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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 8 — Apr. 13, 2009
  • pp: 6301–6310
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Negative refractive index metamaterials using only metallic cut wires

Alexandre Sellier, Shah Nawaz Burokur, Boubacar Kanté, and André de Lustrac  »View Author Affiliations


Optics Express, Vol. 17, Issue 8, pp. 6301-6310 (2009)
http://dx.doi.org/10.1364/OE.17.006301


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Abstract

We present, design and analyze a novel planar Left-Handed (LH) metamaterial at microwave frequencies. This metamaterial is composed of only metallic cut wires and is used under normal-to-plane incidence. Using Finite Element Method (FEM) based simulations and microwave experiments, we have investigated the material properties of the structure. Simultaneous negative values are observed for the permittivity e and permeability μ by the inversion method from the transmission and reflection responses. A negative index n is verified in a bulk prism engineered by stacking several layers of the metamaterial. Our work demonstrates the feasibility of a LH metamaterial composed of only cut wires.

© 2009 Optical Society of America

1. Introduction

Left-Handed (LH) metamaterials are in general artificial composite structures exhibiting simultaneously a negative effective permittivity ε eff and permeability μ eff over a common frequency range [1

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

]. Such metamaterials can be constructed from conductive metals and dielectrics. Since the first demonstration of a LH material by Smith et al. [2

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

] in 2000, following the work by Pendry et al. [3-4

3. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett . 76, 4773–4776 (1996). [CrossRef] [PubMed]

], a lot of work has been done and is still in progress in order to simplify the structures for optical wavelengths. Due to the saturation of the magnetic response of Split-Ring Resonators (SRR) at optical frequencies [5

5. J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett . 95, 223902 (2005). [CrossRef] [PubMed]

], a different topology composed of metal wire pairs with dielectric spacing has been introduced theoretically by Podolskiy et al. to exhibit a negative refractive index n [6

6. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express 11, 735–745 (2003). [CrossRef] [PubMed]

]. Later, Shalaev et al. [7

7. 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, 3356–3358 (2005). [CrossRef]

] used this configuration to show experimentally a negative index under normal-to-plane incidence (when the wave vector k is perpendicular to the structure) in the optical range at the telecommunication wavelength λ = 1.5 μm. In a recent review paper [8

8. V. M. Shalaev, “Optical negative-index metamaterials,” Nature Photonics 1, 41–48 (2007). [CrossRef]

], Shalaev stated that it is very difficult to achieve a negative refractive index with exclusively wire pairs and the negative index value observed in [7

7. 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, 3356–3358 (2005). [CrossRef]

] was accomplished in part because of the significant contribution from the imaginary part of the permeability. Other experiments on short wire pairs by Dolling et al. have not shown evidence of negative n due to two distinct frequency bands for the negative permeability μ and permittivity ε [9

9. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett . 30, 3198–3200 (2005). [CrossRef] [PubMed]

]. In the meantime, Zhou et al. emphasized that the condition to obtain simultaneously negative permittivity and permeability by pairs of finite metallic wires is very restrictive [10

10. J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006). [CrossRef]

]. The authors then showed the possibility of obtaining a negative refractive index in the microwave regime from bilayered structures by combining periodic continuous and cut wires as shown in Fig. 1(a). The continuous wires are used to provide the negative effective permittivity. The negative permeability is obtained by exciting resonant circular currents in the cut wire pair in order to create a strong magnetic resonance. Zhou et al. also theoretically demonstrated a left-handed material using only cut wire pairs by increasing the equivalent capacitance between two consecutive short wires on the same face to adjust the electric resonance frequency [11

11. J. Zhou, E. Economou, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett . 31, 3620–3622 (2006). [CrossRef] [PubMed]

]. However this increase of capacitance can only be achieved by strongly reducing the spacing between two consecutive wires and this is quite difficult to achieve at optical wavelengths. Another bi-layered structure shown in Fig. 1(b) and referred to as “fishnet” has been reported to exhibit a negative index at optical [12

12. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett . 32, 53–55 (2007). [CrossRef]

] and microwave frequencies [13

13. 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, 235114 (2007). [CrossRef]

]. The main drawback of the cut-continuous wires and fishnet topologies is the high level of metallization which is an important source of losses at high frequencies, particularly in the optical domain.

In this paper, we present a systematic study of the novel cut wires structure presented in Fig. 1(c) under normal-to-plane incidence in the microwave domain. This structure is made only of cut-wires on a dielectric substrate. We demonstrate numerically and experimentally that this simplified structure (Fig. 1(c)) using fewer metallic parts compared to the cut-continuous wires (Fig. 1(a)) and the fishnet (Fig. 1(b)) structures, exhibits simultaneously a negative permittivity and a negative permeability. Numerical simulations performed using the FEM based software HFSS [14

14. High Frequency Structure Simulator, HFSS v11.1, Ansoft Ltd.

] are run to show and understand the electromagnetic behavior of the design. A single layer of the metamaterial is characterized by reflection and transmission measurements. The retrieved parameters show simultaneous resonances in the permittivity and permeability responses leading to a negative index of refraction. The results are confirmed by experimental measurements. A prism made of this metamaterial is engineered and used not only to observe a negative refraction, but also to estimate and verify the refractive index.

Fig. 1. Unit cell of: (a) cut-continuous wires structure, (b) fishnet structure, and (c) only cut wires structure under normal-to-plane propagation (ax = 9.5 mm, ay = 19 mm, w = 0.3 mm, l = 9.5 mm). The inserts show the direction and the polarization of the wave.

2. Material properties of the cut wires metamaterial

In this study, the cut wires metamaterial illustrated by its unit cell in Fig. 1(c) is employed to operate in the microwave regime. It consists of a bi-layered structure composed of periodic cut wires of finite length. Compared to the cut wires structure of ref. [6-8

6. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express 11, 735–745 (2003). [CrossRef] [PubMed]

] (Fig. 1(a)), the finite wires in our case do not face each other entirely on the dielectric board. In fact, the wires on one face are laterally shifted along the y-axis by the length l. The structure is printed on both faces of an epoxy dielectric board of thickness t = 1.2 mm and of relative permittivity ε r = 3.9. For the different samples reported here, the width of the cut wires denoted by w is 0.3 mm. The length of the cut wires is l = 9.5 mm and the unit cell size in the x and y direction is respectively ax = 9.5 mm and ay = 19 mm. These dimensions have been optimized to operate around 10 GHz and remain the same throughout the whole paper.

The reflection and transmission spectra of the metamaterial are calculated using HFSS by applying the necessary periodic boundary conditions on the unit cell. Several samples of the structure consisting of 10 × 5 cells on a 120 mm × 120 mm epoxy surface are fabricated using conventional commercial chemical etching technique. Measurements are done in an anechoic chamber using an Agilent 8722ES network analyzer and two X-band horn antennas. In the transmission measurements, the plane waves are incident normal to the prototype surface and a calibration to the transmission in free space (the metamaterial sample is removed) between the two horn antennas is done. The reflection measurements are done by placing the emitting and receiving horn antennas on the same side of the prototype and inclined with an angle of about 5° with respect to the normal on the prototype surface. The calibration for the reflection is done using a sheet of copper as reflecting mirror.

Fig. 2. Calculated and measured reflection (S 11) and transmission (S 21) responses of the metamaterial for a single layer: (a) magnitude, and (b) phase.

Figure 2 shows the calculated (continuous lines) and measured (dashed lines) S-parameters of the metamaterial for a single layer configuration. There is a very good qualitative agreement between simulations and measurements. The calculated and measured magnitudes of S 21 presented in Fig. 2(a) show clearly two resonance dips, the first one at 9.58 GHz and a second one at 11.39 GHz. We can note in Fig. 2(b) that a change in sign occurs for the transmission phase at the first resonance dip. At the second resonance dip, a peak and a dip is respectively observed in the transmission and reflection phase.

Using the retrieval procedure described in [15

15. A. M. Nicolson and G. F. Ross, “Measurement of the intrinsic properties of materials by time-domain techniques,” IEEE Trans. Instrum. Meas . 19, 377–382 (1970). [CrossRef]

], based on the inversion of the reflection and transmission coefficients, the effective parameters of the bi-layered metamaterial structure are extracted. The metamaterial has a period very small compared to the wavelength λ (less than λ/20) in the propagation direction. The propagation of the electromagnetic wave travelling along this direction is dominated by this deep sub-wavelength period and not by the in-plane period ax or ay. There is only a single propagating mode in the negative-index frequency region, justifying the description of the cut wires metamaterial with an effective index [16

16. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three Dimensional Optical Metamaterial Exhibiting Negative Refractive Index,” Nature 455, 376 (2008). [CrossRef] [PubMed]

].

The extracted permittivity ε, permeability μ and refractive index n are shown in the various parts of Fig. 3. Two extraction procedures have been performed: the first one uses the calculated S-parameters and the second one is based on the measured S-parameters. It must be noted that the extraction from the measured spectra are presented without any fitting. As illustrated by the extracted parameters from the calculated and measured S-parameters, the cut wires structure shows firstly an electric resonance at the first resonance dip observed at 9.58 GHz in Fig. 2. This electric resonance exhibits values going negative for the real part of the permittivity in the vicinity of the resonance. Secondly a magnetic resonance with negative values appears at the right hand side of the second resonance dip at 11.5 GHz. Around the same frequency, the real part of the permittivity is still negative. The extracted real part of the refractive index is therefore negative around 11.5 GHz which is the frequency of the LH peak. However, we can also notice that the zero value for the e response is very close to 13 GHz where a full transmission band is observed in Fig. 2(a). This frequency constitutes the frequency of the RH transmission peak. We can therefore deduce that this RH transmission peak is due to an impedance matching between the structure and vacuum.

Fig. 3. Extracted electromagnetic properties of the cut wires metamaterial using the simulated and experimental data of Fig. 2: (a)-(c) real parts, and (d)-(f) imaginary parts of the permittivity ε, of the permeability μ and the refraction index n. The shaded yellow area delineates the frequency region where the measured real parts of ε and μ are simultaneously negative.

Since the real part of n(n’) is given by n’ = εz’ - εz” from n = εz and z = √(μ/ε), the imaginary parts of the permittivity (ε”) and the permeability (μ”) also accounts for n’. Therefore, a negative real part of n can be accomplished without having ε’ and μ’ simultaneously negative. This can happen only if ε” and μ” are sufficiently large compared to ε’ and μ’. A wider negative n’ frequency band is observed due to the dispersion of the fabricated prototype. The shaded yellow area in Fig. 3 highlights the frequency region where the measured real parts of the permittivity (ε’) and the permeability (μ’) are simultaneously negative to emphasize the desired measured negative values of n’. Concerning the imaginary parts, a very good qualitative agreement is observed between calculations and experiments. We shall note that the imaginary part of n (n”) is very low in the negative n’ frequency region.

The proposed cut wires structure can be viewed as a simplification of the S-shaped resonator previously presented in [17

17. H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004). [CrossRef]

]. While the face-to-face cut wire pair is issued from the elimination of the horizontal arms of a conventional one loop SRR as described in [9

9. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett . 30, 3198–3200 (2005). [CrossRef] [PubMed]

], we can similarly cancel the horizontal arms of a single S-shaped resonator so as to consider only the vertical arms as presented by the proposed cut wire pair in Fig. 1(c). The magnetic coil is still present to produce a negative permeability since a capacitance is created between the ends of the wires on the opposite faces of the dielectric board.

3. Stacking of layers

Stacking multiple layers of LH materials may be useful in many practical applications such as subwavelength imaging [18

18. K. Aydin, I. Bulu, and E. Ozbay, “Focusing of electromagnetic waves by a left-handed metamaterial flat lens,” Opt. Express 13, 8753–8759 (2005). [CrossRef] [PubMed]

, 19

19. G. Wang, J. R. Fang, and X. T. Dong, “Refocusing of backscattered microwaves in target detection by using LHM flat lens,” Opt. Express 15, 3312–3317 (2007). [CrossRef] [PubMed]

] and directive antennas [20

20. R. W. Ziolkowski and A. Kipple, “Application of double negative metamaterials to increase the power radiated by electrically small antennas,” IEEE Trans. Antennas Propag . 51, 2626–2640 (2003). [CrossRef]

, 21

21. S. N. Burokur, M. Latrach, and S. Toutain, “Theoretical investigation of a circular patch antenna in the presence of a left-handed medium,” IEEE Antennas Wireless Propag. Lett . 4, 183–186 (2005). [CrossRef]

]. In this paper, the stacking of layers is considered as a preliminary study before the verification of the negative index of refraction from a prism-shaped bulk metamaterial. It is obvious that the effective properties obtained from the inversion method on a single layer give a good idea about the effective properties of the metamaterial. However, other effect such as inter-layer coupling must be taken into account because it affects the material properties of the structure. Therefore, two, three and four layers of the designed bi-layered metamaterial are stacked with a 1 mm air spacing between each layer as presented in Fig. 4(a). Numerical simulations are run to show the expected performances of a bulk metamaterial composed of multiple layers. The transmission spectra for the different number of layers are presented in Fig. 4(b).

Fig. 4. (a) A bulk metamaterial composed of four layers interleaved with 1 mm air spacing, and (b) transmission spectra for different number of layers.

From the spectra of Fig 4(b), we can note that the frequency of the first transmission dip remains constant with an increasing number of layers while the second dip shifts slightly towards higher frequencies. However, peaks and valleys appear at lower frequencies suggesting a coupling mechanism between consecutive layers. The number of these peaks and valleys increases with an increasing number of layers as shown in Fig. 4(b). The transmission spectra together with the corresponding reflection spectra are used for the extraction of the material properties presented in Fig. 5. It should be noted that the first transmission dip in the single layer case corresponds to an electric resonance where ε’ exhibits negative values. However, other ε’ < 0 frequency bands can be observed in Fig. 5(a) for the multiple layers cases due to the valleys noted in the transmission spectra. And, since the magnitude of the transmission dips decreases with the number of layers, the magnitude of ε’ also decreases as shown in Fig. 5(a). At higher frequencies near 12 GHz, a magnetic resonance is also observed for multiple layers as for the single layer case. However the magnitude tends to decrease while the number of layers increases (Fig. 5(b)). For more than two layers, μ’ exhibits only positive values at the resonance near 12 GHz. Besides, another magnetic resonance with μ’ < 0 can be observed at lower frequencies with simultaneously ε’ < 0 when more than one layer is used. So even if the μ’ < 0 frequency band disappears at the second transmission dip due to the μ’ > 0, a negative index band is observed at lower frequencies as shown in Fig. 5(c). This negative refractive index results from the coupling mechanism created when several layers of the bi-layered structure are stacked. The negative index frequency band widens when the number of layers increases.

Fig. 5. Extracted material properties for different number of layers. (a) Re(ε), (b) Re(μ), and (c) Re(n).
Fig. 6. Different air spacing for the two layers case. (a) S 21 (dB), and (b) Re(ε), Re(μ), and Re(n). The colored dashed regions highlight the frequency region where Re(ε) and Re(μ) are simultaneously negative for each case.

We shall also note that when a bigger air spacing is left between the layers, the only major change is the shift towards lower frequencies for the transmission peak around 8 GHz. This phenomenon is clearly shown in Fig. 6(a) for a two layers case when the air spacing varies from 1 mm to 2.5 mm. At 12 GHz, a very slight shift in frequency can be noted. The variation in air spacing therefore causes a consequent shift in the μ’ < 0 frequency band at 8 GHz as shown in Fig. 6(b). Since the ε’ < 0 frequency band presents only a very slight shift, one must be very careful in choosing the right spacing between the different layers so that overlapping of ε’ < 0 and μ’ < 0 frequency bands is maintained. As it can observed from the colored dashed regions, the frequency region where Re(ε) and Re(μ) are simultaneously negative tends to become narrower when the air spacing is too high.

3. Refraction experiment

The refractive index n can also be scaled by a refraction experiment based on Snell’s law where an electromagnetic wave passes through a prism made from a slab of the metamaterial under test [22

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

]. The incident face of the prism is illuminated with a beam of microwaves whose electric field is polarized such that it is parallel to the wires as shown in Fig. 7(a). To determine the refractive index n, the deflection of the beam of microwave radiation as it passes through the prism-shaped metamaterial is measured. Knowing the angle of incidence α, the angle of refraction β is easily determined and used to calculate the index of refraction n at different frequencies by Snell’s law. These values are plotted in Fig. 7(b) where a negative index can be observed around 9.7 GHz. This frequency band is different from that obtained from the extraction on one layer but is in good agreement with the one observed from the study made on stacking multiple layers if we consider that the microwave beam passes through several number of layers.

Fig. 7. (a) Experimental setup for the refraction experiment. The inset shows a side view of the fabricated prism shaped metamaterial. (b) Refractive index n obtained by the refraction experiment.

4. Conclusion

In conclusion, we studied the propagation of a normal-to-plane incident electromagnetic wave through a bi-layered cut wires structure and we investigated numerically and experimentally its electromagnetic properties. Numerical simulations have been performed in order to present the reflection and transmission spectra together with the effective parameters responses. The LH structure exhibits two transmission peaks, the first one corresponding to an electric resonance and another one corresponding to a magnetic resonance. Based on these responses, the effective parameters have been extracted to show a negative refractive index. A parameterized study of a material made of a stack of several layers showed that the coupling between layers modifies strongly the LH response of the material and shifts the LH band at lower frequencies. This result has then been verified by a refraction experiment made on an engineered prism from several layers of the metamaterial.

The results obtained from this metamaterial therefore show the possibility of obtaining a negative index from a judicious tailoring of the cut wires structures without the need for additional continuous wires as proposed in [10

10. J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006). [CrossRef]

]. This reduces strongly the use of metallic parts which is quite advantageous particularly in the optical regime.

References and links

1.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of permittivity and permeability,” Sov. Phys. Usp . 10, 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, 4184–4187 (2000). [CrossRef] [PubMed]

3.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett . 76, 4773–4776 (1996). [CrossRef] [PubMed]

4.

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

5.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett . 95, 223902 (2005). [CrossRef] [PubMed]

6.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express 11, 735–745 (2003). [CrossRef] [PubMed]

7.

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, 3356–3358 (2005). [CrossRef]

8.

V. M. Shalaev, “Optical negative-index metamaterials,” Nature Photonics 1, 41–48 (2007). [CrossRef]

9.

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett . 30, 3198–3200 (2005). [CrossRef] [PubMed]

10.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73, 041101 (2006). [CrossRef]

11.

J. Zhou, E. Economou, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett . 31, 3620–3622 (2006). [CrossRef] [PubMed]

12.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett . 32, 53–55 (2007). [CrossRef]

13.

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, 235114 (2007). [CrossRef]

14.

High Frequency Structure Simulator, HFSS v11.1, Ansoft Ltd.

15.

A. M. Nicolson and G. F. Ross, “Measurement of the intrinsic properties of materials by time-domain techniques,” IEEE Trans. Instrum. Meas . 19, 377–382 (1970). [CrossRef]

16.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three Dimensional Optical Metamaterial Exhibiting Negative Refractive Index,” Nature 455, 376 (2008). [CrossRef] [PubMed]

17.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004). [CrossRef]

18.

K. Aydin, I. Bulu, and E. Ozbay, “Focusing of electromagnetic waves by a left-handed metamaterial flat lens,” Opt. Express 13, 8753–8759 (2005). [CrossRef] [PubMed]

19.

G. Wang, J. R. Fang, and X. T. Dong, “Refocusing of backscattered microwaves in target detection by using LHM flat lens,” Opt. Express 15, 3312–3317 (2007). [CrossRef] [PubMed]

20.

R. W. Ziolkowski and A. Kipple, “Application of double negative metamaterials to increase the power radiated by electrically small antennas,” IEEE Trans. Antennas Propag . 51, 2626–2640 (2003). [CrossRef]

21.

S. N. Burokur, M. Latrach, and S. Toutain, “Theoretical investigation of a circular patch antenna in the presence of a left-handed medium,” IEEE Antennas Wireless Propag. Lett . 4, 183–186 (2005). [CrossRef]

22.

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

OCIS Codes
(260.2110) Physical optics : Electromagnetic optics
(260.2065) Physical optics : Effective medium theory
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: December 1, 2008
Revised Manuscript: January 15, 2009
Manuscript Accepted: January 15, 2009
Published: April 2, 2009

Citation
Alexandre Sellier, Shah Nawaz Burokur, Boubacar Kanté, and André de Lustrac, "Negative refractive index metamaterials using only metallic cut wires," Opt. Express 17, 6301-6310 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-8-6301


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References

  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of permittivity and permeability," Sov. Phys. Usp. 10, 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, 4184-4187 (2000). [CrossRef] [PubMed]
  3. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996). [CrossRef] [PubMed]
  4. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999). [CrossRef]
  5. J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902 (2005). [CrossRef] [PubMed]
  6. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735-745 (2003). [CrossRef] [PubMed]
  7. 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, 3356-3358 (2005). [CrossRef]
  8. V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007). [CrossRef]
  9. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett. 30, 3198-3200 (2005). [CrossRef] [PubMed]
  10. J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, "Negative index materials using simple short wire pairs," Phys. Rev. B 73, 041101 (2006). [CrossRef]
  11. J. Zhou, E. Economou, T. Koschny, and C. M. Soukoulis, "Unifying approach to left-handed material design," Opt. Lett. 31, 3620-3622 (2006). [CrossRef] [PubMed]
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