Abstract

We studied both experimentally and theoretically the influence of the distance between adjacent cut-wire-pair layers on the magnetic and the electric resonances in the microwave-frequency regime. Besides the dependence on the separation between cut-wire pairs, along the electric-field direction, the electric resonance strongly depends on the distance between cut-wire-pair layers, while the magnetic resonance is almost unchanged. This contrast can be understood by the difference in the distribution of induced-charge density and in the direction of the induced current between the electric and magnetic resonances. A simple model is proposed to simulate our experimental results and the simulation results are in good agreement with the experiment. This result provides important information in obtaining left-handed behavior when the cut-wire pairs are combined with the continuous wire.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2007 (3)

2006 (3)

2005 (3)

2004 (5)

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]

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

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef] [PubMed]

N. Katsarahis, T. Koschny, M. Kafesaki, E. N. Economou, E. Ozbay, and C. M. Soukoulis, "Left- and righthanded transmission peaks near the magnetic resonance frequency in composite metamaterials," Phys. Rev. B 70, 201101, (2004).
[CrossRef]

K. Aydin, K. Guven, N. Katsaraki, C. M. Soukoulis, and E. Ozbay, "Effect of disorder on magnetic resonance band gap of split-ring resonator structures," Opt. Express 12, 5896-5901 (2004).
[CrossRef] [PubMed]

2002 (2)

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

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

2000 (1)

D. R. Smith, W. Padilla, D. Vier, S. Nemat-Nesser, and S. Chultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

1999 (1)

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

1968 (1)

V. G. Veselago, "The electrodynamics of substances with negative ∑ and ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Adv. Mater. (1)

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, "Negative-Index Materials: new frontiers in optics," Adv. Mater. 18, 1941-1952 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

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

IEEE Trans. Microwave Theory Tech. (1)

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

J. Appl. Phys. (1)

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

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. B (4)

Z. G. Dong, S. Y. Lei, Q. Li, M. X. Xu, H. Liu, T. Li, F. M. Wang, and S. N. Zhu, "Non-left-handed transmission and bianisotropic effect in a □-shaped metallic metamaterial," Phys. Rev. B 75, 075117 (2007).
[CrossRef]

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

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

N. Katsarahis, T. Koschny, M. Kafesaki, E. N. Economou, E. Ozbay, and C. M. Soukoulis, "Left- and righthanded transmission peaks near the magnetic resonance frequency in composite metamaterials," Phys. Rev. B 70, 201101, (2004).
[CrossRef]

Phys. Rev. E (1)

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]

Phys. Rev. Lett. (2)

D. R. Smith, W. Padilla, D. Vier, S. Nemat-Nesser, and S. Chultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402 (2004).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substances with negative ∑ and ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (1)

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(R) (2006).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(Color online) (a) Geometry of the cut-wire pair with the length of cut wire is l=5.5 mm and the width w=1.0 mm. t 1 is the thickness of the PCB board and t 2 that for the CU cut-wire. (b) Periods of cut-wire pairs.

Fig. 2.
Fig. 2.

(Color online) Measured transmission spectra of the cut-wire-pair structure with different numbers of layers in the propagation direction, where the distance between layers is kept 1.0 mm.

Fig. 3.
Fig. 3.

(Color online) Measured transmission spectra of various cut-wire-pair structures; (a) two and (b) three layers. The period of cut-wire pair in the x-y plane is kept constant to be ax =3.5 mm and ay =7.0 mm; while the distance between layers is varied from 1.0 to 4.0 mm.

Fig. 4.
Fig. 4.

(Color online) (a) Schematic of misaligned cut-wire-pair boards. (b) Comparison of the measured transmission spectra between aligned and misaligned cut-wire-pair layers.

Fig. 5.
Fig. 5.

Calculated electric and magnetic resonance frequencies as a function of the distance between cut-wire-pair layers for 3-layer structure. The solid lines are guide to the eyes only.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

J = J ( y ) y ̂ = σ E o y ̂ α ρ = σ E o y ̂ α ρ y y ̂ ,
· J + ρ t = J y + ρ t = α d 2 ρ d y 2 + ρ t = 0 .
d 2 ρ d y 2 + ω α ρ = 0 .
ρ = ρ o sin ( ω α y )
J = σ E o y ̂ α ρ o ω α cos ( ω α y ) y ̂ ,
r [ · J + ρ t ] d 3 r = J d 3 r + p t = 0 ,
ρ = ρ o sin ( π l y ) ,
J = 4 α ρ o l [ 1 π 4 cos ( π l y ) ] y ̂ .
U E = 1 2 ε E 2 d v = Q 2 2 C eff
U B = 1 2 B 2 μ d v = 1 2 L eff I 2 .
ω e = 1 L e , eff C e , eff
ω m = 1 L m , eff C m , eff ,

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