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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 2 — Jan. 17, 2011
  • pp: 1563–1568
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Electrically controllable fishnet metamaterial based on nematic liquid crystal

Fuli Zhang, Weihong Zhang, Qian Zhao, Jingbo Sun, Kepeng Qiu, Ji Zhou, and Didier Lippens  »View Author Affiliations


Optics Express, Vol. 19, Issue 2, pp. 1563-1568 (2011)
http://dx.doi.org/10.1364/OE.19.001563


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Abstract

A variable index metamaterial is demonstrated by embedding nematic liquid crystal inside fishnet layers’ void at microwave frequencies. With an external electric field, the left handed passband can be reversibly shifted from 9.14 to 8.80 GHz, whereas the upper right handed passband is nearly unchanged. It is shown that during LC molecular reorientation, magnetic resonance is shifted to a lower frequency because of the permittivity increase between fishnet layers, leading to an effective index change of 1.1 within negative index regime.

© 2011 OSA

1. Introduction

Index variation plays an important role in the novel optical devices. In recent years, tunable negative index metamaterial (NIM) [1

1. 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]

] has attracted more and more attention since conventional NIM operates in a narrow bandwidth, resulting from its high dispersive characteristics. As a result, several methods have been proposed for tuning its properties via capacitance variation by the incorporation of active devices, such as varactor diode [2

2. I. Gil, J. García-García, J. Bonache, F. Martín, M. Sorolla, and R. Marqués, “Varactor-loaded split ring resonators for tunablenotch filters at microwave frequencies,” Electron. Lett. 40(21), 1347–1348 (2004). [CrossRef]

4

4. H. Chen, B.-I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, “Controllable left-handed metamaterial and its application to a steerable antenna,” Appl. Phys. Lett. 89(5), 053509 (2006). [CrossRef]

], semiconductors [5

5. A. Degiron, J. J. Mock, and D. R. Smith, “Modulating and tuning the response of metamaterials at the unit cell level,” Opt. Express 15(3), 1115–1127 (2007). [CrossRef] [PubMed]

7

7. Z. L. Sámson, K. F. MacDonald, F. De Angelis, B. Gholipour, K. Knight, C. C. Huang, E. Di Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96(14), 143105 (2010). [CrossRef]

], ferroelectric [8

8. T. H. Hand and S. A. Cummer, “Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings,” J. Appl. Phys. 103(6), 066105 (2008). [CrossRef]

] and anisotropic materials [9

9. R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, “Nonmagnetic nanocomposites for optical and infrared negative-refractive-index media,” J. Opt. Soc. Am. B 23(3), 498–505 (2006). [CrossRef]

16

16. A. Minovich, D. N. Neshev, D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, “Tunable fishnet metamaterials infiltrated by liquid crystals,” Appl. Phys. Lett. 96(19), 193103 (2010). [CrossRef]

]. So far, most of these works are concentrated on single negative metamaterial, i.e., negative permeability metamaterial. Recently, liquid crystal (LC), has been proposed as a promising material for a tunable NIM substrate due to its large birefringence and ease of incorporation [17

17. I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5-6), 221–267 (2009). [CrossRef]

]. Khoo et al. reported a theoretical analysis on tunable index metamaterials based on core-shell nanospheres randomly dispersed in LCs [13

13. I. C. Khoo, D. H. Werner, X. Liang, A. Diaz, and B. Weiner, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett. 31(17), 2592–2594 (2006). [CrossRef] [PubMed]

]. Werner et al. proposed a reconfigurable metamaterial by sandwiching a nematic LC as a substrate into the conventional NIM [14

14. D. H. Werner, D.-H. Kwon, I.-C. Khoo, A. V. Kildishev, and V. M. Shalaev, “Liquid crystal clad near-infrared metamaterials with tunable negative-zero-positive refractive indices,” Opt. Express 15(6), 3342–3347 (2007). [CrossRef] [PubMed]

]. We demonstrated experimentally a tunable omega type NIM infiltrated by nematic LC whose orientation was controlled by a magnetic field [15

15. F. Zhang, L. Kang, Q. Zhao, J. Zhou, X. Zhao, and D. Lippens, “Magnetically tunable left handed metamaterials by liquid crystal orientation,” Opt. Express 17(6), 4360–4366 (2009). [CrossRef] [PubMed]

]. Very recently, Minovich et al. numerically investigated the effective index variation of tunable fishnet structure infiltrated by LC [16

16. A. Minovich, D. N. Neshev, D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, “Tunable fishnet metamaterials infiltrated by liquid crystals,” Appl. Phys. Lett. 96(19), 193103 (2010). [CrossRef]

]. The fishnet structure is actually one of the most promising approaches for tunable optical metamaterial via LC reorientation. However, due to the fabrication challenges for frequencies above THz, LC can be just infiltrated into the holes between neighboring cells. As a consequence, the dielectric permittivity variation only occurs around the fringing regions of fishnet layers with a limited tuning effect.

In this paper, we show an experimental demonstration of an electrically tunable fishnet NIM operating at microwave frequencies. Instead of an infiltration limited to the holes, nematic LC was poured into the sub-millimeter void which acts as NIM substrate layer in order to pursue a large frequency shift. By applying a relatively low static electric field for the alignment of LC, an index variation within the left handed (LH) passband, as a result of frequency shift of LH passband, was observed. The frequency shift of magnetic and electric resonances was investigated to give an insight into the underlying physics of tunability of NIM.

2. Tunable fishnet metamaterial infiltrated by LC

Figures 1(a)
Fig. 1 Tunable fishnet type of NIM based on nematic LC. (a) Side view (b) 3-D view of four elementary cells. (c) Photograph of metamaterial sample (The top layer of fishnet array was removed for clarity). The initial alignment of LC molecules, also depicted in (a), is parallel to the metallic surface. The geometrical parameters of unit cell are as follows: W = 8.00, L = 12.00, Px = 15.00 Py = 10.00, t LC = 0.50, t s = 1.00 (unit: mm). Teflon fiberglass (εr =2.65, tanδ=0.001) was chosen as the host material. The copper layer has a thickness of 0.03 mm.
and 1(b) depict schematic views of a tunable fishnet metamaterial structure, which is composed of three layers, i.e., a pair of fishnet array was patterned on the surface of Teflon fiberglass slabs with a void in between which was subsequently infiltrated with a nematic LC. The underlying idea for tuning the LH passband is to change the effective permittivity of substrate via LC molecular reorientation, by applying a dc voltage between the top and bottom metal layers. In order to achieve all angle LC reorientation between 0 and 90° and hence a large tuning range, a thin layer of polyimide (PI) was spanned on the surface of Teflon substrate and copper element to force nematic LC to align parallel to the surface of metallic layer surface. As a combination of electrical dipoles and current loops providing simultaneously negative permittivity and permeability, the fishnet structure can operate under normal incidence [18

18. C. M. Soukoulis, S. Linden, and M. Wegener, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312, 892–894 (2007).

22

22. A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101(10), 103902 (2008). [CrossRef] [PubMed]

]. Unlike the high transmission of optical fishnet arising from the plasmon resonances [22

22. A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101(10), 103902 (2008). [CrossRef] [PubMed]

], the prototype used here operating at microwave can produce LH passband from artificial plasmon of periodic structure [23

23. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

]. An incident wave with electric field polarized along the x direction and magnetic field polarized along the y direction was illuminated along the z direction.

Employing standard printed circuit board technology, we fabricated fishnet layers and stacked two resulting metamaterial layers in a face-to-face configuration but separated by an epoxy glass spacer in between (Fig. 1(c)). In the fishnet pattern, elementary cells are contiguous in the x and y directions due to the periodic replication. It is therefore not necessary to give a special design for the extra bar to connect adjacent cells. The surface of fishnet layer was treated with a thin PI film rubbed along the x direction. Therefore the injected nematic LC molecular director was initially aligned parallel to the surface of fishnet pattern as the pretilt angle of PI is 4°. The bias voltage is supplied by a standard dc power. The scattering spectra were measured under free space condition using an HP8720 ES vector network analyzer and a pair of standard horns serving as a source and a receiver antenna. The transmission and reflection coefficient can be obtained by comparing the scattering parameters of sample with the calibration data. For the transmission spectra measurement, the calibration was carried out when the sample was removed whereas a metal plane was used as a reference for the reflection measurement.

At the first stage, we performed a numerical analysis of the tunability of transmission via LC alignment employing a commercial finite element solver, High Frequency Structure Simulator (HFSS). A commercial nematic LC, TEB 30A, with a moderate birefringence Δn = 0.08 (n0 = 1.65 and ne =1.73, where n0 and ne represent the respective ordinary and extraordinary indices of LC) at 10 GHz was employed. Let us mention that the birefringence is lower at microwave than that at higher frequencies due to the intrinsic dielectric dispersion [24

24. K. C. Lim, J. D. Margerum, and A. M. Lackner, “Liquid crystal millimeter wave electronic phase shifter,” Appl. Phys. Lett. 62(10), 1065–1067 (1993). [CrossRef]

26

26. C. Weil, St. Müller, P. Scheele, P. Best, G. Lüssem, and R. Jakoby, “Highly-anisotropic liquid-crystal mixtures for tunable microwave devices,” Electron. Lett. 39(24), 1732–1734 (2003). [CrossRef]

]. In view of the different distribution of electric field between cut wire pair and hole regions [16

16. A. Minovich, D. N. Neshev, D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, “Tunable fishnet metamaterials infiltrated by liquid crystals,” Appl. Phys. Lett. 96(19), 193103 (2010). [CrossRef]

], LC layer is treated rigorously by using a permittivity tensor approach during the numerical calculation [27

27. F. Zhang, Q. Zhao, D. P. Gaillot, X. Zhao, and D. Lippens, “Numerical Investigation of Metamaterials Infiltrated by Liquid Crystal,” J. Opt. Soc. Am. B 25(11), 1920 (2008). [CrossRef]

]. As shown in Fig. 2(a)
Fig. 2 (a) Simulated transmission of tunable fishnet metamaterial when LC director was reorientated. The inset is the schematic view of LC molecular reorientation in the xz plane. (b) Experimental transmission magnitude of fishnet metamaterial as a function of external dc bias voltage.
, for the initial alignment with LC director parallel to the surface of fishnet surface, there is a well-resolved and high intensity transmission peak around 9.01 GHz, which is separated from a quasi unity transmission shoulder starting from 11.0 GHz, by a shallow dip. As the LC director is reorientated from 0° to 90°, it is shown that the ground transmission peak is shifted downward 8.60 GHz, accounting for 400 MHz frequency variation, whereas the second passband is nearly unchanged. Figure 2(b) displays the measured transmission spectra of fishnet array under various bias voltages. For zero-bias voltage, the fishnet structure exhibits a transmission passband around 9.14 GHz and another higher passband starting at 10.60 GHz with a minor dip in between. Compared with the simulation results, a considerably good agreement can be noticed. The relatively broader bandwidth of the first passband results from the nonuniform distribution of the void thickness along the 120 mm-long lateral side of fishnet metamaterial sample. Interestingly, for the second passband in the vicinity of the spectral region where n is near zero, some focusing effects seem to occur for the finite size sample which could explain a transmission level more than unity [28

28. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002). [CrossRef] [PubMed]

]. Quantitatively, as the bias voltage increases up to 60 Volt, the first transmission peak shifts from 9.14 GHz downward to 8.80 GHz, accounting for a frequency shift of 340 MHz, whereas the second passband is unchanged. Further results demonstrate that the shift of the first passband saturates at bias voltage in excess of 60 V (not shown here). It is worthing noted that the frequency tuning process is reversible and repeatable.

The effective index variation of metamaterial was measured by comparing the transmission phase change as function a bias voltage, as given in Fig. 4
Fig. 4 (a) The experimental phase advances of metamaterial as a function of bias voltage. (b)The magnification view of phase advance variation around the LH passband peak as indicated in Fig. 2.
. It can be noted that a dip of the transmission phase occurs from 7.5 to 9.2 GHz, indicating the presence of negative index within the first passband [31

31. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005). [CrossRef] [PubMed]

]. Obviously, for a fixed operating frequency, a tuning of the effective index is achieved as bias voltage increases. For a given frequency point around the first transmitted peak (See Fig. 2),f= 8.98 GHz, the transmission phase is varied by nearly 30.0°, corresponding to an index change of 1.1 in the negative index band by using the phase formula, ΔΦ= k 0 d Δn, where ΔΦ is transmission phase variation, Δn is the effective index change of metamaterial, k 0 is the wave number in free space, d is the thickness of tri-layer metamaterial structure. It is noted such a large index variation, which is achieved from LC substrate birefringence of 0.08, mainly arises from the strong dispersion property of effective index of metamaterial.

3. Conclusion

In conclusion, we experimentally demonstrated an electrically variable fishnet type NIM at microwave frequencies. Under an increasing external static electric field, the fishnet structure exhibits a frequency shift of LH passband by 340 MHz as a consequence of the decrease of magnetic resonance when LC director was aligned perpendicular to the substrate. The effective index within LH band varies more than unity correspondingly. It is believed that this work can be helpful for the experimental realization of tunable metamaterial based devices such as tunable-focus flat lens.

Acknowledgments

We gratefully acknowledge the financial support from National Natural Science Foundation of China (Grant Nos. 10925212, 11002112, 60978053, 10774087, 90922025), the NPU Foundation for Fundamental Research (NPU-FFR-JC20100243), 111 Project (Grant No. B07050), and Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090002120008).

References and links

1.

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]

2.

I. Gil, J. García-García, J. Bonache, F. Martín, M. Sorolla, and R. Marqués, “Varactor-loaded split ring resonators for tunablenotch filters at microwave frequencies,” Electron. Lett. 40(21), 1347–1348 (2004). [CrossRef]

3.

I. V. Shadrivov, S. K. Morrison, and Y. S. Kivshar, “Tunable split-ring resonators for nonlinear negative-index metamaterials,” Opt. Express 14(20), 9344–9349 (2006). [CrossRef] [PubMed]

4.

H. Chen, B.-I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, “Controllable left-handed metamaterial and its application to a steerable antenna,” Appl. Phys. Lett. 89(5), 053509 (2006). [CrossRef]

5.

A. Degiron, J. J. Mock, and D. R. Smith, “Modulating and tuning the response of metamaterials at the unit cell level,” Opt. Express 15(3), 1115–1127 (2007). [CrossRef] [PubMed]

6.

H.-T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterial,” Nat. Photonics 2(5), 295–298 (2008). [CrossRef]

7.

Z. L. Sámson, K. F. MacDonald, F. De Angelis, B. Gholipour, K. Knight, C. C. Huang, E. Di Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96(14), 143105 (2010). [CrossRef]

8.

T. H. Hand and S. A. Cummer, “Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings,” J. Appl. Phys. 103(6), 066105 (2008). [CrossRef]

9.

R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, “Nonmagnetic nanocomposites for optical and infrared negative-refractive-index media,” J. Opt. Soc. Am. B 23(3), 498–505 (2006). [CrossRef]

10.

S. Xiao, U. K. Chettiar, A. V. Kildishev, V. Drachev, I. C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. 95(3), 033115 (2009). [CrossRef]

11.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007). [CrossRef]

12.

F. Zhang, Q. Zhao, L. Kang, D. P. Gaillot, X. Zhao, J. Zhou, and D. Lippens, “Magnetic control of negative permeability metamaterials based on liquid crystals,” Appl. Phys. Lett. 92(19), 193104 (2008). [CrossRef]

13.

I. C. Khoo, D. H. Werner, X. Liang, A. Diaz, and B. Weiner, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett. 31(17), 2592–2594 (2006). [CrossRef] [PubMed]

14.

D. H. Werner, D.-H. Kwon, I.-C. Khoo, A. V. Kildishev, and V. M. Shalaev, “Liquid crystal clad near-infrared metamaterials with tunable negative-zero-positive refractive indices,” Opt. Express 15(6), 3342–3347 (2007). [CrossRef] [PubMed]

15.

F. Zhang, L. Kang, Q. Zhao, J. Zhou, X. Zhao, and D. Lippens, “Magnetically tunable left handed metamaterials by liquid crystal orientation,” Opt. Express 17(6), 4360–4366 (2009). [CrossRef] [PubMed]

16.

A. Minovich, D. N. Neshev, D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, “Tunable fishnet metamaterials infiltrated by liquid crystals,” Appl. Phys. Lett. 96(19), 193103 (2010). [CrossRef]

17.

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5-6), 221–267 (2009). [CrossRef]

18.

C. M. Soukoulis, S. Linden, and M. Wegener, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312, 892–894 (2007).

19.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]

20.

M. Kafesaki, I. Tsiapa, N. Katsarakis, Th. Koschny, C. M. Soukoulis, and E. N. Economou, “Left-handed metamaterials: The fishnet structure and its variations,” Phys. Rev. B 75(23), 235114 (2007). [CrossRef]

21.

J. Carbonell, C. Croënne, F. Garet, E. Lheurette, J. L. Coutaz, and D. Lippens, “Lumped elements circuit of terahertz fishnet-like arrays with composite dispersion,” J. Appl. Phys. 108(1), 014907 (2010). [CrossRef]

22.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101(10), 103902 (2008). [CrossRef] [PubMed]

23.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

24.

K. C. Lim, J. D. Margerum, and A. M. Lackner, “Liquid crystal millimeter wave electronic phase shifter,” Appl. Phys. Lett. 62(10), 1065–1067 (1993). [CrossRef]

25.

F. Yang and J. R. Sambles, “Determination of the microwave permittivities of nematic liquid crystals using a single-metallic slit technique,” Appl. Phys. Lett. 81(11), 2047–2049 (2002). [CrossRef]

26.

C. Weil, St. Müller, P. Scheele, P. Best, G. Lüssem, and R. Jakoby, “Highly-anisotropic liquid-crystal mixtures for tunable microwave devices,” Electron. Lett. 39(24), 1732–1734 (2003). [CrossRef]

27.

F. Zhang, Q. Zhao, D. P. Gaillot, X. Zhao, and D. Lippens, “Numerical Investigation of Metamaterials Infiltrated by Liquid Crystal,” J. Opt. Soc. Am. B 25(11), 1920 (2008). [CrossRef]

28.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002). [CrossRef] [PubMed]

29.

C. Croënne, B. Fabre, D. Gaillot, O. Vanbésien, and D. Lippens, “Bloch impedance in negative index photonic crystals,” Phys. Rev. B 77(12), 125333 (2008). [CrossRef]

30.

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]

31.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005). [CrossRef] [PubMed]

OCIS Codes
(160.1190) Materials : Anisotropic optical materials
(160.3710) Materials : Liquid crystals
(190.4400) Nonlinear optics : Nonlinear optics, materials
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: November 17, 2010
Revised Manuscript: December 18, 2010
Manuscript Accepted: December 19, 2010
Published: January 13, 2011

Citation
Fuli Zhang, Weihong Zhang, Qian Zhao, Jingbo Sun, Kepeng Qiu, Ji Zhou, and Didier Lippens, "Electrically controllable fishnet metamaterial based on nematic liquid crystal," Opt. Express 19, 1563-1568 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-1563


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References

  1. 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]
  2. I. Gil, J. García-García, J. Bonache, F. Martín, M. Sorolla, and R. Marqués, “Varactor-loaded split ring resonators for tunablenotch filters at microwave frequencies,” Electron. Lett. 40(21), 1347–1348 (2004). [CrossRef]
  3. I. V. Shadrivov, S. K. Morrison, and Y. S. Kivshar, “Tunable split-ring resonators for nonlinear negative-index metamaterials,” Opt. Express 14(20), 9344–9349 (2006). [CrossRef] [PubMed]
  4. H. Chen, B.-I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, “Controllable left-handed metamaterial and its application to a steerable antenna,” Appl. Phys. Lett. 89(5), 053509 (2006). [CrossRef]
  5. A. Degiron, J. J. Mock, and D. R. Smith, “Modulating and tuning the response of metamaterials at the unit cell level,” Opt. Express 15(3), 1115–1127 (2007). [CrossRef] [PubMed]
  6. H.-T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterial,” Nat. Photonics 2(5), 295–298 (2008). [CrossRef]
  7. Z. L. Sámson, K. F. MacDonald, F. De Angelis, B. Gholipour, K. Knight, C. C. Huang, E. Di Fabrizio, D. W. Hewak, and N. I. Zheludev, “Metamaterial electro-optic switch of nanoscale thickness,” Appl. Phys. Lett. 96(14), 143105 (2010). [CrossRef]
  8. T. H. Hand and S. A. Cummer, “Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings,” J. Appl. Phys. 103(6), 066105 (2008). [CrossRef]
  9. R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, “Nonmagnetic nanocomposites for optical and infrared negative-refractive-index media,” J. Opt. Soc. Am. B 23(3), 498–505 (2006). [CrossRef]
  10. S. Xiao, U. K. Chettiar, A. V. Kildishev, V. Drachev, I. C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. 95(3), 033115 (2009). [CrossRef]
  11. Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90(1), 011112 (2007). [CrossRef]
  12. F. Zhang, Q. Zhao, L. Kang, D. P. Gaillot, X. Zhao, J. Zhou, and D. Lippens, “Magnetic control of negative permeability metamaterials based on liquid crystals,” Appl. Phys. Lett. 92(19), 193104 (2008). [CrossRef]
  13. I. C. Khoo, D. H. Werner, X. Liang, A. Diaz, and B. Weiner, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett. 31(17), 2592–2594 (2006). [CrossRef] [PubMed]
  14. D. H. Werner, D.-H. Kwon, I.-C. Khoo, A. V. Kildishev, and V. M. Shalaev, “Liquid crystal clad near-infrared metamaterials with tunable negative-zero-positive refractive indices,” Opt. Express 15(6), 3342–3347 (2007). [CrossRef] [PubMed]
  15. F. Zhang, L. Kang, Q. Zhao, J. Zhou, X. Zhao, and D. Lippens, “Magnetically tunable left handed metamaterials by liquid crystal orientation,” Opt. Express 17(6), 4360–4366 (2009). [CrossRef] [PubMed]
  16. A. Minovich, D. N. Neshev, D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, “Tunable fishnet metamaterials infiltrated by liquid crystals,” Appl. Phys. Lett. 96(19), 193103 (2010). [CrossRef]
  17. I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471(5-6), 221–267 (2009). [CrossRef]
  18. C. M. Soukoulis, S. Linden, and M. Wegener, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312, 892–894 (2007).
  19. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]
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