## Optical properties of metamaterials based on asymmetric double-wire structures |

Optics Express, Vol. 19, Issue 7, pp. 6269-6283 (2011)

http://dx.doi.org/10.1364/OE.19.006269

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### 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

## 1. Introduction

1. U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, “Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm,” Opt. Lett. **32**, 1671–1673 (2007). [CrossRef] [PubMed]

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

3. C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, “The origin of magnetic polarizability in metamaterials at optical frequencies - an electrodynamic approach,” Opt. Express **15**, 8871–8883 (2007). [CrossRef] [PubMed]

4. B. Kanté, 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]

7. Z.-G. Dong, H. Liu, M.-X. Xu, T. Li, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Role of asymmetric environment on the dark mode excitation in metamaterial analogue of electromagnetically-induced transparency,” Opt. Express **18**, 22412–22417 (2010). [CrossRef] [PubMed]

8. K. Aydin, I. M. Pryce, and H. A. Atwater, “Symmetry breaking and strong coupling in planar optical metamaterials,” Opt. Express **18**, 13407–13417 (2010). [CrossRef] [PubMed]

10. 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]

5. 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]

8. K. Aydin, I. M. Pryce, and H. A. Atwater, “Symmetry breaking and strong coupling in planar optical metamaterials,” Opt. Express **18**, 13407–13417 (2010). [CrossRef] [PubMed]

4. B. Kanté, 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]

5. 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]

10. 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]

11. 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]

12. 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]

12. 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]

10. 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]

**25**, 659–667 (2008). [CrossRef]

**25**, 659–667 (2008). [CrossRef]

12. 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]

## 2. Theoretical approach for the description of metamaterials with an asymmetrical unit cell

*L*

_{1,2}in

*x*direction (Fig. 1(a)). We use the notation length (

*L*) for this dimension, because it corresponds to the length of the plasmonic resonator in our consideration. The parameter Δ

*L*=

*L*

_{1}–

*L*

_{2}characterized the asymmetry quantitatively. The length of the first wire ranged from

*L*

_{1}+

*L*

_{2}=

*constant*). The wires were placed in air with a separation distance of 40 nm between them. This was a simplification compare to the common experimental arrangement, where structures are placed on a substrate and are separated with a dielectric. The presence of a substrate breaks the symmetry of the structure even for wires of the same length. The consideration of the system in a symmetric environment allowed us to concentrate on effects caused by the asymmetry of the wires only. Nevertheless, the simplified model qualitatively describes the effects observed in the experimental system as it is shown in section 3.5.

**78**, 043811 (2008). [CrossRef]

*x*

_{1}and

*x*

_{2}correspond to the elongation of the negativly charged carrier density driven by the electric field;

*ω*

_{01},

*ω*

_{02}are the eigenfrequencies of the oscillators;

*γ*

_{1},

*γ*

_{2}are damping constants;

*q*

_{1},

*q*

_{2}are effective carriers;

*m*is the mass of the effective carrier;

*σ*is the coupling constant; −

*y*

_{1}and

*y*

_{1}are the positions of the carriers along the

*y*coordinate.

*x*(

*t*) =

*x̃*(

*ω*)exp(−

*iωt*): In the case considered here the description of the electromagnetic wave propagation is expressed through the non-zero elements of the electric polarisability

*P̃*(

*y*,

*ω*), quadrupole tensor

*Q̃*(

*y*,

*ω*), and magnetization

*M̃*(

*y*,

*ω*), which can be written as: where

*η*is the density of the metaatoms (double-wires). Having calculated the dipole, quadrupole and magnetic dipole contributions, the wave equation can be solved, and the dispersion relation

*k*(

*ω*) is: where In oder to connect the model with the simmulated system the characteristic parameters of the oscillators (

*ω*

_{01},

*ω*

_{02},

*γ*

_{1},

*γ*

_{2},

*a*

_{1},

*a*

_{2}) have to be found. For this purpose we calculated the complex transmission and reflection coefficients of corresponding layers of MMs using Fourier Modal Method (FMM) [14

14. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A **14**, 2758–2767 (1997). [CrossRef]

15. 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]

**78**, 043811 (2008). [CrossRef]

## 3. Results and discussion

### 3.1. Eigenmodes of asymmetric double-wire structures

11. 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]

16. 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]

17. 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]

*L*can be extracted from the spectra presented in Fig. 2(a)–(c), where the resonances corresponding to the excitation of the two modes can be easily identified. Both resonances appear in the spectra as a minimum of the transmission - see Fig. 2(a). The antisymmetric mode is associated with a carrier distribution having a pronounced quadrupole moment. Therefore, excitation of the antisymmetric mode is accompanied by an increase of absorption, which is enhanced by its non-radiating character - see Fig. 2(c). The symmetric mode, in contrast, has a radiating property of a dipole and appears as high reflection in the spectra - see Fig. 2(b). Thus, we observe that the resonances in Fig. 2 indeed have the largest spectral separation in the symmetric case (Δ

*L*= 0 nm) and move towards the eigenfrequencies of the uncoupled wires if the difference of their lengths increases. In this work, we use spatial frequencies 1/

*λ*for the presentation of the spectral information to facilitate considerations of the modes spitting.

### 3.2. Parameters of harmonic oscillators

*ω*

_{0i},

*γ*,

_{i}*a*) and the coupling constant (

_{i}*σ*) corresponding to the systems under consideration have to be defined. This problem is reduced to finding the connection between

*ω*

_{0i},

*γ*,

_{i}*a*,

_{i}*σ*and the length

*L*of a wire. This dependency is the same for the two wires. The parameters of the oscillators can be found from the simulations of the single-wire (Fig. 1(b)) and the double-wire (Fig. 1(d)) structures. To demonstrate the accuracy of the fitting procedure, we show in Fig. 3 the wave vectors obtained from the fitting procedure (black curves) and from numerical calculations (red curves) for double-wire structures. The wave vectors from the numerical simulations were calculated with the retrieval algorithm [15

15. 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]

*σ*can be elaborated using a model of two interacting point dipoles. The potential energy of two point dipoles, modeling the wires, with dipole moments arranged parallel to the

*x*-axis: where

*q*

_{1}

*x*

_{1}and

*q*

_{2}

*x*

_{2}are the dipole moments of the dipoles and

*R*is the distance between them.

*σ*can be easily introduced [18] as: Now, if we assume that the carrier of the oscillator is proportional to the length of the wire

*q*=

*αL*, which corresponds to the results presented in Fig. 4(c), we obtain:

*α*from the symmetric case (Δ

*L*= 0) we calculate the dependence of

*σ*on Δ

*L*- see Fig. 4(d) (red line). Comparison of

*σ*from Eq. (15) with the coupling constant from the fitting procedure (Fig. 4(d), green triangles) shows that the model of two coupled dipoles describes qualitatively the interaction between the wires.

### 3.3. Dynamics of currents in an asymmetric double-wire system

*L*= 100 nm and Δ

*L*= −100 nm. Data corresponding to the system with Δ

*L*= 100 nm are presented in Fig. 5(a)–(g), where the phase information for the amplitudes

*x*

_{1,2}(Fig. 5(b)) and the currents

*j*

_{1}=

*q*

_{1}

*ẋ*

_{1}and

*j*

_{2}=

*q*

_{2}

*ẋ*

_{2}(Fig. 5(d)) are given with respect to the phase of the electric field in the center of the unit cell. It is seen, that at frequencies around the eigenfrequency of the antisymmetric mode (0.9

*μ*m

^{−1}– 1.1

*μ*m

^{−1}, see Fig. 5(a)), the first oscillator

*x*

_{1}has a larger amplitude than the second one

*x*

_{2}. The possible reasons are the larger size and the top position of the first wire, which is affected by the incoming wave first. In this case, according to Eq. (1), the first largest oscillator dominates over the second one, whereas the influence of

*x*

_{2}on the dynamics of

*x*

_{1}is negligible. Indeed, out of the resonance, at frequencies lower than the eigenfrequency of the antisymmetric mode (1.05

*μ*m

^{−1}) the first oscillator follows the electric field almost in phase (Fig. 5(b)). The second oscillator is mostly driven by the first one and acquires a phase shift of about

*π*with respect to

*x*

_{1}at frequencies close to the eigenfrequency of the antisymmetric mode. In the resonance both oscillators undergo a phase jump close to

*π*; as a result for frequencies higher than the resonance frequency,

*x*

_{1}oscillates out of phase and

*x*

_{2}in phase with the electric field. The currents

*j*

_{1}and

*j*

_{2}associated with these oscillations are presented in Figs. 5(c) and (d).

*L*= −100 nm (see Fig. 5(h)–(n)) the situation should be inverse, as the larger oscillator is

*x*

_{2}, which is below the first one. However, excitation conditions for

*x*

_{2}are not optimal, due to the first oscillator, which absorbs a part of the energy of the electric field. As a result, the amplitudes of oscillators

*x*

_{1}and

*x*

_{2}are of the same order and smaller than in the case Δ

*L*= 100 nm. Nevertheless, the phase of the larger oscillator

*x*

_{2}is closer to the phase of the electric field than the phase of the smaller one

*x*

_{1}, however, it deviates from the phase of the electric field, due to the stronger influence of the oscillator

*x*

_{2}. As a result, at the frequencies below the frequency of the magnetic resonance, the loop current orientation is reversed to that of the structure with Δ

*L*= 100 nm. An additional minimum in the amplitudes at frequencies around the eigenfrequency of the antisymmetric mode can be explained as a complex answer of the system on the excitation.

### 3.4. Effective magnetic response of double-wire structures

*χ*(

*ω*) =

*χ*′ (

*ω*) +

*iχ*″ (

*ω*) which defines the relation between the magnetic field of the wave and the magnetization of the MM: Coefficient

*χ*(

*ω*) can be easily derived from Eq. (7) taking into account the relation between the electric and the magnetic field in a plane wave: The absolute value and the phase of

*χ*(

*ω*) for the structure Δ

*L*= 100 nm is shown in Figs. 5(e) and (f). In the resonance the phase of

*χ*(

*ω*) is

*π*(see Fig. 5(f)), i.e. the equivalent microscopic loop currents (Figs. 5(c) and (d)) produce the magnetization oscillating out of phase with the magnetic field. The phase relations between the fields, the magnetization and the currents at the frequencies below (0.97

*μm*

^{−1}), at (1.05

*μm*

^{−1}) and above (1.15

*μm*

^{−1}) the resonance are illustrated in Fig. 6, where normalized real parts of these quantities are presented. In Figs. 6(c),(f), and (i) the phase relations between the fields, the magnetization, and the currents are illustrated in phase diagrams. The absolute value and the phase of

*χ*(

*ω*) for the structure Δ

*L*= −100 nm is shown in Figs. 5(i) and (m). One can see that the microscopic currents of the structure Δ

*L*= −100 nm give a magnetization which is almost in phase with the magnetic field (−

*π*/2 <

*arg*(

*χ*(

*ω*)) <

*π*/2), and only at frequencies above the resonant frequency the phase shift between the magnetization and the magnetic field becomes larger than

*π*/2. The phase relations between the fields, the magnetization and the currents at the frequencies below (0.97

*μm*

^{−1}), at (1.05

*μm*

^{−1}) and above (1.15

*μ*m

^{−1}) the resonance are shown in Fig. 7. To describe effective magnetic properties of MMs, in some cases it is useful to introduce the effective magnetic permeability

*μ*

_{eff}(

*ω*), for instance, for the consideration of boundary conditions. Definition of an effective magnetic permeability in a common way as for plasmonic MMs has formal character only, because the magnetization of the structures is caused by the electric field. Calculated according to Eq. (7) magnetizations using the parameters from Fig. 4 are shown in Fig. 8; the phase of the magnetization is given relative to the phase of the electric field of an incoming wave. In Fig. 9, the effective magnetic permeability calculated according Eq. (20) (black curves) together with the results from numerical simulations (red curves) are shown. It is seen that the larger the wire on the top, the higher the absolute value of the effective permeability. That may appear contradictory to the behavior of the magnetization shown in Fig. 8. However, a thorough consideration of the relation between

*μ*(

_{eff}*ω*) and the magnetization clears up this seeming discrepancy. According to Eq. (17) and Eq. (20) the absolute value of the permeability can be written as and the real part as Now one can see that, if the real parts of

*χ*(

*ω*) increases, the sign of

*χ*(

*ω*), i.e. the phase of the magnetization with respect to the magnetic field, defines whether

*μ*

_{eff}(

*ω*) increases or decreases.

*χ*′ (

*ω*) > 0) and grows, the absolute value of

*μ*

_{eff}(

*ω*) increases, as the denominator in Eq. (21) decreases. This is the case for structures with a negative Δ

*L*, for which the phases of

*χ*(

*ω*) lie between −

*π*/2 and

*π*/2 (Fig. 5(m)). Further, if the magnetization increases and is out of phase with the magnetic field (

*χ*′(

*ω*) < 0),

*μ*

_{eff}(

*ω*) decreases, as the denominator in Eq. (21) increases. This is the case for structures with positive Δ

*L*, for which the phases of

*χ*(

*ω*) lie between

*π*/2 and −

*π*/2 (Fig. 5(f)).

*μ*

_{eff}(

*ω*) becomes negative if

*χ*′(

*ω*) exceeds 1/

*μ*

_{0}, which means that the magnetization oscillates in phase with the magnetic field and is strong enough. Furthermore, if the magnetization is out of phase with the magnetic field the real part of

*μ*

_{eff}(

*ω*) is always positive.

### 3.5. Experimental investigations of the asymmetric double-wire structures

^{2}, where the size of each sample was 1 mm x 50

*μ*m. Such a compact arrangement of the samples assured that the observed effects were caused by the variation of the wire length only. The measurements of transmission and reflection spectra were performed using a Bruker Vertex 80 spectrometer combined with a Hyperion 2000 microscope. The light was focused on the set of the samples with an objective with NA = 0.4 and a certain sample was selected by an appropriate aperture setting.

*μm*

^{−1}and the symmetric mode as a minimum at about 1.1

*μm*

^{−1}. The difference in the absolute values for the resonance positions in the numerical simulations and in the experiment is due to the different refractive index of the spacer and slightly different lengths of the wires - see Fig. 1 and Fig. 10. In addition, in the presence of the substrate the wire on the bottom becomes effectively longer. As a result, the spectral separation of the resonances for Δ

*L*= 0 nm is smaller for the experimental system with a substrate as for the system without a substrate considered earlier. Nevertheless, the splitting of the symmetric and antisymmetric modes becomes weaker when Δ

*L*tends to −100

*nm*. It is interesting to note that in both experiment and simulation the absorption of the material at the antisymmetric resonance is maximal (Fig. 2(c) and Fig. 11(c)) for negative Δ

*L*and decreases when Δ

*L*becomes positive, whereas the reflection of the material (Fig. 2(b) and Fig. 11(b)) increases. This behavior can be explained by the increase of the electric dipole moment of the double-wire structure as Δ

*L*becomes positive (the length of the wire on the top increases), which was also confirmed by numerical calculations (not shown here).

*χ*(

*ω*) characterizing the magnetic moment of the structures can be expressed as a function of the effective magnetic permeability. The absolute values and phases of the parameters

*χ*(

*ω*) for the structures with Δ

*L*= 0 nm and Δ

*L*= −100 nm are presented in Fig.12. As the amount of metal in the experimental systems was not conserved (

*L*

_{2}=constant for all structures), an interpretation of the absolute values of

*χ*(

*ω*) can be misleading. The phase of the coefficients

*χ*(

*ω*) is a more appropriate parameter in this case. It is seen that for the structure with Δ

*L*= −100 nm the magnetic moment oscillates almost in phase with the magnetic field (

*arg*[

*χ*(

*ω*)]≈ 0), at the eigenfrequency of the antisymmetric mode (0.85

*μm*

^{−1}).The phase delay increases when the length of the wire on the top becomes larger. For the structure with Δ

*L*= 0 nm the phase delay is about

*π*/4 at the frequency 0.65

*μm*

^{−1}. Thus, the orientation of the magnetic moment relative to the magnetic field in the experimental system corresponds to the predictions of the analytical model.

## 4. Conclusion

**78**, 043811 (2008). [CrossRef]

**78**, 043811 (2008). [CrossRef]

*π*with respect to the magnetic field of the illuminating wave. This leads to a decreasing of the effective magnetic permeability. In the configuration where the wire on top is shorter than the one on the bottom, the magnetization is weaker and oscillates in phase with the magnetic field; the corresponding effective magnetic permeability grows. The obtained results correlate with the ones presented in Ref. [10

**25**, 659–667 (2008). [CrossRef]

## Acknowledgments

## References and links

1. | U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, “Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm,” Opt. Lett. |

2. | G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. |

3. | C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, “The origin of magnetic polarizability in metamaterials at optical frequencies - an electrodynamic approach,” Opt. Express |

4. | B. Kanté, S. N. Burokur, A. Sellier, A. de Lustrac, and J.-M. Lourtioz, “Controlling plasmon hybridization for negative refraction metamaterials,” Phys. Rev. B |

5. | 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 |

6. | R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Asymmetric planar terahertz metamaterials,” Opt. Express |

7. | Z.-G. Dong, H. Liu, M.-X. Xu, T. Li, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Role of asymmetric environment on the dark mode excitation in metamaterial analogue of electromagnetically-induced transparency,” Opt. Express |

8. | K. Aydin, I. M. Pryce, and H. A. Atwater, “Symmetry breaking and strong coupling in planar optical metamaterials,” Opt. Express |

9. | M. Decker, S. Linden, and M. Wegener, “Coupling effects in low-symmetry planar split-ring resonator arrays,” Opt. Lett. |

10. | 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 |

11. | 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. |

12. | J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A |

13. | J. D. Jackson, |

14. | L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A |

15. | C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B |

16. | N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Plasmon hybridization in stacked cut-wire metamaterials,” Adv. Mater. |

17. | 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. |

18. | L. D. Landau and E. M. Lifshitz, |

**OCIS Codes**

(260.2065) Physical optics : Effective medium theory

(160.3918) Materials : Metamaterials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: January 14, 2011

Revised Manuscript: February 10, 2011

Manuscript Accepted: February 14, 2011

Published: March 18, 2011

**Citation**

E. Pshenay-Severin, A. Chipouline, J. Petschulat, U. Hübner, A. Thünnerman, and T. Pertsch, "Optical properties of metamaterials based on asymmetric double-wire
structures," Opt. Express **19**, 6269-6283 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-7-6269

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### References

- U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, “Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm,” Opt. Lett. 32, 1671–1673 (2007). [CrossRef] [PubMed]
- G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32, 53–55 (2007). [CrossRef]
- C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, “The origin of magnetic polarizability in metamaterials at optical frequencies - an electrodynamic approach,” Opt. Express 15, 8871–8883 (2007). [CrossRef] [PubMed]
- 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]
- R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Asymmetric planar terahertz metamaterials,” Opt. Express 18, 13044–13050 (2010). [CrossRef] [PubMed]
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