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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 6 — Mar. 16, 2009
  • pp: 4360–4366
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Magnetically tunable left handed metamaterials by liquid crystal orientation

Fuli Zhang, Lei Kang, Qian Zhao, Ji Zhou, Xiaopeng Zhao, and Didier Lippens  »View Author Affiliations


Optics Express, Vol. 17, Issue 6, pp. 4360-4366 (2009)
http://dx.doi.org/10.1364/OE.17.004360


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Abstract

The tunability of an omega–type left handed metamaterial was demonstrated at microwave frequencies via the magnetic control of liquid crystal (LC) orientation. From the experimental and simulation results, it is shown that the left handed pass-band can be tuned by 220 MHz by changing the orientation of LC molecules by 90°. A maximum index variation of 0.25 was obtained in the negative index regime with a measured LC birefringence of 0.05 in the 10 - 12GHz frequency band.

© 2009 Optical Society of America

1. Introduction

Over the past few years, electromagnetic metamaterials with unique properties have attracted much attention [1–4

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

] with a rapid development from microwave frequencies [5

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

] to optical regime [6

6. C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007). [CrossRef] [PubMed]

]. As resonant restructures, metamaterials exhibit strong frequency dispersion and hence narrow bandwidth operation with the center frequency determined by geometry and dimensions of constitutive materials. In fact, all the interesting effects achieved by metamaterials, such as negative refraction [1

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

], perfect lensing [2

2. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 39663969 (2000). [CrossRef] [PubMed]

] and cloaking [3

3. 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, 977–980 (2006). [CrossRef] [PubMed]

, 4

4. D. P. Gaillot, C. Croënne, and D. Lippens, “An all dielectric route for Terahertz cloaking,” Opt. Express , 16, 3986–3992 (2008). [CrossRef] [PubMed]

], are limited to a fixed narrow spectral bandwidth. For many potential applications, the fabrication of frequency tunable metamaterials whose operating frequency can be adjusted, is of great interest to alleviate these limitations. There have been some efforts to realize tunable metamaterial by the judicious incorporation of active devices or materials, such as varactor diode [7–9

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

], semiconductors [10–12

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

], ferroelectics [13

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

] and more generally anisotropic materials [14–18

14. 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, 498–505 (2006). [CrossRef]

], as a part of the metamaterial elements to change the resonance condition. Among these works, liquid crystals (LCs), possessing a large birefringence which can be controlled by an external field, have shown promise as tunable metamaterial substrates, over a relatively large spectrum of the electromagnetic waves [15–17

15. 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, 3342–3347 (2007). [CrossRef] [PubMed]

]. However, up to now, the experimental demonstrations of LC-based metamaterial are mainly focused on single negative metamaterials fabricated via Split Ring Resonator (SRR) technology [17

17. 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, 011112 (2007). [CrossRef]

, 18

18. 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, 193104 (2008). [CrossRef]

]. In this context, the tuning of left handed metamaterials (LHMs) properties, which can be realized by controlling the LC molecular orientation, deserves attention with the prospect of tunable negative index. Although several numerical works have shown that tunable LHMs can be achieved by the infiltration of LC [14–16

14. 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, 498–505 (2006). [CrossRef]

], the experimental verification has yet to be reported.

In this paper, we report on the experimental results of a frequency-tunable LHM operating at microwave frequencies, which incorporated LC into sub-millimeter voids as multilayered substrate. By using an external magnetic field excitation on the alignment of LC, a frequency shift of the left handed pass-band was observed. In addition, the index variation of metamaterial was also assessed by both numerical retrieval effective parameters on the basic cell and a measurement of phase offset of a nine-cell prototype. Generally, the LC compounds exhibit dipole relaxation in the low frequency part of the microwave spectrum notably at radio frequency. As a consequence, their dielectric constants and hence refractive indexes considered here are quite comparable to those measured in the optical range. On the other hand, it was shown by several groups in the literature notably in [6

6. C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007). [CrossRef] [PubMed]

] that the operating frequency of the SRR array can be extended at optical wavelengths. Under this condition, it is believed that the conclusions drawn in the present work on the basis of a microwave demonstration still hold at least at terahertz frequencies, in which the metal loss can be maintained at a reasonable level.

2. Tunable Metamaterial infiltrated by LC

Figure 1(a) shows the schematic of the basic unit of the tunable metamaterial, which is composed of two omega patterns stacked in a reversed orientation in order to cancel the magneto-electric effects [19

19. J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004). [CrossRef]

]. Under an illumination with E-polarized along the x and H-polarized along the y axis, the basic unit operates as a combination of broadside-coupled C-shaped-split right resonators (BC-SRRs), providing negative permeability and wire arrays, yielding negative permittivity below the plasma frequency. As a consequence, the device exhibits negative index due to simultaneous negative permittivity and permeability in a frequency band between the resonant frequency and the magnetic plasma frequency of BC-SRR arrays. In the present work, the omega patterns are supported by Teflon fiberglass with infiltration of LC in between. Let us suppose that the LC director lies in the x-y plane (Fig. 1(a)). For the LC slab with the director of the molecules aligned along x, the director axis n can take all values {cos θ,sin θ,0} by applying a magneto-static field based on the Fréedericksz effect, where θ denotes the rotation angle of the molecular director with respect to the x axis. With the reorientation of the LC molecular director, we can control the effective permittivity of LC layer which influences the magnetic resonance of BC-SRR [18

18. 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, 193104 (2008). [CrossRef]

], and consequently modifies the condition of the negative index regime.

Fig. 1. (a) Schematic of the basic unit cell of the tunable negative index metamaterial as well as the reorientation of the LC molecule in the x-y plane. The geometry dimensions are as follows: R = 0.5, g = 0.4, w =1.0, tteflon = 1.0, tLC = 0.5 (unit: mm). The unit cell is stacked along the x and z directions with periodicities of 10.0 and 6.0 mm, respectively. (b) Close-up view of the mid-plane of the sample with the other part was removed to clarify the configuration of the voids.

Figure 1(b) shows a close-up view of the metamaterial sample. By using the standard print circuit board technology, two omega motifs with the same orientation were firstly patterned on both sides of a 1.0-mm-thick Teflon fiberglass board. In this way, there is no possibility for magnetic coupling occurring between omega patterns on both sides of one Teflon fiberglass board. By means of a numerically controlled machine, a U-shaped thin slice of epoxy fiberglass with a thickness of 0.5 mm was fabricated and then used as a spacer between Teflon fiberglass boards with voids for LC infiltration. The width of the spacer edge was set to 1.0 mm, thus leaving enough room for the LC infiltration. Finally, Teflon fiberglass boards and spacers were alternatively stacked and aligned by means of via holes and plastic rods. It is worth mentioning that omega patterns on adjacent Teflon fiberglass boards were stacked in a back-to-back configuration to form BC-SRRs as shown in Fig. 1(a).

In the experiment, a mixture of nematic LC compounds was synthesized with an overall positive magnetic anisotropy and a large birefringence of 0.22 at optical regime. As the birefringence of LC decreases at microwave or millimeter waves [20–22

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

], it was necessary to measure the dielectric properties of LC at microwave frequencies. By employing the method based on a phase shift in LC cells of different lengths as proposed in Ref. [20

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

], the LC indexes were measured between 10 and 12 GHz. Figure 2(a) shows the frequency dependence of the extraordinary ne and ordinary no in this band. The LC compound exhibits a positive birefringence (ne > no) in the frequency band of interest, in which ne varies between 1.33 and 1.48 whereas no changes from 1.28 to 1.41. The birefringence Δn versus frequency is plotted in Fig. 2 (b). Δn fluctuates around 0.05, which is comparable to the birefringence of some commercial nematic compound such as 5CB in the same frequency range.

Fig. 2. (a) Extraordinary (black triangular) and ordinary (red circle) refractive indexes measured at room temperature as a function of frequency. (b) Birefringence of the nematic compound was deduced in the 10–12 GHz frequency band.

By using a needle tube, the LC compound was infiltrated into the board interspacing via capillary forces. In order to orientate the LC molecules, a pair of permanent magnets with centimeter size was mounted externally to apply a uniform magnetic field in the x-y plane. The external magnetic field of 500 G measured by a digital magnetometer enables a good alignment of the LC molecules as the threshold field is less than 100 G for thin cells [23

23. C.-Y. Chen, T.-R. Tsai, C.-L. Pan, and R.-P. Pan, “Room temperature terahertz phase shifter based on magnetically controlled birefringence in liquid crystals,” Appl. Phys. Lett. 83, 4497 (2003). [CrossRef]

]. The metamaterial sample was then inserted in an X-band hollow waveguide and the scattering parameters were measured by using a HP8720 ES Vectorial Network Analyzer.

Fig. 3. The experimental (a) and simulation (b) transmission responses of the metamaterial with infiltrated by LC under different molecules orientations: θ = 0° (solid black line) and 90° (dashed red line), respectively. (c) The local electric field distribution is plotted in the x-y plane at the magnetic resonance of omega pattern. Teflon fiberglass boards were invisible for clarity.

The measurements of the transmission spectra were carried out (i) with the magnetic field applied along the x axis (θ = 0°) and (ii) along the y axis (θ = 90°). The results are reported in Fig. 3(a). When the magnetic field is applied along the x axis (θ = 0°), the omega arrays exhibit a well-defined transmission pass-band, as expected with negative index material. The transmission maximum is at 11.72 GHz. For θ = 90° and hence for an orthogonal magnetic field excitation, a red-shift of the pass-band was observed with a maximum of transmission at 11.50 GHz. Although the pass-band shift of 220 MHz is not large compared to the relatively broad bandwidth, it can be measured nonetheless without any ambiguity due to the fact that the overall form of the transmission band is relatively unchanged between the two LC reorientation states. In addition, it is also noted that the redshift occurs with an increasing transmittance.

Figure 3(b) shows the simulation results for the transmission response versus frequency For the LC reorientation corresponding to θ = 0°, the omega arrays exhibit a well-defined pass-band with a centre frequency at 11.55 GHz, which is in a fairly good agreement with the experimental results. However, the experimental result (Fig. 3(a)) shows a broader operating bandwidth. This is mainly due to the slightly variations of the voids interspacing as the Teflon fiberglass is not perfectly rigid. Further simulation results confirmed that the pass-band position is very sensitive to the void thickness variation. For instances, a 360 MHz frequency shift occurs when the thickness of voids changes 50 μm. The unwanted spacing differences result in different magnetic resonances between layers, causing multiple adjacent pass-bands and consequently a broader transmission window. Under the orthogonal excitation of external magnetic field (θ = 90°), the pass-band shifts down to 11.40 GHz, showing the same dependence on LC reorientation as the experimental results.

To provide an insight on the relation between the LHM pass-band shift and the reorientation of LC molecules, the electric field map was monitored. It is shown in Fig. 3(c). It can be noticed that local electric field is polarized along the y axis rather than along the x axis which corresponds to the incident electric field polarization. This is a result of the broadside coupling between the omega patterns facing together as explained in Ref. [18

18. 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, 193104 (2008). [CrossRef]

]. In fact, the capacitance of the omega pattern is mainly determined by the permittivity component εy along the y direction which thus dominates the magnetic response as shown in Fig. 3(c). When an external magnetic field is applied to orientate the LC molecules from randomly distributed to parallel to x, εy is mainly experienced as εo. As the LC director is reorientated from θ = 0° to 90°, εy is increased from εo to εe, giving rise to an increase of the capacitance and therefore a redshift of the resonant frequency. Additionally, as the loss tangent of the molecule along the y axis is decreased from tan δo to tan δe, the pass-band transmittance is increased to a higher level.

3. Modeling of the index variation

The frequency dependences of the index real parts were subsequently calculated from the scattering parameters of a basic unit cell by employing a well-established algorithm [24

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

, 25

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

] (Fig .4). In Fig. 4, negative values of index are observed from 11.0 to 13.0 GHz, verifying that the pass-bands correspond to a left handed dispersion branch. With the change of LC orientation by the magnetic field, a shift of the index curve is only noted between 11 and 12.0 GHz. In the lower frequency band identified by shadowed region, the metamaterial transmission is very weak and dominated by the evanescent waves, so that the derivation of a refractive index value becomes questionable.

Fig. 4. The real parts of retrieval indexes for metamaterial infiltrated by LC under different LC molecular reorientations: θ = 0° (solid black line) and 90° (dashed red line).

4. Experimental phase shift of a nine-cell prototype

The measured phase-shift of a nine-cell-long sample (Fig. 1(b)), as a consequence of the index variation between the two orthogonal magnetic field excitations, is shown in Fig. 5. As the director of LC is reorientated from 0° to 90°, the phase shift increases around 10.6 GHz and reaches a maximum value of 174.5° at 10.93 GHz. This phase offset corresponds to an approximate index variation peak of 0.25 for the 5.4-cm-long sample considered here. This enhanced index variation arising from a LC birefringence of 0.05 is mainly due to the intrinsic strong magnetic resonant character around 11.0 GHz.

Fig. 5. The measured phase shift for a nine-cell prototype when the LC molecules are reorientated from θ = 0° to 90°. The inset shows the phase delays for the two orientations of LC.

5. Conclusion

Acknowledgments

This work was carried out in the framework of a CNES (Centre National d’Etudes Spatiales) contract and partially supported by the NPU Foundation for Fundamental Research No. WO18101 and the Chinese State Key Laboratory of Tribology (Grant No. SKLT 08B12). F. Zhang would like to acknowledge the China Scholarship Council and Northwestern Polytechnical University for his fellowship.

References and links

1.

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

2.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 39663969 (2000). [CrossRef] [PubMed]

3.

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, 977–980 (2006). [CrossRef] [PubMed]

4.

D. P. Gaillot, C. Croënne, and D. Lippens, “An all dielectric route for Terahertz cloaking,” Opt. Express , 16, 3986–3992 (2008). [CrossRef] [PubMed]

5.

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

6.

C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science 315, 47–49 (2007). [CrossRef] [PubMed]

7.

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

8.

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

9.

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, 053509 (2006). [CrossRef]

10.

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

11.

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

12.

J. Carbonell, V. E. Boria, and D. Lippens, “Resonators loaded with heterostructure barriere varactos,” Microw. Opt. Technol. Lett. 50, 474–479 (2008). [CrossRef]

13.

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

14.

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, 498–505 (2006). [CrossRef]

15.

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, 3342–3347 (2007). [CrossRef] [PubMed]

16.

X. Wang, D.-H. Kwon, D. H. Werner, I.-C. Khoo, A. V. Kildishev, and V. M. Shalaev, “Tunable optical negative-index metamaterials employing anisotropic liquid crystals,” Appl. Phys. Lett. 91, 143122 (2007). [CrossRef]

17.

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, 011112 (2007). [CrossRef]

18.

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, 193104 (2008). [CrossRef]

19.

J. Huangfu, L. Ran, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004). [CrossRef]

20.

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

21.

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, 2047–2049 (2002). [CrossRef]

22.

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, 1732–1734 (2003). [CrossRef]

23.

C.-Y. Chen, T.-R. Tsai, C.-L. Pan, and R.-P. Pan, “Room temperature terahertz phase shifter based on magnetically controlled birefringence in liquid crystals,” Appl. Phys. Lett. 83, 4497 (2003). [CrossRef]

24.

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

25.

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

26.

T. R. Tsai, C.-Y. Chen, C.-L. Pan, R.-P. Pan, and X.-C. Zhang, “Teraheratz time-domain spectroscopy studies of the optical constants of the nematic liquid crystal 5CB,” Appl. Opt. 42, 2372–2376 (2003). [CrossRef] [PubMed]

27.

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. B. Mahmood, and L. Wen, “Free-standing THz electromagnetic metamaterials,” Opt. Express 16, 13773–13780 (2008). [CrossRef] [PubMed]

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(160.1190) Materials : Anisotropic optical materials
(160.3710) Materials : Liquid crystals
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: October 13, 2008
Revised Manuscript: November 13, 2008
Manuscript Accepted: November 15, 2008
Published: March 4, 2009

Citation
Fuli Zhang, Lei Kang, Qian Zhao, Ji Zhou, Xiaopeng Zhao, and Didier Lippens, "Magnetically tunable left handed metamaterials by liquid crystal orientation," Opt. Express 17, 4360-4366 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-6-4360


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References

  1. V. G. Veselago, "The electrodynamics of substrates with simultaneously negative values of ε and µ," Sov. Phys. Usp. 10, 509-514 (1968). [CrossRef]
  2. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
  3. 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, 977-980 (2006). [CrossRef] [PubMed]
  4. D. P. Gaillot, C. Croënne, and D. Lippens, "An all dielectric route for Terahertz cloaking," Opt. Express 16, 3986-3992 (2008). [CrossRef] [PubMed]
  5. R. A. Shelby, D. R. Smith, and Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001). [CrossRef] [PubMed]
  6. C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007). [CrossRef] [PubMed]
  7. I. Gil, J. García-García, J. Bonache, F. Martín, M. Sorolla, and R. Marqués, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40, 1347-1348 (2004). [CrossRef]
  8. I. V. Shadrivov, S. K. Morrison, and Y. S. Kivshar, "Tunable split-ring resonators for nonlinear negative-index metamaterials," Opt. Express. 14, 9344-9349 (2006). [CrossRef] [PubMed]
  9. 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, 053509 (2006). [CrossRef]
  10. A. Degiron, J. J. Mock, and D. R. Smith, "Modulating and tuning the response of metamaterials at the unit cell level," Opt. Express 15, 1115-1127 (2007). [CrossRef] [PubMed]
  11. H.-T. Chen, J. F. O’Harai, A. K. Azadi, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, "Experimental demonstration of frequency-agile terahertz metamaterial," Nat. Photon. 2, 295-298 (2008). [CrossRef]
  12. J. Carbonell, V. E. Boria, and D. Lippens, "Resonators loaded with heterostructure barriere varactos," Microw. Opt. Technol. Lett. 50, 474-479 (2008). [CrossRef]
  13. T. H. Hand and S. A. Cummer, "Frequency tunable electromagnetic metamaterial using ferroelectric loaded split rings," J. Appl. Phys. 103, 066105 (2008). [CrossRef]
  14. 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, 498-505 (2006). [CrossRef]
  15. 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, 3342-3347 (2007). [CrossRef] [PubMed]
  16. X. Wang, D.-H. Kwon, D. H. Werner, I.-C. Khoo, A. V. Kildishev, and V. M. Shalaev, "Tunable optical negative-index metamaterials employing anisotropic liquid crystals," Appl. Phys. Lett. 91, 143122 (2007). [CrossRef]
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