Abstract

We performed theoretical and experimental investigations of the magnetic properties of metamaterials based on asymmetric double-wire structures. Using the multipole model for the description of metamaterials, we investigated the influence of the geometrical asymmetry of the structure on the macroscopic effective parameters. The results show that the larger wire in the system dominates the dynamics of the structure and defines the orientation and the strength of the microscopic currents. As a result the magnetization of the structure can be significantly enhanced for certain asymmetric configurations of the double-wire structure.

© 2011 Optical Society of America

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References

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2010 (4)

2009 (3)

2008 (3)

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
[CrossRef]

T. Pakizeh, A. Dmitriev, M. S. Abrishamian, N. Granpayeh, and M. Kaell, “Structural asymmetry and induced optical magnetism in plasmonic nanosandwiches,” J. Opt. Soc. Am. B 25, 659–667 (2008).
[CrossRef]

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78, 043811 (2008).
[CrossRef]

2007 (4)

2005 (1)

1997 (1)

Abrishamian, M. S.

Al-Naib, I. A. I.

Atwater, H. A.

Aydin, K.

Burokur, S. N.

B. Kant’e, S. N. Burokur, A. Sellier, A. de Lustrac, and J.-M. Lourtioz, “Controlling plasmon hybridization for negative refraction metamaterials,” Phys. Rev. B 79, 075121 (2009).
[CrossRef]

Cai, W.

Cao, J.-X.

Chettiar, U. K.

Chipouline, A.

de Lustrac, A.

B. Kant’e, S. N. Burokur, A. Sellier, A. de Lustrac, and J.-M. Lourtioz, “Controlling plasmon hybridization for negative refraction metamaterials,” Phys. Rev. B 79, 075121 (2009).
[CrossRef]

Decker, M.

Dmitriev, A.

Dolling, G.

Dong, Z.-G.

Drachev, V. P.

Fu, L.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19, 3628 (2007).
[CrossRef]

Giessen, H.

Gorkunov, M. V.

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
[CrossRef]

Granpayeh, N.

Guo, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19, 3628 (2007).
[CrossRef]

Helgert, C.

Hübner, U.

Kaell, M.

Kaiser, S.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19, 3628 (2007).
[CrossRef]

Kant’e, B.

B. Kant’e, S. N. Burokur, A. Sellier, A. de Lustrac, and J.-M. Lourtioz, “Controlling plasmon hybridization for negative refraction metamaterials,” Phys. Rev. B 79, 075121 (2009).
[CrossRef]

Kildishev, A. V.

Kivshar, Y. S.

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
[CrossRef]

Koch, M.

Kuhl, J.

Lapine, M.

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
[CrossRef]

Lederer, F.

Li, L.

Li, T.

Linden, S.

Liu, H.

Liu, N.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19, 3628 (2007).
[CrossRef]

Lourtioz, J.-M.

B. Kant’e, S. N. Burokur, A. Sellier, A. de Lustrac, and J.-M. Lourtioz, “Controlling plasmon hybridization for negative refraction metamaterials,” Phys. Rev. B 79, 075121 (2009).
[CrossRef]

Menzel, C.

E. Pshenay-Severin, U. Hübner, C. Menzel, C. Helgert, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Double-element metamaterial with negative index at near-infrared wavelengths,” Opt. Lett. 34, 1678–1680 (2009).
[CrossRef] [PubMed]

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
[CrossRef]

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78, 043811 (2008).
[CrossRef]

Pakizeh, T.

Paul, T.

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
[CrossRef]

Pertsch, T.

Petschulat, J.

Powell, D. A.

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
[CrossRef]

Pryce, I. M.

Pshenay-Severin, E.

Rockstuhl, C.

Sarychev, A. K.

Schweizer, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19, 3628 (2007).
[CrossRef]

Sellier, A.

B. Kant’e, S. N. Burokur, A. Sellier, A. de Lustrac, and J.-M. Lourtioz, “Controlling plasmon hybridization for negative refraction metamaterials,” Phys. Rev. B 79, 075121 (2009).
[CrossRef]

Shadrivov, I. V.

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
[CrossRef]

Shalaev, V. M.

Singh, R.

Soukoulis, C. M.

Tünnermann, A.

Wang, S.-M.

Wegener, M.

Xiao, S.

Xu, M.-X.

Yuan, H.-K.

Zentgraf, T.

Zhang, W.

Zhang, X.

Zhu, S.-N.

Adv. Mater. (1)

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. 19, 3628 (2007).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. A (1)

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78, 043811 (2008).
[CrossRef]

Phys. Rev. B (3)

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77, 195328 (2008).
[CrossRef]

B. Kant’e, S. N. Burokur, A. Sellier, A. de Lustrac, and J.-M. Lourtioz, “Controlling plasmon hybridization for negative refraction metamaterials,” Phys. Rev. B 79, 075121 (2009).
[CrossRef]

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
[CrossRef]

Other (2)

L. D. Landau, and E. M. Lifshitz, Mechanics, vol. 1 (Butterworth-Heinemann, 1976), 3rd ed.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

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Figures (12)

Fig. 1
Fig. 1

(Color online) (a) - Arrangement of the structure used in the analytical model. (d) - Single-wire structure. (e) - Double wire structure.

Fig. 2
Fig. 2

(Color online) (a) - Transmission, (b) - reflection, and (c) - absorption spectra in dependence on the structural asymmetry (ΔL).

Fig. 3
Fig. 3

(Color online) In the columns are the data for the structures with ΔL = 100 nm, ΔL = 0 nm, and ΔL = −100 nm. Red curves represent wave vectors obtained from the numerical simulations. Black lines represent wave vectors obtained from the fitting procedure.

Fig. 4
Fig. 4

(Color online) (a), (b), and (c) - Parameters of the oscillators as functions of the length L of the corresponding wire (L reads as L1 for the first oscillator and as L2 for the second one). Blue triangle marks and red diamond marks correspond to the parameters obtained from the single-wire configurations and double-wire configurations, respectively. In (d) the red line represents coupling constant obtained from the theoretical expression Eq. (15), the green triangles show the results of the fitting.

Fig. 5
Fig. 5

(Color online) In the left column - plots (a)–(g) are the data for the structure with ΔL = 100 nm, in the right column - plots (h)–(n) are the data for the structure with ΔL = −100 nm. (a), (h) - Absolute values and (b), (i) - phases of the amplitudes of the oscillators. (c), (j) - Absolute values and (d), (k) - the phases of the currents. (e), (i) - Absolute values, the real, and the imaginary parts and (f), (m) - phases of the parameter χ (ω). (g), (n) - Absolute values, real and imaginary parts of the effective magnetic permeability.

Fig. 6
Fig. 6

(Color online) Phase relation between the electric field (blue), magnetic field (red), magnetization (green), current j1 (black), and current j2 (gray) are presented at the frequency 0.95 μm−1 in the left column (a)–(c), at 1.05 μm−1 in the central column (d)–(f), and at 1.15 μm−1 in the right column (g)–(i). Presented data is for the structure with ΔL = 100 nm.

Fig. 7
Fig. 7

(Color online) The same data as in Fig. 6 for the structure with ΔL = −100 nm. Phase relation between the electric field (blue), magnetic field (red), magnetization (green), current j1 (black), and current j2 (gray) are presented at the frequency 0.95 μm−1 in the left column (a)–(c), at 1.05 μm−1 in the central column (d)–(f), and at 1.15 μm−1 in the right column (g)–(i).

Fig. 8
Fig. 8

Absolute values and phases of the magnetization for structures with ΔL = −100 nm, ΔL = 0 nm, and ΔL = 100 nm.

Fig. 9
Fig. 9

(Color online) Real and imaginary parts of the effective permeabilities of the set of the double-wire structures. Red curves present magnetic permeabilities obtained from the numerical simulations; black lines present magnetic permeabilities obtained from the analytical model.

Fig. 10
Fig. 10

(a) - SEM image of the realized structure with ΔL = −40 nm, (b) - arrangement of the structure in the experiment.

Fig. 11
Fig. 11

(Color online) Measured transmission, reflection, and absorption of a set of asymmetric double-wires. The wire at the bottom had the constant length (L2 = 260 nm), whereas the length of the wire on the top ranged from 160 nm to 260 nm.

Fig. 12
Fig. 12

(Color online) Absolute values and phases of χ (ω) for the experimental structures with ΔL = −100 nm and ΔL = 0 nm.

Equations (22)

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x ¨ 1 ( t ) + γ 1 x ˙ 1 ( t ) + ω 01 2 x 1 ( t ) σ x 2 ( t ) = q 1 m E 1 x ( y y 1 , t ) , x ¨ 2 ( t ) + γ 2 x ˙ 2 ( t ) + ω 02 2 x 2 ( t ) σ x 1 ( t ) = q 2 m E 2 x ( y + y 1 , t ) .
x ˜ 1 ( ω ) = a 1 ( ω 02 2 ω 2 i γ 2 ω ) E ˜ 1 x ( y y 1 , ω ) + σ a 2 E ˜ 2 x ( y + y 1 , ω ) ( ω 01 2 ω 2 i γ 1 ω ) ( ω 2 2 ω 2 i γ 2 ω ) σ 2 ,
x ˜ 2 ( ω ) = a 2 ( ω 01 2 ω 2 i γ 1 ω ) E ˜ 2 x ( y + y 1 , ω ) + σ a 1 E ˜ 1 x ( y y 1 , ω ) ( ω 01 2 ω 2 i γ 1 ω ) ( ω 02 2 ω 2 i γ 2 ω ) σ 2 ,
a 1 = q 1 m , a 2 = q 2 m .
P ˜ x ( y , ω ) = 2 η [ q 1 x ˜ 1 ( ω ) + q 2 x ˜ 2 ( ω ) ] ,
Q ˜ x y ( y , ω ) = y 1 η [ q 2 x ˜ 2 ( ω ) q 1 x ˜ 1 ( ω ) ] ,
M ˜ z ( y , ω ) = y 1 η [ q 2 x ˜ ˙ 2 ( ω ) q 2 x ˜ ˙ 1 ( ω ] ) ,
2 E ˜ x ( y , ω ) y 2 = ω 2 μ 0 ( ɛ 0 E ˜ x ( y , ω ) + P ˜ x ( y , ω ) Q ˜ x y ( y , ω ) y ) + i ω μ 0 M ˜ z ( y , ω ) y
k y 2 ( ω ) = 2 ω 2 c 2 R 1 R 2 σ 2 + A ( a 1 R 2 + a 2 R 1 2 σ a 1 a 2 ) 2 ( R 1 R 2 σ 2 ) ω 2 c 2 A y 1 2 ( a 1 R 2 + a 2 R 1 3 σ a 1 a 2 ) ,
R 1 = ( ω 01 2 ω 2 i γ 1 ω ) , R 2 = ( ω 02 2 ω 2 i γ 2 ω ) .
U = 2 q 1 x 1 q 2 x 2 R 3 ,
U x 1 = 2 q 1 q 2 x 2 R 3 = σ x 2 ,
U x 2 = 2 q 1 q 2 x 1 R 3 = σ x 1 ,
σ = 2 q 1 q 2 R 3 .
σ = α 2 R 3 ( S 2 Δ L 2 ) 2 ,
S = L 1 + L 2 .
M ˜ z ( y , ω ) = χ ( ω ) B ˜ z ( y , ω ) .
E ˜ x ( y , ω ) = ω k y ( ω ) B ˜ z ( y , ω ) .
H ˜ z ( ω ) = 1 μ 0 B ˜ z ( ω ) M ˜ z ( ω ) = 1 μ eff ( ω ) μ 0 B ˜ z ( ω ) ,
μ eff ( ω ) = B ˜ z ( y , ω ) B ˜ z ( y , ω ) μ 0 M ˜ z ( y , ω )
| μ eff ( ω ) | 2 = 1 ( 1 μ 0 χ ( ω ) ) 2 + ( μ 0 χ ( ω ) ) 2
Re [ μ eff ( ω ) ] = ( 1 μ 0 χ ( ω ) ) ( 1 μ 0 χ ( ω ) ) 2 + ( μ 0 χ ( ω ) ) 2 .

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