Wang  »View Author Affiliations


Optics Express, Vol. 20, Issue 11, pp. 12515-12520 (2012)
http://dx.doi.org/10.1364/OE.20.012515


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Abstract

An ultrathin and simultaneously broadband high impedance surface absorber based on a metamaterial (MM) substrate is presented at microwave frequencies. The MM substrate is designed using metallic split ring resonators (SRRs) vertically embedded into a dielectric slab. Both the simulated and experimental results display two absorption peaks and an expanded absorption bandwidth of less than −10 dB compared to conventional ultrathin absorbers. By analyzing the field distributions and the substrate impedance characteristics, it is found that this feature is mainly related to the LC resonance of the substrate caused by the embedded SRRs. Our results demonstrate the great feasibility of broadening the absorption bandwidth of the ultrathin high impedance surface absorbers by the MMs incorporation.

© 2012 OSA

1. Introduction

Metamaterials (MMs) have undergone rapid development during the last decade due to their engineered electromagnetic (EM) responses not usually found in nature materials. Based on these exotic properties, many novel materials/devices have been reported, such as invisibility cloaks [1

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

–3

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009). [CrossRef] [PubMed]

], superlens [4

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

,5

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]

] and perfect absorbers [6

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef] [PubMed]

–13

L. Li, Y. Yang, and C. H. Liang, “A wide-angle polarization-insensitive ultra-thin metamaterial absorber with three resonant modes,” J. Appl. Phys. 110(6), 063702 (2011). [CrossRef]

]. Among many other researches, there have been some studies demonstrating that the microwave permeability of general magnetic materials can be enhanced by MM structures [14

O. Acher, “Permeability enhancement of soft magnetic films through metamaterial structures,” J. Magn. Magn. Mater. 320(23), 3276–3281 (2008). [CrossRef]

–16

Z. W. Li, R. F. Huang, and L. B. Kong, “Permeability and resonance characteristics of metamaterial constructed by a wire coil wound on a ferrite core,” J. Appl. Phys. 106(10), 103929 (2009). [CrossRef]

]. It is also found that MMs incorporated with external-source-controlled natural materials can exhibit novel properties, such as thermal tunability [17

Q. Y. Wen, H. W. Zhang, Q. H. Yang, Y. S. Xie, K. Chen, and Y. L. Liu, “Terahertz metamaterial with VO2 cut-wires for thermal tunability,” Appl. Phys. Lett. 97(2), 021111 (2010). [CrossRef]

] and the blueshift switch [18

N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, “Optically implemented broadband blueshift switch in the terahertz regime,” Phys. Rev. Lett. 106(3), 037403 (2011). [CrossRef] [PubMed]

]. These successful combinations of traditional materials with the MMs promise great opportunities in the creation of useful materials/devices by bringing together the advantages of both types of materials.

As is well known, ultrathin absorbers consisting of high impedance surfaces developed in recent years can be characterized by an electrical thickness of much less than λ/4 at the operating frequency [12

S. Gu, J. P. Barrett, T. H. Hand, B. I. Popa, and A. Cummer, “A broadband low-reflection metamaterial absorber,” J. Appl. Phys. 108(6), 064913 (2010). [CrossRef]

,19

Q. Gao, Y. Yin, D. B. Yan, and N. C. Yuan, “Application of metamaterials to ultra-thin radar-absorbing material design,” Electron. Lett. 41(17), 936–937 (2005). [CrossRef]

]. However, they suffer from narrow operating bandwidths, greatly limiting their utility in most applications. Ultrathin and simultaneously wideband absorbers are urgently desired. In this work, we present an ultrathin high impedance surface absorber based on a MM substrate at microwave frequencies. Unlike the conventional ultrathin absorbers, our proposed absorber exhibits wideband absorption properties demonstrated numerically as well as experimentally. Here, the bandwidth is defined as the frequency band where the reflectivity is less than −10 dB. Finally, both the field analysis and impedance characteristic of the MM substrate are proposed to explain why the absorption bandwidth is enhanced after the metal SRRs being integrated into a conventional ultrathin high impedance surface absorber.

2. Design and experiment

A single unit cell of the designed MM based absorber is illustrated in Fig. 1(a) , which consists of a capacitive array of square resistive patches placed on top of a 2.0 mm thick meta-backed substrate. The period of the unit cell is P = 11.8 mm and the dimension of the patches is D = 8.7 mm. The surface resistance of the patches is Rs = 9.5 Ω/sq. What is different from conventional high impedance surface absorbers is that this absorber is constructed by a MM substrate instead of dielectric slabs. As shown in Figs. 1(b) and 1(c), the designed MM substrate consists of a dielectric slab embedded with copper split-ring resonators (SRRs) symmetrically. Each unit cell only includes one SRR. The SRRs have the dimension parameters as follows: the strip width w = 0.2 mm, the gap width s = 0.2 mm, the lengths of stalks are L1 = 10.6 mm and L2 = 1.2 mm. The dielectric slab used throughout this work is the commercial FR-4 with a relative permittivity of 4.4 and a tangential loss of 0.02. We perform numerical simulations of the absorber using the standard finite difference time domain method. In the simulations, periodic boundary conditions are set in both the x-axis and y-axis directions. In the z-axis direction, one port is added above the absorber surface for the EM wave incidence, and an electric boundary is set at the substrate bottom to model the backed metal. The incident plane wave is expected to be normal to the absorber surface, as shown in Fig. 1(b). The copper SRRs are modeled as 18 μm thick metal strips with an electrical conductivity σ = 5.8 × 107 S/m. Since the MM substrate is metal-backed, the transmission is zero and thus the absorption can be determined only by the reflection response. Here, the reflectivity is used to characterize the absorption properties of the absorbers.

Fig. 1 Schematic of the designed MM based absorber: (a) Single unit cell of the MM based absorber, (b) perspective view and (c) sectional view of the MM substrate. The geometry of the array is square in shape and the thickness of h is less than λ/4 at the operating frequency. Each unit cell only includes one SRR symmetrically and vertically.

The simulated results are presented in Fig. 2 . When the incident electric field propagates along the x-axis direction [see Fig. 1(b)], two absorption peaks can be observed clearly at the frequencies of 5.9 GHz and 6.7 GHz. However, in the case of the incident electric field propagating along the y-axis direction [see Fig. 1(b)], the absorber shows only one absorption peak at 6.5 GHz. This is due to the fact that the used SRRs are polarization sensitive with the incident EM wave. When the incident electric field is perpendicular to the SRRs, i.e. along the y-axis direction, neither an electrical response nor a magnetic response can be driven. As a result, the reflection response exhibits the same behavior as the absorber without the SRR inclusions, as shown in Fig. 2(b). It should be noted that the metal-backed MM substrate, i.e. the SRR absorber, also displays an absorption peak near 5.9 GHz as shown in Fig. 2(a). Thus we can infer that the absorption peak at 5.9 GHz for the MM based absorber is mainly related to the resonance of the metal-backed SRR substrate, and this will be confirmed in the latter section.

Fig. 2 Simulated and measured reflectivity of the MM based absorber with the incident electric field propagating along (a) the x-axis and (b) y-axis directions. Inserts show the power loss density at the corresponding absorption peaks. Dash line shows the reflectivity of the absorber without the SRR inclusions. Green curves show the simulated reflectivity of the SRR absorber.

In experiments, we first fabricated the copper SRRs on RF-4 dielectric strips using the LPKF H100 circuit board plotter as shown in Fig. 3(a) , and then vertically inserted these strips into a slotted FR-4 slab to construct the MM substrate. The thickness of copper is about 18 μm. Afterward, the resistive patch array was printed on a 0.025 mm thick PET film with a relative permittivity of 3.6 by the silk-screen technique and then pasted on the fabricated MM substrate. A photograph of the fabricated absorber is shown in Fig. 3(b). The measurement was performed by an Agilent 8720ET network analyzer with a pair of antenna horns. The absorber was placed on a metal plate to eliminate the transmission in the measurements. An incident EM wave from one horn reflects on the absorber surface and is then received by the other horn, so the reflectivity can be derived.

Fig. 3 Photographs of the experimental prototypes: (a) SRRs and (b) the MM based absorber.

The measured results of the fabricated MM based absorber are presented in Fig. 2. It can be observed that both intensities and frequencies at the absorption peaks are smaller than the simulation results. This is most likely caused by the introduction of the super thin PET film as well as the fabrication imperfections. In spite of these discrepancies, considerable agreements can be found between the numerical and experimental results. For example, both the simulated and measured reflectivity show two absorption peaks, and as a consequence an enhanced absorption bandwidth of less than −10 dB compared with the conventional ultrathin absorbers when the electric field propagates along the x-axis direction. These results indicate that the proposed absorbing structure offers a possible approach to design ultrathin and simultaneously broadband absorbers.

3. Discussions

We now give an investigation into the physical origin of two absorption peaks shown in Fig. 2(a). Because the loss of the copper SRRs and the FR-4 is relatively small and can be neglected, the absorbed energy is mainly dissipated by the resistive loss of the patch array. The power loss density of the absorber at the two absorption frequencies is shown in inserts of Fig. 2(a). It can be observed that most of the power is lost in central region of the resistive patches at 6.7 GHz, and in both the central and edge areas at 5.9 GHz. However, for the case of the incident electric field propagating along the y-axis direction, i.e. the conventional absorber, the power is mainly lost in edge region of the resistive patches, as shown in insert of Fig. 2(b). Therefore, we can conjecture that the proposed MM based absorber with two absorption peaks has different resonance mechanisms from the conventional absorbers. This can be verified by examining the surface current distributions at the corresponding absorption frequencies [8

X. Shen, T. J. Cui, J. Zhao, H. F. Ma, W. X. Jiang, and H. Li, “Polarization-independent wide-angle triple-band metamaterial absorber,” Opt. Express 19(10), 9401–9407 (2011). [CrossRef] [PubMed]

,10

B. Wang, T. Koschny, and C. M. Soukoulis, “Wide-angle and polarization-independent chiral metamaterial absorber,” Phys. Rev. B 80(3), 033108 (2009). [CrossRef]

,13

L. Li, Y. Yang, and C. H. Liang, “A wide-angle polarization-insensitive ultra-thin metamaterial absorber with three resonant modes,” J. Appl. Phys. 110(6), 063702 (2011). [CrossRef]

].

Figures 4(a) and 4(b) show the surface current distributions of the MM based absorber at the two absorption frequencies of 5.9 GHz and 6.7 GHz, respectively. From the result in Fig. 4(a), both magnetic and electrical resonances can be observed at the absorption peak of 5.9 GHz. For the magnetic resonance, the backed metal layer and the lower stalk of the SRR carry electrical charges with opposite signs leading to a circulating current, which creates the magnetic flux coupling with the incident magnetic field. At the electrical resonance, the induced current flows through the long stalks of the SRRs parallel to the incident electric field. However, with regard to the other absorption peak at 6.7 GHz, only the electrical resonance phenomenon can be found as shown in Fig. 4(b). Therefore, these two absorption peaks relies on the localized magnetic and electrical resonances, but have a little difference on the physical origin.

Fig. 4 Surface current distributions of the absorber at the two absorption frequencies of (a) 5.9 GHz and (b) 6.7 GHz.

To further understand the absorption mechanism of the proposed absorber, we present the impedance characteristic of the metal-backed MM substrate, which can be extracted using reflection and transmission responses (Here the transmission is zero because of the backed metal.). Figure 5 shows the calculated normalized complex impedance of the metal-backed MM substrate with different incident electric field directions. When the incident electric field propagates along the y-axis direction, the MM substrate behaviors as an inductor with a positive imaginary part of the complex impedance [see Fig. 5(b)], which can be modeled as an L circuit. As a result, only one resonance occurs in conjunction with the capacitive response of the patch array layer. This is similar to the ultrathin high impedance surface absorbers based on the conventional substrates as reported in [20

O. Luukkonen, F. Costa, C. R. Simovski, A. Monorchio, and S. A. Tretyakov, “A thin electromagnetic absorber for wide incidence angle and both polarization,” IEEE Trans. Antenn. Propag. 57(10), 3119–3125 (2009). [CrossRef]

–22

A. Kazemzadeh and A. Karlsson, “On the absorption mechanism of ultra thin absorbers,” IEEE Trans. Antenn. Propag. 58(10), 3310–3315 (2010). [CrossRef]

]. However, in the case of the incident electric field propagating along the x-axis direction, the MM substrate displays exotic impedance characteristics with presence of a resonance phenomenon, which can be easily designed by adjusting the length of the SRR long stalks, as shown in Fig. 5(a). Within the frequency range below its intrinsic resonance frequency, the metal-backed MM substrate shows an inductive behavior and can be modeled as an L circuit, while an LC circuit at the high frequency range. This substantial impedance characteristic offers the potential of forming a multi-resonance circuit, and thus a wideband absorber can be achieved by designing the dimension parameters carefully.

Fig. 5 Normalized complex impedance of the metal-backed MM substrate: (a) Incident electric field propagates along the x-axis direction. The MM substrates with L1 = 9.0 mm and L1 = 11.2 mm are also presented. (b) Incident electric field propagates along the y-axis direction. Inserts show the equivalent circuit model of imaginary part of the complex impedance.

To the end, it should be noted that the absorber presented in this work is polarization sensitive, which may be not desirable for some practical applications. However, we believe this drawback can be conquered by the use of high symmetry elements as other polarization insensitive MMs [8

X. Shen, T. J. Cui, J. Zhao, H. F. Ma, W. X. Jiang, and H. Li, “Polarization-independent wide-angle triple-band metamaterial absorber,” Opt. Express 19(10), 9401–9407 (2011). [CrossRef] [PubMed]

,10

B. Wang, T. Koschny, and C. M. Soukoulis, “Wide-angle and polarization-independent chiral metamaterial absorber,” Phys. Rev. B 80(3), 033108 (2009). [CrossRef]

,11

M. H. Li, H. L. Yang, X. W. Hou, Y. Tian, and D. Y. Hou, “Perfect metamaterial absorber with dual bands,” Prog. Electromag. Res. 108, 37–49 (2010). [CrossRef]

,13

L. Li, Y. Yang, and C. H. Liang, “A wide-angle polarization-insensitive ultra-thin metamaterial absorber with three resonant modes,” J. Appl. Phys. 110(6), 063702 (2011). [CrossRef]

].

4. Conclusion

In this work, we have presented an ultrathin high impedance surface absorber based on a MM substrate. The overall thickness of the absorber is just 2.0 mm, which is almost 1/24 of the free space wavelength at the band central frequency of 6.25 GHz. Both the numerical simulation and experimental measurement demonstrate that the proposed absorber exhibits two absorption peaks and a broadened absorption bandwidth of less than −10 dB. In contrast, conventional ultrathin high impedance surface absorbers are a class of single band absorbers. By analyzing the distributions of the power loss density and the surface current, as well as the impedance characteristics of the MM substrate, it is found that this feature is mainly related to the LC resonance ability of the metal-backed MM substrate.

References and links

1.

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

2.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]

3.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science 323(5912), 366–369 (2009). [CrossRef] [PubMed]

4.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

5.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]

6.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef] [PubMed]

7.

P. K. Singh, K. A. Korolev, M. N. Afsar, and S. Sonkusale, “Single and dual band 77/95/110 GHz metamaterial absorbers on flexible polyimide substrate,” Appl. Phys. Lett. 99(26), 264101 (2011). [CrossRef]

8.

X. Shen, T. J. Cui, J. Zhao, H. F. Ma, W. X. Jiang, and H. Li, “Polarization-independent wide-angle triple-band metamaterial absorber,” Opt. Express 19(10), 9401–9407 (2011). [CrossRef] [PubMed]

9.

Y. Q. Xu, P. H. Zhou, H. B. Zhang, L. Chen, and L. J. Deng, “A wide-angle planar metamaterial absorber based on split ring resonator coupling,” J. Appl. Phys. 110(4), 044102 (2011). [CrossRef]

10.

B. Wang, T. Koschny, and C. M. Soukoulis, “Wide-angle and polarization-independent chiral metamaterial absorber,” Phys. Rev. B 80(3), 033108 (2009). [CrossRef]

11.

M. H. Li, H. L. Yang, X. W. Hou, Y. Tian, and D. Y. Hou, “Perfect metamaterial absorber with dual bands,” Prog. Electromag. Res. 108, 37–49 (2010). [CrossRef]

12.

S. Gu, J. P. Barrett, T. H. Hand, B. I. Popa, and A. Cummer, “A broadband low-reflection metamaterial absorber,” J. Appl. Phys. 108(6), 064913 (2010). [CrossRef]

13.

L. Li, Y. Yang, and C. H. Liang, “A wide-angle polarization-insensitive ultra-thin metamaterial absorber with three resonant modes,” J. Appl. Phys. 110(6), 063702 (2011). [CrossRef]

14.

O. Acher, “Permeability enhancement of soft magnetic films through metamaterial structures,” J. Magn. Magn. Mater. 320(23), 3276–3281 (2008). [CrossRef]

15.

Z. W. Li, R. F. Huang, and L. B. Kong, “Greatly enhanced azimuthal permeability of a ferrite core with a wire coil metamaterial,” Appl. Phys. Lett. 94(16), 162502 (2009). [CrossRef]

16.

Z. W. Li, R. F. Huang, and L. B. Kong, “Permeability and resonance characteristics of metamaterial constructed by a wire coil wound on a ferrite core,” J. Appl. Phys. 106(10), 103929 (2009). [CrossRef]

17.

Q. Y. Wen, H. W. Zhang, Q. H. Yang, Y. S. Xie, K. Chen, and Y. L. Liu, “Terahertz metamaterial with VO2 cut-wires for thermal tunability,” Appl. Phys. Lett. 97(2), 021111 (2010). [CrossRef]

18.

N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, “Optically implemented broadband blueshift switch in the terahertz regime,” Phys. Rev. Lett. 106(3), 037403 (2011). [CrossRef] [PubMed]

19.

Q. Gao, Y. Yin, D. B. Yan, and N. C. Yuan, “Application of metamaterials to ultra-thin radar-absorbing material design,” Electron. Lett. 41(17), 936–937 (2005). [CrossRef]

20.

O. Luukkonen, F. Costa, C. R. Simovski, A. Monorchio, and S. A. Tretyakov, “A thin electromagnetic absorber for wide incidence angle and both polarization,” IEEE Trans. Antenn. Propag. 57(10), 3119–3125 (2009). [CrossRef]

21.

F. Costa, A. Monorchio, and G. Manara, “Analysis and design of ultrathin electromagnetic absorbers comprising resistively loaded high impedance surfaces,” IEEE Trans. Antenn. Propag. 58(5), 1551–1558 (2010). [CrossRef]

22.

A. Kazemzadeh and A. Karlsson, “On the absorption mechanism of ultra thin absorbers,” IEEE Trans. Antenn. Propag. 58(10), 3310–3315 (2010). [CrossRef]

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

ToC Category:
Metamaterials

History
Original Manuscript: April 5, 2012
Revised Manuscript: April 24, 2012
Manuscript Accepted: May 2, 2012
Published: May 17, 2012

Citation
Yongqiang Pang, Haifeng Cheng, Yongjiang Zhou, Zenggnag Li, and Jun Wang, "Ultrathin and broadband high impedance surface absorbers based on metamaterial substrates," Opt. Express 20, 12515-12520 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-12515


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References

  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  2. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006). [CrossRef] [PubMed]
  3. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009). [CrossRef] [PubMed]
  4. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  5. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005). [CrossRef] [PubMed]
  6. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett.100(20), 207402 (2008). [CrossRef] [PubMed]
  7. P. K. Singh, K. A. Korolev, M. N. Afsar, and S. Sonkusale, “Single and dual band 77/95/110 GHz metamaterial absorbers on flexible polyimide substrate,” Appl. Phys. Lett.99(26), 264101 (2011). [CrossRef]
  8. 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. Express19(10), 9401–9407 (2011). [CrossRef] [PubMed]
  9. Y. Q. Xu, P. H. Zhou, H. B. Zhang, L. Chen, and L. J. Deng, “A wide-angle planar metamaterial absorber based on split ring resonator coupling,” J. Appl. Phys.110(4), 044102 (2011). [CrossRef]
  10. B. Wang, T. Koschny, and C. M. Soukoulis, “Wide-angle and polarization-independent chiral metamaterial absorber,” Phys. Rev. B80(3), 033108 (2009). [CrossRef]
  11. M. H. Li, H. L. Yang, X. W. Hou, Y. Tian, and D. Y. Hou, “Perfect metamaterial absorber with dual bands,” Prog. Electromag. Res.108, 37–49 (2010). [CrossRef]
  12. S. Gu, J. P. Barrett, T. H. Hand, B. I. Popa, and A. Cummer, “A broadband low-reflection metamaterial absorber,” J. Appl. Phys.108(6), 064913 (2010). [CrossRef]
  13. L. Li, Y. Yang, and C. H. Liang, “A wide-angle polarization-insensitive ultra-thin metamaterial absorber with three resonant modes,” J. Appl. Phys.110(6), 063702 (2011). [CrossRef]
  14. O. Acher, “Permeability enhancement of soft magnetic films through metamaterial structures,” J. Magn. Magn. Mater.320(23), 3276–3281 (2008). [CrossRef]
  15. Z. W. Li, R. F. Huang, and L. B. Kong, “Greatly enhanced azimuthal permeability of a ferrite core with a wire coil metamaterial,” Appl. Phys. Lett.94(16), 162502 (2009). [CrossRef]
  16. Z. W. Li, R. F. Huang, and L. B. Kong, “Permeability and resonance characteristics of metamaterial constructed by a wire coil wound on a ferrite core,” J. Appl. Phys.106(10), 103929 (2009). [CrossRef]
  17. Q. Y. Wen, H. W. Zhang, Q. H. Yang, Y. S. Xie, K. Chen, and Y. L. Liu, “Terahertz metamaterial with VO2 cut-wires for thermal tunability,” Appl. Phys. Lett.97(2), 021111 (2010). [CrossRef]
  18. N. H. Shen, M. Massaouti, M. Gokkavas, J. M. Manceau, E. Ozbay, M. Kafesaki, T. Koschny, S. Tzortzakis, and C. M. Soukoulis, “Optically implemented broadband blueshift switch in the terahertz regime,” Phys. Rev. Lett.106(3), 037403 (2011). [CrossRef] [PubMed]
  19. Q. Gao, Y. Yin, D. B. Yan, and N. C. Yuan, “Application of metamaterials to ultra-thin radar-absorbing material design,” Electron. Lett.41(17), 936–937 (2005). [CrossRef]
  20. O. Luukkonen, F. Costa, C. R. Simovski, A. Monorchio, and S. A. Tretyakov, “A thin electromagnetic absorber for wide incidence angle and both polarization,” IEEE Trans. Antenn. Propag.57(10), 3119–3125 (2009). [CrossRef]
  21. F. Costa, A. Monorchio, and G. Manara, “Analysis and design of ultrathin electromagnetic absorbers comprising resistively loaded high impedance surfaces,” IEEE Trans. Antenn. Propag.58(5), 1551–1558 (2010). [CrossRef]
  22. A. Kazemzadeh and A. Karlsson, “On the absorption mechanism of ultra thin absorbers,” IEEE Trans. Antenn. Propag.58(10), 3310–3315 (2010). [CrossRef]

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