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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 26 — Dec. 21, 2009
  • pp: 23914–23919
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All-metal self-supported THz metamaterial – the meta-foil

H.O. Moser, L.K. Jian, H.S. Chen, M. Bahou, S.M.P. Kalaiselvi, S. Virasawmy, S.M. Maniam, X.X. Cheng, S.P. Heussler, Shahrain bin Mahmood, and B.-I. Wu  »View Author Affiliations


Optics Express, Vol. 17, Issue 26, pp. 23914-23919 (2009)
http://dx.doi.org/10.1364/OE.17.023914


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Abstract

Modern metamaterials face functional constraints as they are commonly embedded in or deposited on dielectric materials. We provide a new solution by microfabricating a completely free-standing all-metal self-supported metamaterial. Using upright S-string architecture with the distinctive feature of metallic transverse interconnects, we form a locally stiff, globally flexible space-grid. Infrared Fourier transform interferometry reveals the typical double-peak structure of a magnetically excited left-handed and an electrically excited right-handed pass-band that is maintained under strong bending and heating, and is sensitive to dielectrics. Exploiting UV/X-ray lithography and ultimately plastic moulding, meta-foils can be mass manufactured cost-effectively to serve as optical elements.

© 2009 OSA

Controlling and manipulating electromagnetic radiation by its interaction with materials is a cornerstone of optics. The study of metamaterials that allow selecting their permittivity and permeability freely from positive to negative values has led to new visions including sub-wavelength-resolution imaging [1

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

3

3. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]

], invisibility cloaking [4

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

6

6. 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]

], and mimicking celestial mechanics [7

7. D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009). [CrossRef]

]. Obviously, seeing sharper or becoming invisible are strong driving forces. However, the development of practical metamaterials for the THz range up to the visible is lagging behind theoretical studies and envisaged applications. A practical metamaterial would be available in copious quantities and enable customized solutions, much like a foil, whereas most of present-day metamaterials are made by time-consuming primary pattern generation and involve dielectric substrates or matrices, which might substantially restrict their usefulness and applicability due to electric, mechanical, and thermal properties of dielectrics as well as their sensitivity to humidity and radiation degradation [8

8. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef] [PubMed]

14

14. 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(24), 3356–3358 (2005). [CrossRef] [PubMed]

].

In earlier work, we mitigated such restrictions by micromanufacturing of free-standing metamaterials from metal-string arrays suspended in free space by plastic window-frames [15

15. H. O. Moser, J. A. Kong, L. K. Jian, H. S. Chen, G. Liu, M. Bahou, S. M. P. Kalaiselvi, S. M. Maniam, X. X. Cheng, B. I. Wu, P. D. Gu, A. Chen, S. P. Heussler, S. bin Mahmood, and L. Wen, “Free-standing THz electromagnetic metamaterials,” Opt. Express 16(18), 13773–13780 (2008). [CrossRef] [PubMed]

]. Strings are a preferred architecture of metamaterials as they extend continuously along one dimension. Made of gold, strings were S-shaped longitudinally. Aligned assembly of two chips of strings created a bi-layer chip in which two layers of S-strings, typically 1 to 10 μm apart, were opposed such as to form the well-known S-string resonator loops [16

16. H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(5 Pt 2), 057605 (2004). [CrossRef] [PubMed]

]. However, window-frames were still rigid and restricted the useful range of incidence angles.

Here, we demonstrate an all-metal approach where the conducting metal is the structural material simultaneously and no rigid window-frame is needed anymore. Individual S-strings are connected by transverse rods creating a space-grid that is self-supporting, locally stiff, but globally flexible. Connections are made between oscillation nodes of the current in the strings to minimize any influence on resonances. Introducing such bonds between the “atoms” of the metamaterial, we form a “crystal lattice”, overcoming conventional “frozen-in solutions” like matrix embedding or thin films on substrates. For their foil-like appearance, we dub such space-grids “meta-foil”. Meta-foils can be tailor-made to virtually any shape, bent, and wrapped around objects to hide and shield them from electromagnetic radiation, thus becoming true metamaterials on curved surfaces. Owing to the metallic interconnects, they are much more robust than earlier bi-layer chips [15

15. H. O. Moser, J. A. Kong, L. K. Jian, H. S. Chen, G. Liu, M. Bahou, S. M. P. Kalaiselvi, S. M. Maniam, X. X. Cheng, B. I. Wu, P. D. Gu, A. Chen, S. P. Heussler, S. bin Mahmood, and L. Wen, “Free-standing THz electromagnetic metamaterials,” Opt. Express 16(18), 13773–13780 (2008). [CrossRef] [PubMed]

].

The spectral behavior of samples was characterized by Fourier transform interferometry in the far infrared between 2 and 14 THz. Beam spot size on sample was 1.5 mm at normal incidence, total beam divergence 60°. Figure 2(a)
Fig. 2 (a) Measured and (b) simulated transmission spectra of a 1SE sample with the incidence angle α as a parameter varying from 0°(9°)81°, the electric field pointing along the z axis. Spectra are vertically shifted with respect to each other for clarity. (c) and (d) Retrieval calculation of the relative complex permittivity ε, permeability μ, and refractive index n of the 1SE sample. In the shaded frequency ranges <3 THz and >7.4 THz Re(n) reaches the edge of the Brillouin zone.
displays measured transmission spectra of a 1SE foil versus frequency with the incidence angle α around the z axis running from 0°(9°)81° in comparison with simulated spectra (Fig. 2(b)). Peak positions and widths agree fairly well. MWS commercial software was used for full-wave simulation [18

18. Microwave Studio (MWS) is a registered trademark of CST GmbH, Darmstadt, Germany.

]. Two dominant peaks appear at 3.2 THz and 6.8 THz. From parameter and index retrieval calculations (Fig. 2(c) and (d)) [19

19. X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco Jr, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004). [CrossRef] [PubMed]

], we see that both Re(ε) and Re(μ) are negative around 3.2 THz, so the peak at 3.2 THz (λ = 94 μm) is assigned the well-known left-handed resonance of the fig-8 loop in S-strings [16

16. H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(5 Pt 2), 057605 (2004). [CrossRef] [PubMed]

]. Its wavelength-structure-size ratio of λ/b = 94/15 = 6.26 indicates a reasonable effective-medium approximation. The figure-of-merit FOM = abs(Re(n)/Im(n)) is 3 at 3.27 THz and 5.6 at 3.47 THz from simulation. The peak at 6.8 THz (λ = 44 μm) is a right-handed electrical resonance of one half S acting as an antenna between coupling capacitors or interconnecting rods as nodes. Here, the length of the shortest such resonator is a/2+h = (15.5+5) μm = 20.5 µm, in 7%-agreement with λ/2 = 22 μm. Note that in the shaded frequency ranges <3 THz and >7.4 THz, the refractive index reaches the edge of the Brillouin zone π/(k⋅b), as shown in Fig. 2(d). Therefore, a resonance of permeability (permittivity) and anti-resonance of permittivity (permeability) behavior accompanied by a negative imaginary part of the permittivity (permeability) can be observed. This resonance and anti-resonance behavior is very similar to that observed in the left-handed metamaterial composed of rod and split-ring resonators, which was shown to be a result of the periodic medium model with resonant structures [20

20. Th. Koschny, P. Markoš, 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(24), 245105 (2005). [CrossRef]

]. Reaching the edge of the Brillouin zone in the periodic medium deforms the Drude-like (permittivity) and Lorentz-like (permeability) resonance behavior of the left-handed metamaterial [20

20. Th. Koschny, P. Markoš, 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(24), 245105 (2005). [CrossRef]

]. Below 3 THz, the retrieved refractive index reaches the edge of the Brillouin zone, and the wavelength inside the metamaterial is comparable or smaller than the structure period ruling out the use of an effective permittivity and permeability to characterize the sample. Note as well that the transmission peak at 6.8 THz is due to an electric plasma frequency around 6 THz accompanied by a higher electric resonant frequency around 7.6 THz. From 6 THz to 7.6 THz, both permittivity and permeability are positive corresponding to a pass-band. Above the electrical resonance of 7.6 THz, the negative value of the permittivity and positive value of the permeability lead to a stop-band for which reason we see an isolated transmission peak at 6.8 THz instead of a continuous pass-band.

When the incidence angle α, defined as the angle between the normal to the meta-foil plane y-z and the wave vector k keeping the latter perpendicular to the z-axis, is varied, the magnetic field component normal to the induction loops changes as Hn=H0cosα while the electric field points along the S-strings independently of α. H0 is the magnetic field amplitude of the incident wave. Thus, the magnetically excited left-handed peak at 3.2 THz should vary as cosα which is the case over the wide range from 0° to 81° implying a large latitude for choosing α which may practically lie between ±30° or more (Fig. 3
Fig. 3 Transmission peak areas versus incidence angle with a cosα-fit to the 3.2 THz left-handed magnetic resonance and a cos2α–fit to the 6.8 THz right-handed electric resonance (1SE sample).
). The relative peak width of about 25% also facilitates operation. The cos2α-dependency of the electrical resonance peak is due to the relative phase shift of the electric field between adjacent strings and the short-circuit current generated. Simulated data also fit well.

Meta-foils can be strongly bent without compromising their function as shown by spectra of a 2SE sample with bending radii varying from infinity to 1 cm (Fig. 4(a)
Fig. 4 (a) Spectral response under bending from flat to 1 cm radius around z axis (2SE) under normal incidence. (b) Peak shift and damping upon filling with PMMA (1SP) under normal incidence. Spectra are vertically shifted with respect to each other for clarity.
). The absence of any significant change of the spectra confirms the local rigidity and global flexibility of the meta-foil. Bending to a cylinder around the z-axis deforms cells from their original parallel to a wedge shape. With 1 cm bending radius, the wedge angle between two adjacent strings is 1 mrad and the change of capacitor gap ±15 nm. The relative change being only 0.003, the gap expansion in the upper half of the capacitor and the contraction in the lower cancel each other leaving no measurable effect. The slight amplitude reductions result from the decrease of the normal magnetic field component towards the edges.

From the 60%-transmission of the left-handed peak at 4 THz (Fig. 4(a)) we infer that the double spacing of interconnecting lines in structure 2SE as compared to 1SE (Fig. 2) favors larger resonance peaks. Moreover, the frequency shift from 3.2 to 4 THz is explained essentially by the actual resonance loops. In the 1SE case, loops are formed by one capacitor short-circuited over the interconnecting line. In the 2SE case, half of the loops are like 1SE, but the other half consists of the canonical S-string loop that has two capacitors in series. Therefore, the frequency is 1.41 times higher, i.e., 4.5 THz. Superposition of peaks at 3.2 THz 3.2(1+2/2)1/2and 4.5 THz gives one peak at 3.85 THz, close to the measured 4 THz. A more accurate analytical calculation yields a frequency of THz = 4.18 THz, in fair agreement as well.

The resonance frequency of all-metal meta-foils can be shifted by adding dielectrics which enables sensing and tuning (Fig. 4(b)). Peak shift and broadening caused by PMMA reflect quantitatively the relative permittivity of PMMA. The ratio of the three peaks without and with PMMA is 1.54, 1.52, and 1.5 for the 3.5, 6.3, and 7.7 THz peaks, respectively, proportional to the square root of the permittivity and, hence, to the refractive index. In fair agreement, the latter is found as 1.57 in the THz region [21

21. C. S. Ponseca Jr, R. Pobre, E. Estacio, N. Sarukura, A. Argyros, M. C. J. Large, and M. A. van Eijkelenborg, “Transmission of terahertz radiation using a microstructured polymer optical fiber,” Opt. Lett. 33(9), 902–904 (2008). [CrossRef] [PubMed]

]. The observed damping indicates a PMMA-induced loss and supports the initial statement that matrix-embedded metamaterials may be significantly restricted in their function. Finally, we note without showing graphs that the meta-foil was operated from room temperature to >120 °C without a detectable change of results.

The meta-foil is a new photonic material implementing a “crystalline state” of the “atoms” of the meta-material, i.e., the S-string resonant loops. Its easy handling enables a wide range of THz frequency applications. Optical elements like filters, polarizers, reflectors, and absorbers may be made from meta-foils in various geometrical shapes benefiting from the relative insensitivity of meta-foils to incidence angle, deformation, spatial or angular misalignment, and temperature. Meta-foils can be filled with dielectrics for sensing and tuning. Forthcoming work will focus on stacking to provide extended three-dimensional arrangements and enhance optical properties including resonance widths. Stacks of meta-foils may also serve as polarizing devices. Ultimately, meta-foils will allow introducing an almost arbitrary spatial distribution of refractive index by corresponding variations of geometric parameters, thus enabling index-gradient optics for infrared microscopy and THz imaging as well as radically new optical components.

Acknowledgements

Work partly performed at SSLS under NUS Core Support C-380-003-003-001, A*STAR/ MOE RP 3979908M and A*STAR 12 105 0038 grants. HSC, XXC, and BIW want to acknowledge the support from NNSFC (Nos. 60801005, 60531020, 60990320 and 60990322), the FANEDD (No. 200950), the ZJNSF (No. R1080320), the MEC (No. 200803351025), the ONR (No. N00014-06-1-0001), and the DAF (No. FA8721-05-C-0002).

References and links

1.

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

2.

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

3.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]

4.

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

5.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006). [CrossRef] [PubMed]

6.

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]

7.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009). [CrossRef]

8.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef] [PubMed]

9.

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]

10.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, “Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial,” Phys. Rev. Lett. 94(6), 063901 (2005). [CrossRef] [PubMed]

11.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005). [CrossRef] [PubMed]

12.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006). [CrossRef] [PubMed]

13.

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef] [PubMed]

14.

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(24), 3356–3358 (2005). [CrossRef] [PubMed]

15.

H. O. Moser, J. A. Kong, L. K. Jian, H. S. Chen, G. Liu, M. Bahou, S. M. P. Kalaiselvi, S. M. Maniam, X. X. Cheng, B. I. Wu, P. D. Gu, A. Chen, S. P. Heussler, S. bin Mahmood, and L. Wen, “Free-standing THz electromagnetic metamaterials,” Opt. Express 16(18), 13773–13780 (2008). [CrossRef] [PubMed]

16.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(5 Pt 2), 057605 (2004). [CrossRef] [PubMed]

17.

H. O. Moser, L. K. Jian, G. Liu, S. M. P. Kalaiselvi, S. M. Maniam, S. P. Heussler, J. A. Kong, H. S. Chen, and B. I. Wu, “A metamaterial and methods for producing the same,” PCT SG2009(000098), 19 (2009).

18.

Microwave Studio (MWS) is a registered trademark of CST GmbH, Darmstadt, Germany.

19.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco Jr, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004). [CrossRef] [PubMed]

20.

Th. Koschny, P. Markoš, 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(24), 245105 (2005). [CrossRef]

21.

C. S. Ponseca Jr, R. Pobre, E. Estacio, N. Sarukura, A. Argyros, M. C. J. Large, and M. A. van Eijkelenborg, “Transmission of terahertz radiation using a microstructured polymer optical fiber,” Opt. Lett. 33(9), 902–904 (2008). [CrossRef] [PubMed]

OCIS Codes
(220.4000) Optical design and fabrication : Microstructure fabrication
(260.3090) Physical optics : Infrared, far
(160.1245) Materials : Artificially engineered materials
(160.3918) Materials : Metamaterials
(170.6795) Medical optics and biotechnology : Terahertz imaging
(240.3990) Optics at surfaces : Micro-optical devices

ToC Category:
Metamaterials

History
Original Manuscript: October 26, 2009
Revised Manuscript: December 2, 2009
Manuscript Accepted: December 3, 2009
Published: December 15, 2009

Citation
H. O. Moser, L. K. Jian, H. S. Chen, M. Bahou, S. M. P. Kalaiselvi, S. Virasawmy, S. M. Maniam, X. X. Cheng, S. P. Heussler, Shahrain bin Mahmood, and B.-I. Wu, "All-metal self-supported THz metamaterial – the meta-foil," Opt. Express 17, 23914-23919 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23914


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References

  1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  2. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]
  3. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]
  4. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  5. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006). [CrossRef] [PubMed]
  6. 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]
  7. D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009). [CrossRef]
  8. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004). [CrossRef] [PubMed]
  9. S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004). [CrossRef] [PubMed]
  10. H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, “Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial,” Phys. Rev. Lett. 94(6), 063901 (2005). [CrossRef] [PubMed]
  11. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005). [CrossRef] [PubMed]
  12. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006). [CrossRef] [PubMed]
  13. N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7(1), 31–37 (2008). [CrossRef] [PubMed]
  14. 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(24), 3356–3358 (2005). [CrossRef] [PubMed]
  15. H. O. Moser, J. A. Kong, L. K. Jian, H. S. Chen, G. Liu, M. Bahou, S. M. P. Kalaiselvi, S. M. Maniam, X. X. Cheng, B. I. Wu, P. D. Gu, A. Chen, S. P. Heussler, S. bin Mahmood, and L. Wen, “Free-standing THz electromagnetic metamaterials,” Opt. Express 16(18), 13773–13780 (2008). [CrossRef] [PubMed]
  16. H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(5 Pt 2), 057605 (2004). [CrossRef] [PubMed]
  17. H. O. Moser, L. K. Jian, G. Liu, S. M. P. Kalaiselvi, S. M. Maniam, S. P. Heussler, J. A. Kong, H. S. Chen, and B. I. Wu, “A metamaterial and methods for producing the same,” PCT SG2009(000098), 19 (2009).
  18. Microwave Studio (MWS) is a registered trademark of CST GmbH, Darmstadt, Germany.
  19. 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 Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004). [CrossRef] [PubMed]
  20. Th. Koschny, P. Markoš, 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(24), 245105 (2005). [CrossRef]
  21. C. S. Ponseca, R. Pobre, E. Estacio, N. Sarukura, A. Argyros, M. C. J. Large, and M. A. van Eijkelenborg, “Transmission of terahertz radiation using a microstructured polymer optical fiber,” Opt. Lett. 33(9), 902–904 (2008). [CrossRef] [PubMed]

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