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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 8 — Apr. 11, 2011
  • pp: 6990–6998
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Broadband multi-layer terahertz metamaterials fabrication and characterization on flexible substrates

N. R. Han, Z. C. Chen, C. S. Lim, B. Ng, and M. H. Hong  »View Author Affiliations


Optics Express, Vol. 19, Issue 8, pp. 6990-6998 (2011)
http://dx.doi.org/10.1364/OE.19.006990


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Abstract

Microscopic split-ring-resonator (SRR) arrays are fabricated on 100 μm thick polyethylene naphthalate (PEN) films by femtosecond laser micro-lens array (MLA) lithography. The transmission properties of these metamaterials are characterized by THz Time Domain Spectroscopy (THz-TDS). Tunable resonance responses can be achieved by changing SRR structural design parameters. By stacking 2D PEN metamaterial films with different frequency responses together, a broadband THz filter with full width at half maximum (FWHM) of 0.38 THz is constructed. The bandwidth of the resonance response increases up to 4.2 times as compared to the bandwidths of single layer metamaterials. Numerical simulation reveals that SRR layers inside the multi-layer metamaterials are selectively excited towards specific frequencies within the broadband response. Meanwhile, more than one SRR layers respond to the chosen frequencies, resulting in the enhancement of the resonance properties. The multi-layer metamaterials provide a promising way to extend SRR based metamaterial operating region from narrowband to broadband with a tunable feature.

© 2011 OSA

1. Introduction

Metamaterials, which are artificial composite materials being designed to have specific electromagnetic responses, have been receiving increasing research attentions during the last decade. With proper utilization of metamaterials, exotic phenomena, such as negative refractive index [1

1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [CrossRef]

3

3. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

], perfect lens [4

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

] and invisible cloaking [5

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

,6

6. 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]

], can be achieved. The unique electromagnetic (EM) response from metamaterials has been proven to be especially valuable in the terahertz (THz) regime, where most naturally occurring materials exhibit weak EM response to the THz wave. The THz regime, usually defined between 0.1 and 10 THz, remains to be the least developed region in the EM spectrum due to the lack of efficient sources, detectors and functional devices. The advent of metamaterials is expected to close the “THz gap”. Metamaterials based on split-ring-resonator (SRR) structures, which exhibit strong magnetic response in designed narrowband frequency region, was first proposed and analyzed by Pendry et al. [7

7. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

]. The ease of fabrication in the micrometer level makes SRRs applicable and practical for the THz regime. Different design variations based on the SRR structures, such as electric SRR [8

8. D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006). [CrossRef]

], dynamically active SRR [9

9. 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]

11

11. H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009). [CrossRef]

] and structurally reconfigurable SRR [12

12. H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009). [CrossRef] [PubMed]

], were proposed by other researchers and bolstered the development of the THz metamaterial research. Functional THz metamaterial devices, such as switches [10

10. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006). [CrossRef] [PubMed]

], modulators [11

11. H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009). [CrossRef]

], perfect absorbers [13

13. 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(10), 7181–7188 (2008). [CrossRef] [PubMed]

] and filters [14

14. H.-T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007). [CrossRef] [PubMed]

], were successfully demonstrated.

2. Sample design and fabrication

3. Multi-layer metamaterials

To fabricate the multi-layer broadband metamaterials, all the five samples with different a values are stacked in sequence from SRR1 to SRR5 with SRR1 on top facing the incident THz wave. Meanwhile, one more bare PEN film is stacked on top of the SRR1 film to keep all the SRR arrays inside the bulk PEN materials for protection purpose as illustrated in Fig. 3(a)
Fig. 3 (a) Multi-layer metamaterials stacking illustration, (b) photograph of the flexible PEN film, indicating its potential for implanting non-planar THz devices, and (c) photograph of the multi-layer metamaterials.
. Figure 3(c) is the image of the fabricated broadband THz filter. The size of this THz filter device is 1.8 cm × 1.8 cm with an effective functional area of 1 cm × 0.6 cm. This is suitable to be applied in a compact THz system. The transmission spectra of the combined 5-layer metamaterials and each corresponding single layer metamaterials are shown in Fig. 4(a)
Fig. 4 (a) Transmission spectra of the overall multi-layer metamaterials and the corresponding single layer metamaterials. A broadband filter with a bandwidth of 0.38 THz is constructed. The resonance dips from the overall transmission spectrum match with those from individual samples, and (b) simulated spectrum of the multi-layer metamaterials. The resonance dips are at 0.41, 0.45, 0.50, 0.56 and 0.62 THz with an overall frequency red-shift compared to the experimental spectrum.
. A broadband response with a center frequency of about 0.61 THz is observed, which is clearly the addition of the resonance responses from each single layer metamaterials. The positions of the five resonance dips in the overall frequency response spectrum match with the resonance dips from individual samples. The FWHM of this filter is measured to be 0.38 THz which is about 2.5 times greater than the FWHM of SRR1 (a = 40 μm) and 4.2 times greater than that of SRR5 (a = 80 μm), indicating that a broader response is achieved by sample stacking. Meanwhile, the stopband is suppressed down to −30 dB, which is much lower than that in single layer metamaterials. This feature is adequate for most filtering applications. The filter exhibits a fast roll-off of more than 100 dB/THz on the edge of the stopband. Interestingly, the resonance dip at 0.66 THz is especially strong compared to other resonance dips. Further investigation will be carried out to explore the underlying physics behind this phenomenon. The Fabry–Pérot fringes on the passband are caused by internal reflections within the multi-layer sample with an overall thickness of about 600 μm. This also agrees well with our simulation results. The reason why they are not observed in single layer sample transmission spectrum is due to the different sample thickness between multi-layer and single-layer metamaterials. The much smaller thickness (100 μm) of the single layer metamaterials shifts the internal reflections, and thus the fringes, to frequency regions that are not seen from the plot scale. The broadband filter built by multi-layer SRR based metamaterials can be used in controlling and manipulating THz wave. The bandwidth of the stopband can also be tuned by adding or subtracting metamaterial layers based on the positions of the resonance dips from individual layers.

Finite-integration time-domain simulation is carried out using commercial software CST Microwave Studio 2009. For PEN, the real part of the permittivity ε and the loss tangent are set as 2.56 and 0.003 over the frequency of interest. For simplicity, all the SRRs are aligned perfectly as illustrated in Fig. 3(a). The simulated transmission spectrum is plotted in Fig. 4(b). It shows a broadband resonance response with a bandwidth of around 0.30 THz. On the transmission spectrum, five resonance dips corresponding to each metamaterial layer are found to be at 0.41, 0.45, 0.50, 0.56 and 0.62 THz. As compared to the experimental spectrum, the resonance dips in simulation are much sharper. This is due to the ideal assumption of sample materials and structures in simulation. Meanwhile, there is an overall resonance frequency red-shift for the simulated spectrum. The reason behind this result is that in the simulation, the SRRs are assumed to be enclosed in close contact by the surround PEN films, whereas in experiment there is a thin air gap between adjacent layers, resulting from the stacking process. Consequently, the simulated SRRs are in a homogeneous dielectric environment of a higher refractive index than air, leading to a resonance red-shift [33

33. T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91(6), 062511 (2007). [CrossRef]

]. Both experiment and simulation reveal that the stacking of the single layer metamaterials with different structural designs provides a promising way to extend the metamaterial frequency response region from narrowband to broadband.

In order to further understand the performance of each individual layer in the 5-layer metamaterials, we investigated the cross-sectional E-field intensity through numerical simulation. Five specific frequencies at 0.62, 0.56, 0.50, 0.45 and 0.41 THz, which correspond to the five transmission dips in the simulated multi-layer metamaterials transmission spectrum, are selected. Each chosen frequency corresponds to the LC resonance frequency for one of the SRR layers. For example, SRR1 has its LC resonance frequency at 0.62 THz while SRR5 has its LC resonance frequency at 0.41 THz. We define resonant SRR layer as the SRR layer with the chosen frequency as its LC resonance frequency. The cross-sectional plane is along the y-z plane and cuts through the center of all the SRR gaps. The E-field intensity distributions at the five chosen frequencies in this cross-sectional plane are presented in Figure 5(a)
Fig. 5 (a)–(e) Cross sectional E-field intensity distribution at the gaps of the multi-layer metamaterials under selected frequencies. The frequencies are chosen to coincide with the five resonance dips from the overall transmission spectrum. The localized E-field intensity enhancement at the gaps indicates a strong resonance response towards the selected frequency. The magnitude of the localized E-field enhancement is up to 10 times larger than the magnitude of the incident E-field.
to 5(e). It is observed that at each chosen frequency, the SRR layers are selectively excited with a strong E-field concentration in the gap due to charge accumulation at the ends of the SRR. As the selected frequency changes from 0.62 to 0.41 THz, the resonant SRR layer, which is the excited SRR layer with the largest z position value, shifts from SRR1 to SRR5 correspondingly. This indicates a selective LC resonance excitation from the SRR layers in response to the chosen frequency. Furthermore, it can also be seen that more than one SRR layers are excited strongly at each given frequency since the LC resonance frequencies of adjacent layers are close to each other. This multi-layer excitation further enhances the resonance intensity of the overall transmission performance due to more excited SRR layers, resulting in much deeper transmission dips in the multi-layer metamaterials transmission spectrum as compared to transmission dips of the individual single layer metamaterials. Meanwhile, the number of excited SRR layers at each chosen frequency is limited up to three, since SRR does not respond to frequency ranges that are too far away from its LC resonance frequency. For f = 0.56, 0.50, 0.45 and 0.41 THz, the localized E-field intensity of the excited SRR layer to the left of the resonant SRR layer is comparable or even stronger than the localized E-field intensity of the resonant SRR layer, as can be seen in Figure 5(b) to 5(e). On the contrary, it can also be observed that SRR layers to the right of the resonant SRR layer are generally not excited by the selected frequency. This may be due to the reason of the asymmetric line shape of the SRR resonance curve.

4. Conclusions

In conclusion, we report a broadband frequency response from multi-layer metamaterials. SRR arrays with LC resonance frequencies of 0.49, 0.54, 0.59, 0.66 and 0.74 THz are fabricated on 100 μm thick flexible PEN films by femtosecond laser MLA lithography. A broadband filter with a bandwidth of 0.38 THz is constructed by stacking individual 2D metamaterials together. Simulation results reveal that SRR layers inside the multi-layer metamaterials are selectively excited towards specific frequencies within the broadband response. Meanwhile, more than one SRR layers respond to the chosen frequencies with a localized E-field intensity enhancement, which strengthens the resonance properties of the overall performance. Multi-layer metamaterials have potential use in building functional broadband THz devices.

Acknowledgments

The author would like to acknowledge support by National University of Singapore Start-up Grant (Project No. R-263-000-515-133) and ASTAR SERC Terahertz Program (Project: Terahertz Spectroscopy, Project No. 082 141 0039).

References and links

1.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [CrossRef]

2.

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(18), 4184–4187 (2000). [CrossRef] [PubMed]

3.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

4.

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

5.

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

6.

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]

7.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

8.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006). [CrossRef]

9.

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]

10.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006). [CrossRef] [PubMed]

11.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009). [CrossRef]

12.

H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009). [CrossRef] [PubMed]

13.

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(10), 7181–7188 (2008). [CrossRef] [PubMed]

14.

H.-T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007). [CrossRef] [PubMed]

15.

C. M. Bingham, H. Tao, X. L. Liu, R. D. Averitt, X. Zhang, and W. J. Padilla, “Planar wallpaper group metamaterials for novel terahertz applications,” Opt. Express 16(23), 18565–18575 (2008). [CrossRef]

16.

Y. Yuan, C. Bingham, T. Tyler, S. Palit, T. H. Hand, W. J. Padilla, D. R. Smith, N. M. Jokerst, and S. A. Cummer, “Dual-band planar electric metamaterial in the terahertz regime,” Opt. Express 16(13), 9746–9752 (2008). [CrossRef] [PubMed]

17.

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008). [CrossRef]

18.

W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photon. J. 1(2), 99–118 (2009). [CrossRef]

19.

M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrivov, and Y. S. Kivshar, “Effect of microscopic disorder on magnetic properties of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(5), 056605 (2006). [CrossRef] [PubMed]

20.

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, Th. Koschny, and C. M. Soukoulis, “Magnetic response of split-ring resonators in the far-infrared frequency regime,” Opt. Lett. 30(11), 1348–1350 (2005). [CrossRef] [PubMed]

21.

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22.

H. Tao, A. C. Strikwerda, K. Fan, C. M. Bingham, W. J. Padilla, X. Zhang, and R. D. Averitt, “Terahertz metamaterials on free-standing highly-flexible polyimide substrates,” J. Phys. D Appl. Phys. 41(23), 232004 (2008). [CrossRef]

23.

X. G. Peralta, M. C. Wanke, C. L. Arrington, J. D. Williams, I. Brener, A. Strikwerda, R. D. Averitt, W. J. Padilla, E. Smirnova, A. J. Taylor, and J. F. O’Hara, “Large-area metamaterials on thin membranes for multilayer and curved applications at terahertz and higher frequencies,” Appl. Phys. Lett. 94(16), 161113 (2009). [CrossRef]

24.

A. K. Azad, H.-T. Chen, X. Lu, J. Gu, N. R. Weisse-Bernstein, E. Akhadov, A. J. Taylor, W. Zhang, and J. F. O’Hara, “Flexible quasi-three-dimensional terahertz electric metamaterials,” Terahertz Sci. Technol. 2, 15–22 (2009).

25.

P. Gay-Balmaz and O. J. F. Martin, “Electromagnetic resonances in individual and coupled split-ring-resonators,” J. Appl. Phys. 92(5), 2929–2936 (2002). [CrossRef]

26.

C. S. Lim, M. H. Hong, Z. C. Chen, N. R. Han, B. Luk’yanchuk, and T. C. Chong, “Hybrid metamaterial design and fabrication for terahertz resonance response enhancement,” Opt. Express 18(12), 12421–12429 (2010). [CrossRef] [PubMed]

27.

Y. Lin, M. H. Hong, T. C. Chong, C. S. Lim, G. X. Chen, L. S. Tan, Z. B. Wang, and L. P. Shi, “Ultrafast laser induced parallel phase change nanolithography,” Appl. Phys. Lett. 89(4), 041108 (2006). [CrossRef]

28.

Z. C. Chen, M. H. Hong, C. S. Lim, N. R. Han, L. P. Shi, and T. C. Chong, “Parallel laser microfabrication of large-area asymmetric split ring resonator metamaterials and its structural tuning for terahertz resonance,” Appl. Phys. Lett. 96(18), 181101 (2010). [CrossRef]

29.

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B 65(14), 144440 (2002). [CrossRef]

30.

A. K. Azad, A. J. Taylor, E. Smirnova, and J. F. O’Hara, “Characterization and analysis of terahertz metamaterials based on rectangular split-ring resonators,” Appl. Phys. Lett. 92(1), 011119 (2008). [CrossRef]

31.

F. Miyamaru, M. W. Takeda, and K. Taima, “Characterization of terahertz metamaterials fabricated on flexible plastic films: toward fabrication of bulk metamaterials in terahertz region,” Appl. Phys. Express 2, 042001 (2009). [CrossRef]

32.

F. Miyamaru, S. Kuboda, K. Taima, K. Takano, M. Hangyo, and M. W. Takeda, “Three-dimensional bulk metamaterials operating in the terahertz range,” Appl. Phys. Lett. 96(8), 081105 (2010). [CrossRef]

33.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, and D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91(6), 062511 (2007). [CrossRef]

OCIS Codes
(160.3918) Materials : Metamaterials
(300.6495) Spectroscopy : Spectroscopy, teraherz
(230.7408) Optical devices : Wavelength filtering devices

ToC Category:
Metamaterials

History
Original Manuscript: December 7, 2010
Revised Manuscript: February 21, 2011
Manuscript Accepted: February 21, 2011
Published: March 28, 2011

Citation
N. R. Han, Z. C. Chen, C. S. Lim, B. Ng, and M. H. Hong, "Broadband multi-layer terahertz metamaterials fabrication and characterization on flexible substrates," Opt. Express 19, 6990-6998 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-8-6990


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References

  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [CrossRef]
  2. 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(18), 4184–4187 (2000). [CrossRef] [PubMed]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]
  4. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  5. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  6. 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]
  7. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]
  8. D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006). [CrossRef]
  9. 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]
  10. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006). [CrossRef] [PubMed]
  11. H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009). [CrossRef]
  12. H. Tao, A. C. Strikwerda, K. Fan, W. J. Padilla, X. Zhang, and R. D. Averitt, “Reconfigurable terahertz metamaterials,” Phys. Rev. Lett. 103(14), 147401 (2009). [CrossRef] [PubMed]
  13. 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(10), 7181–7188 (2008). [CrossRef] [PubMed]
  14. H.-T. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007). [CrossRef] [PubMed]
  15. C. M. Bingham, H. Tao, X. L. Liu, R. D. Averitt, X. Zhang, and W. J. Padilla, “Planar wallpaper group metamaterials for novel terahertz applications,” Opt. Express 16(23), 18565–18575 (2008). [CrossRef]
  16. Y. Yuan, C. Bingham, T. Tyler, S. Palit, T. H. Hand, W. J. Padilla, D. R. Smith, N. M. Jokerst, and S. A. Cummer, “Dual-band planar electric metamaterial in the terahertz regime,” Opt. Express 16(13), 9746–9752 (2008). [CrossRef] [PubMed]
  17. F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008). [CrossRef]
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