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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 23 — Nov. 5, 2012
  • pp: 25744–25751
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Numerical study of a new negative index material in mid-infrared spectrum

Dengmu Cheng, Jianliang Xie, Huibin Zhang, Nan Zhang, and Longjiang Deng  »View Author Affiliations


Optics Express, Vol. 20, Issue 23, pp. 25744-25751 (2012)
http://dx.doi.org/10.1364/OE.20.025744


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Abstract

We explored numerically a new negative index material in mid-infrared spectrum, based on a thin wire net pairs and a square ring pairs array, which exhibits simultaneously hyper-transmission, polarization independence and small period. The mechanism implementing the negative refractive index was analyzed using retrieved optical constants as well as a valid analytical expression of the effective permeability that was deduced by virtue of a simple equivalent circuit model and applied to account for the magnetic property of this metamaterial.

© 2012 OSA

1. Introduction

Negative index material (NIM) has been intensively researched especially in near infrared and visible light spectra because of its potential stunning optical applications. The representative work is the classic “fishnet” structure on account of its outstanding performance and simple preparation process, which was proposed firstly and demonstrated experimentally by S. Zhang et al in near infrared [1

1. S. Zhang, W. Fan, K. J. Malloy, S. R. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express 13(13), 4922–4930 (2005). [CrossRef] [PubMed]

, 2

2. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]

]. The original design of the fishnet is physical connection of a two dimension array of wide infinite long stripe pairs with orthogonal thinner one, which is able to give a low absorptive loss in terms of the figure of merit (FOM) of 6.0 [1

1. S. Zhang, W. Fan, K. J. Malloy, S. R. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express 13(13), 4922–4930 (2005). [CrossRef] [PubMed]

]. The experimental value of 3.0 was achieved by G. Dolling et al through replacing the constituent material and further optimizing geometrical data [3

3. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006). [CrossRef] [PubMed]

]. However, the designs, similarly to SRRs, suffer from polarization dependence that is unacceptable in some applications, for example, the proposed perfect lens based on isotropic NIM in which high symmetry is desirable [4

4. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

].

On behalf of obtaining polarization independence, some effort have been afforded to optimize the fishnet using symmetric patterns such as square or circular holes [5

5. Z. Ku and S. R. Brueck, “Comparison of negative refractive index materials with circular, elliptical and rectangular holes,” Opt. Express 15(8), 4515–4522 (2007). [CrossRef] [PubMed]

, 6

6. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Design-related losses of double-fishnet negative-index photonic metamaterials,” Opt. Express 15(18), 11536–11541 (2007). [CrossRef] [PubMed]

], square and rounding corner cross apertures [7

7. X. Wang, Y. H. Ye, C. Zheng, Y. Qin, and T. J. Cui, “Tunable figure of merit for a negative-index metamaterial with a sandwich configuration,” Opt. Lett. 34(22), 3568–3570 (2009). [CrossRef] [PubMed]

, 8

8. C. Helgert, C. Menzel, C. Rockstuhl, E. Pshenay-Severin, E. B. Kley, A. Chipouline, A. Tünnermann, F. Lederer, and T. Pertsch, “Polarization-independent negative-index metamaterial in the near infrared,” Opt. Lett. 34(5), 704–706 (2009). [CrossRef] [PubMed]

]. Unfortunately, in turn, the transmission property deteriorated substantially subsequently relative to that of the fishnet with rectangular holes at the same operating wavelength. This can be understood qualitatively. In order to obtain the symmetry, one had to substitute narrower strip for wider one. The substitution introduced the larger volume fraction of metal that lead to the blue-shift of electric plasma frequency (this can also be explained quantitatively in cutoff wavelength from the perspective of a hole waveguide [9

9. A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101(10), 103902 (2008). [CrossRef] [PubMed]

]). Correspondingly, the impedance mismatch occurred and resulted in the more reflection loss, which was responsible for the degeneracy of transmission property.

For the sake of getting the impedance match back, a direct idea is to red-shift the electric plasma frequency through enlarging the aperture size [9

9. A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101(10), 103902 (2008). [CrossRef] [PubMed]

]. At the same time, it is essential to expand the period for holding the magnetic resonance frequency, but the permeability also deteriorated subsequently due to the decreasing density of the “magnetic atoms” so that the mismatch still exist and the transmission properties could not be improved substantially. In a word, the dependence between electric and magnetic elements prevented a good transmission of fishnet with symmetric patterns [6

6. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Design-related losses of double-fishnet negative-index photonic metamaterials,” Opt. Express 15(18), 11536–11541 (2007). [CrossRef] [PubMed]

]. Recently, an improved fishnet structure with polarization independence and high FOM (low absorptive loss) were reported by employing a second-order magnetic resonance, which becomes stronger than the first-order magnetic resonance (i.e., the above-mentioned common resonance) with the enlarging of apertures and period [10

10. C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett. 106(6), 067402 (2011). [CrossRef] [PubMed]

]. However, in another side, the large period make the fishnet more like photonic crystal, which is generally operated in their “Bragg regime” where the period is typically of the order of half a guided wavelength (namely λ/a~2) [6

6. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Design-related losses of double-fishnet negative-index photonic metamaterials,” Opt. Express 15(18), 11536–11541 (2007). [CrossRef] [PubMed]

, 11

11. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, 1995).

], rather than metamterial in which the larger ratio of wavelength to period is safer for the effective homogeneous medium approximation. In fact, the most values of all the ratios in symmetric fishnet structures are less than 2.0 [6

6. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Design-related losses of double-fishnet negative-index photonic metamaterials,” Opt. Express 15(18), 11536–11541 (2007). [CrossRef] [PubMed]

, 10

10. C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett. 106(6), 067402 (2011). [CrossRef] [PubMed]

]. This should be ascribed to the limitation about 2.0 of the ratio of cutoff wavelength (corresponding to the effective electric plasma frequency) to period [9

9. A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101(10), 103902 (2008). [CrossRef] [PubMed]

]. Certainly, the ratio of wavelength to period could be designed to be lager by placing the magnetic resonance at those wavelengths that are much larger than the cutoff wavelength but we will face the impedance mismatch.

It is well known that the mid-infrared is an important regime in remote sensing technology, and yet in which there are few reports of NIMs. In this work, we explore firstly a NIM that is made up of a thin wire net pairs (WNP) and a square ring pairs (SRP) array and presents simultaneously hyper-transmission, polarization independence and small period in mid-infrared. We do not only analyze the mechanisms of achieving these performances, but also build a numerical model of the effective permeability based on a simple equivalent circuit model to interpret the magnetic property.

2. Design and simulation

Our NIM consists of three layers of films (metal-dielectric-metal) which were patterned by perforating holes to form a WNP and a SRP array configuration, as schematically shown in Fig. 1(a)
Fig. 1 Sketches of the designed NIM: (a) the periodic arrangement; (b) geometry of the unit cell.
. The WNP is equivalent to a fishnet only composed of thin wires that was employed to provide the negative permittivity in present band, and the permittivity was tuned mainly by the period a and line width wn as indicated in the unit cell in Fig. 1(b). The SRP array was expected to supply negative permeability originating from strong magnetic resonances. The permeability of the SRP can be tuned by scaling geometrical parameters independently or synergistically, which includes the period a, side length l, strip width w, metalization thickness t and dielectric spacer thickness d etc. The separate electric and magnetic elements allow us to overlap easily the negative permittivity and negative permeability in the present spectrum.

The optimization of our structure was performed by the aid of commercial program CST Microwave Studio, which using a finite-difference time domain method to determine complex scattering parameters, namely, reflection parameters S11 and transmission parameters S21. With regard to the constituent material, a loss-free zinc sulfide (ZnS) that is transparent throughout the spectrum from ~1 μm to ~10 μm was chosen as dielectric spacer whose refractive index is nearly 2.24 in the region [12

12. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

]. The metal element was defined as silver whose dielectric behavior is described by Drude dispersion model, i.e., ε(ω)=1ωep2/(ω2+iνcω), where i=1,the plasma frequency ωep = 2π × 21.75 × 1014 rad/s and the collision frequency νc = 2π × 4.35 × 1012 rad/s [13

13. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander Jr, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–20 (1983). [CrossRef] [PubMed]

]. For simplicity, in present work, we did not take the influence of the substrate on the electromagnetic behavior into account and assumed that transverse electromagnetic (TEM) wave impinges on the infinite surface of the structure as depicted in Fig. 1(a).

3. Results and discussion

We acquired a group of optimized geometrical data of a = 2.70 μm, wn = 0.34 μm, l = 1.60 μm w = 0.47 μm, t = 0.06 μm and d = 0.22 μm through the electromagnetic calculation. The complex scattering parameters are displayed in Figs. 2(a)
Fig. 2 Simulated complex scattering parameters and extracted optical constants.
and 2(b). These scattering parameters both the magnitude and phase have the same features as that in the negative index region presented in the Ref [1

1. S. Zhang, W. Fan, K. J. Malloy, S. R. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express 13(13), 4922–4930 (2005). [CrossRef] [PubMed]

]. and [14

14. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005). [CrossRef] [PubMed]

], where the dip in the phase of S21 indicates the presence of a negative index band. The extracted complex refractive index using a classical retrieval procedure within Ref [14

14. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005). [CrossRef] [PubMed]

]. confirms that our metamaterial is a NIM ranging from 7.5 μm to 9.3 μm wavelengths, as is shown in Fig. 2(c), where n(λ) is real part of the refractive index and κ(λ) is extinction coefficient. The figure of merit as an absorptive loss indicter was also calculated byη(λ)=n(λ)/κ(λ). Fig. 2(d) shows that the maximum value of η(λ) is 6.9 around an operating wavelength of 8.1 μm where n(λ) = −1. The corresponding transmission given by |S21|2 is up to 90.2%. Furthermore, a ratio of 3.0 of operating wavelength to period is acquired. It should be mentioned that there is a bad transmission about 60% around 8.8 μm wavelength because of the large extinction coefficient although another n(λ) = −1 is obtained here, which is also the case in literatures.

3.1. Mechanism of implementing the NIM

3.2. Numerical model of permeability

To investigate the underlying magnetic property, we monitored computationally current density, electric and magnetic field distribution at magnetic resonance wavelength (8.7μm). For simplicity, we concentrate our attention on the SRP firstly. As shown in Fig. 3(a)
Fig. 3 The monitored physical quantities distribution at magnetic resonance frequency: (a) current density; (b) z component of E-field on a logarithmic scale in dielectric spacer; (c) a front view along z direction, which displays E-field distribution in a section plane in between the two back-to-back square rings; and (d) magnetic energy density WH on a logarithmic scale.
, two branches of parallel currents with mirror symmetry were independently excited on the surface of the square ring. Besides, another two branches of parallel currents flowing along reverse direction were also exited on the back-to-back square ring spaced by the dielectric layer. We divide the unit cell into two symmetric parts by the central line. Then, the SRP is divided into two groups of U shaped strip pairs (USSP). Each group of USSP sustains antiparallel currents resembling to cut-wire pairs [16

16. 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(24), 3356–3358 (2005). [CrossRef] [PubMed]

, 17

17. J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006). [CrossRef] [PubMed]

]. The antiparallel currents result from the coupling of electric dipole in the U shaped strip with its own image in the back one. The physical scene is revealed by the z component of E-field distribution in between the transversal metallic strips of the square rings and shown in Fig. 3(b). At the same time, the E-field closed the two branches of antiparallel currents sustained by USSP and then a virtual current loop between the metallic layers on a perpendicular plane to the incoming magnetic field formed. Furthermore, due to the accumulated opposite charges in the transversal strips, electric field is also expected to be confined within the separation gap between two nearest square rings. The E-field profiles in the spacer confirmed this picture, as is depicted in Fig. 3(c).

Considering all the description above, by analogy with cut-wire pairs [17

17. J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006). [CrossRef] [PubMed]

, 18

18. J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006). [CrossRef]

], the USSP can be mimicked by an equivalent circuit as shown in Fig. 4(a)
Fig. 4 The equivalent circuit models of: (a) a USSP; and (b) half unit cell.
. The magnetic inductance Lm can be expressed asLm=μ0leffd/(2w),where μ0 is the permeability of vacuum, leff is the effective length of the vertical strip of the square rings under which the most of all magnetic energy was trapped, as depicted in Fig. 3(d). We regard roughly it as the average length of the square ring, i.e., leff = l-w. Since there are the larger charge distribution areas (the transversal strip) at the ends of USSP compared with cut-wire pairs, the plate capacitance Cm has a form of Cm=εε0rf(0.5lw)/d,where ε0 is the permittivity of vacuum, εr is the relative permittivity of the dielectric spacer, and f is a fitting factor less than 1.0, which is used to adjust the effective charge distribution area of the transversal strip when the strip width vary, and 0.8 was chosen here. The gap capacitor approximated by two parallel wires of length 0.5l and diameter t is described asCg=πε0(0.5l)/ln(g/t), where g = a-l is separation distance between two nearest neighboring rings. Since one major source of the line broadening of optical constants originates from the damping of the constituent metal, dispersive resistances of the effective vertical strips are taken into account and have an expression of R=leff(νciω)/(wtε0ωp2) [19

19. J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005). [CrossRef] [PubMed]

].

If a virtual current loop mentioned above is viewed as a magnetic dipole, i.e. an artificial “magnetic atom”, the SRP array can be regarded as a large quantity of conformably oriented magnetic atoms. We simply provided that the loop current I=I0eiωt is induced by the external magnetic field H=H0eiωt, and then the individual magnetic dipole moment is expressed as IS, where S = leffd is the area of the current loop. This leads the magnetizationM=NIS/V, where N is the number of magnetic atoms and V is the volume of the array. One can easily deriveN/V=2/[a2(2t+d)], so that the magnetic susceptibility χeff(ω)=M/H is obtained. Finally, magnetic permeability can be calculated asμeff(ω)=1+χeff(ω). Now we need to find out the relationship between I and H. Applying the mentioned above equivalent circuit model illustrated in Fig. 4(a) and Kirchhoff’s voltage and current law (KVL and KCL), the circuit equations can be written as
2CmIdt+2Up=μ0S(dH/dt),
(1)
Up=IRR+LmdIRdt
(2)
and
CgdUpdt+IR=I,
(3)
where Up is the voltage drop over the parallel branch, and IR is the branch current in the parallel branch of R and Lm. Solve the Eqs. (2) and (3) above and yields
Up=R+iωLm1LmCgω2+iRCgωI.
(4)
We denoteβ=R+iωLm1LmCgω2+iRCgω, and then insert Up into Eq. (1), the expression of I versus H is immediately acquired as following
I=μ0SCmω22+2iCmβωH.
(5)
As a result, the numerical model of analytical permeability is derived as
μeff(ω)=1+μ0S2Cma2(2t+d)ω21+iβCmω.
(6)
For the combined system consisting of a WNP and a SRP array, in fact, we substitute the equivalent circuit model in Fig. 4(a) for 4(b). The resistance and capacitance introduced by WNP have expressions of r=wn(νciω)/(0.5ltε0ωp2)andCg'=0.5πε0l/ln[0.5(gwn)/t]. The two series capacitances have a sum ofCs=0.5Cg'. After some similar algebra, we find that the unique change of permeability lies in β=(R+iLmω)(1+irCsω)1LmCsω2+i(R+r)Csω in contrast to the Eq. (6) for the isolated SRP. In addition, only slight change of the permeability (not shown) is observed relative to that of isolated SRP shown in Fig. 5(a)
Fig. 5 Some physical quantities of three NIMs with different strip widths: (a) analytical permeability calculated by Eq. (6); (b) retrieved real parts of the permeability and permittivity of NIMs using simulated scattering parameters; and (c) corresponding transmission, and their respective double negative regime defined by dashed box. The same color convention in the three figures is indicated.
. This situation is in good agreement with the simulation results discussed in Figs. 2(e) and 2(f). Note that the latter expression of the β will be simplified to the foregoing one if line width wn of the WNP decrease to 0. Additionally, we find Cg (≈7.6 aF) ~Cs (≈6.1 aF), irCsω ~0 and R ~6r, these explain why the WNP has few influence on the magnetic property of the SRP array.

3.3. Achievement of hyper-transmission

A better transmission performance could be expected by simultaneously optimizing two aspects: (i) smaller absorption loss; (ii) smaller reflection loss. Minimizing absorption is fulfilled by selecting low damping metal and transparent dielectric spacer. Minimizing reflection can be satisfied by matching impedanceZeff(λ)=[μeff(λ)/εeff(λ)]1/2 with free space. The generalized conditions of impedance match are ε1(λ) = μ1(λ) and ε2(λ) = μ2(λ). As to the real part, we adjust the “magnetic plasma frequency” to equate the electric plasma frequency so that μ1(λ) as close to ε1(λ) as possible (see Fig. 2(e), Fig. 5(b) also). Although the minus imaginary permittivity ε2(λ) originating from the disturbance of magnetic resonance is much weaker than imaginary permeability μ2(λ) around the magnetic resonance frequency, this does not prevent the accordance of the two imaginary part values at those frequencies far from the center frequency of the magnetic resonance. In Fig. 5(b), the devised NIM with a strip width of 0.47 μm exhibits better impedance match relative to the other two samples, thus present the best transmission performance in double negative regime marked by dashed box, as is shown in Fig. 5(c). It is worth mentioning that the magnetic plasma frequency is more sensitive than the electric plasma frequency to the changing of strip width, as is illustrated in Fig. 5(b). This implies that we can control relatively independently the permittivity and permeability, which allows us to match easily the impedance.

4. Summary

We proposed a new polarization-independent negative index material made up of a WNP and a SRP array. The hyper-transmission and small period were achieved simultaneously. The retrieved optical constants for the isolated WNP, SRP and combined system were employed to analyze the mechanism of implementing the NIM. We found that: (1) the permittivity of SRP and the one of WNP determine jointly the permittivity of the combined system. The addition of SRP broke through the limitation of electric plasma frequency of the WNP (corresponding to the cutoff wavelength of fishnet), and put it into lager wavelength; (2) the permeability can be tuned relatively independently by simply varying the strip width. The two aspects allow us to design the NIM with small period and matching impedance. In addition, we built a numerical model of the analytical permeability. The predicted results are good agreement with that obtained from retrieval method. Moreover, by virtue of the analytical expression, we explained why the WNP has few influence on the magnetic properties of the SRP array.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (NSFC) (grants 51025208 and 61001026).

References and links

1.

S. Zhang, W. Fan, K. J. Malloy, S. R. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express 13(13), 4922–4930 (2005). [CrossRef] [PubMed]

2.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]

3.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006). [CrossRef] [PubMed]

4.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

5.

Z. Ku and S. R. Brueck, “Comparison of negative refractive index materials with circular, elliptical and rectangular holes,” Opt. Express 15(8), 4515–4522 (2007). [CrossRef] [PubMed]

6.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Design-related losses of double-fishnet negative-index photonic metamaterials,” Opt. Express 15(18), 11536–11541 (2007). [CrossRef] [PubMed]

7.

X. Wang, Y. H. Ye, C. Zheng, Y. Qin, and T. J. Cui, “Tunable figure of merit for a negative-index metamaterial with a sandwich configuration,” Opt. Lett. 34(22), 3568–3570 (2009). [CrossRef] [PubMed]

8.

C. Helgert, C. Menzel, C. Rockstuhl, E. Pshenay-Severin, E. B. Kley, A. Chipouline, A. Tünnermann, F. Lederer, and T. Pertsch, “Polarization-independent negative-index metamaterial in the near infrared,” Opt. Lett. 34(5), 704–706 (2009). [CrossRef] [PubMed]

9.

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101(10), 103902 (2008). [CrossRef] [PubMed]

10.

C. García-Meca, J. Hurtado, J. Martí, A. Martínez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett. 106(6), 067402 (2011). [CrossRef] [PubMed]

11.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton University Press, 1995).

12.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

13.

M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander Jr, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–20 (1983). [CrossRef] [PubMed]

14.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 036617 (2005). [CrossRef] [PubMed]

15.

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93(10), 107402 (2004). [CrossRef] [PubMed]

16.

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(24), 3356–3358 (2005). [CrossRef] [PubMed]

17.

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006). [CrossRef] [PubMed]

18.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Negative index materials using simple short wire pairs,” Phys. Rev. B 73(4), 041101 (2006). [CrossRef]

19.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. 95(22), 223902 (2005). [CrossRef] [PubMed]

OCIS Codes
(260.3060) Physical optics : Infrared
(310.6860) Thin films : Thin films, optical properties
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: August 8, 2012
Revised Manuscript: October 13, 2012
Manuscript Accepted: October 18, 2012
Published: October 30, 2012

Citation
Dengmu Cheng, Jianliang Xie, Peiheng Zhou, Huibin Zhang, Nan Zhang, and Longjiang Deng, "Numerical study of a new negative index material in mid-infrared spectrum," Opt. Express 20, 25744-25751 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-23-25744


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References

  1. S. Zhang, W. Fan, K. J. Malloy, S. R. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express 13(13), 4922–4930 (2005). [CrossRef] [PubMed]
  2. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]
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