Abstract

A type of metamaterial composed of a metal waveguide with discrete rod resonators, is investigated in this work for the first time. The simulation results show that the maximum of FOM=-Re(n)/Im(n) reaches 1.12 at the 543.5 nm. For another set of dimensions of the unit cell, the maximum of FOM reaches 1.41 at the wavelength of 721 nm. Our additional large numbers of simulation results show that different negative-index bands in visible wavelengths can be obtained by tuning the geometric dimensions of the unit cell.

© 2008 Optical Society of America

1. Introduction

The refractive index n is a key parameter describing the interaction between light and substance. For a natural medium, the Re(n) is positive. However, for a left-handed material (LHM), originally introduced by Veselogo [1] as a theoretical curiosity, the Re(n) is considered to be negative. Recently, the LHM has attracted the intense interest of researchers for a plenty of unique properties and valuable applications [27], especially after Smith et al [8,9] presented the first demonstration of the LHM at microwave frequencies.

Currently, increasing attention has been paid to the LHMs in the optical frequency band, and many researchers have proposed various the demonstrations. To date, there have been roughly three ways towards the realization of the LHMs in this band. The first one is to design one layer [1013] or a few layers [14] of discrete resonator elements and incident waves are generally perpendicular to these layers. The negative indices of such LHMs were only limited in the infrared frequency band [1012,14] and at the red end of the visible spectrum [13,15]. The second one is to utilize a metal-insulator-metal waveguide as a two-dimensional LHM [16]. In this manner, the negative refraction merely occurs in the blue-green region of the visible spectrum. The last one is a quantum method using either a single probe beam through multi-species media [17], or multiple beams through single species media [18]. This method is limited to theoretical research and has not been verified experimentally.

Below we present an approach to the realization of the LHM, a combination of the first two ways mentioned above. Namely, discrete rod resonators forming a sandwich structure lie in a metal waveguide. Our numerical simulations demonstrate that the negative-index band with high transmission ranges in the visible wavelengths. This approach opens new opportunities for designing negative-index materials in optics.

2. Structure model

As shown in Fig. 1(a), periodic discrete resonator elements, consisting of two metallic rods (24 nm thick Ag) separated by a dielectric layer (12 nm thick MgF2 with the refractive index of 1.38), lie between the two same metallic plates (60 nm thick Ag). All the samples are located on a glass substrate (index n=1.5). This configuration can be fabricated by employing evaporation techniques and standard electron-beam lithography. Obviously, it can be viewed as a two-dimensional metal waveguide. Figure 2(b) exhibits one unit cell, and all dimensions are displayed in the caption under Fig. 1.

 

Fig. 1. (a) Schematic for a metal waveguide with array of H shape within it. (b) A unit cell with geometric dimensions L=600 nm, W=500 nm, a=120 nm, b=300 nm, g=40 nm, t=24 nm, and s=12 nm. The glass substrate is much thicker than the silver layer. The propagation of the polarized electromagnetic wave is along the z axis, and the electric field and the magnetic field are respectively in the x and y directions.

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3. Numerical calculations and discussion

An Electromagnetic Design System (Agilent Corp), based on a finite element method, a commercial electromagnetic mode solver, is employed in our simulations. Furthermore, the optical properties of silver are described by the Drude free electron model,

ε(ω)=1ωp2ω2iωγ,

where ωp is the plasma frequency and γ is the collision frequency. The ωp and γ of silver are respectively 1.22×1016 and 9.0×1013 [19]. In our designed structure, the size of the unit cell ρ (i.e., 2t+s) is much smaller than an electromagnetic resonance wavelength λ, reaching ρ/λ<1/9. Thus, an effective medium model can be used in our research. Following the common method [20], to excite the negative magnetic response of resonators as well as the negative electric response of wires, the incident electromagnetic waves are polarized with the magnetic field parallel to the y axis (Hy axis) and the electric field parallel to the x axis(Ex axis). Consequently, the propagation direction (wave vector k) is along the z axis. The two wave ports are set in the planes perpendicular to the z axis. The symmetrical perfect magnetic boundaries (corresponding to the boundaries perpendicular to the y axes) is also applied.

Using the S-parameter retrieval methods [2123], the complex refractive index n, wave impedance z, effective permittivity ε and effective permeability µ have been retrieved in Fig. 2. Our retrieved indices in Fig. 2(b) confirm the negative-index band ranging from 517 nm to 564 nm. As shown in Figs. 2(e), we find that, in this negative-index band, Re(ε)<0, while Re(µ)>0. Negative Re(n) is achieved throughout as the condition Γ=ε 1 µ 2+µ 1 ε 2<0 is satisfied [24,25,10], where ε=ε 1+iε 2 and µ=µ 1+iµ 2 (see Fig. 1(f)). Figures 3(d) and 3(e) show the strong electromagnetic resonances, occurring near the wavelengths of 545 nm. This resonance can be regarded as an optical LC circuit, with the silver rods providing the inductance L and the MgF2 layer between the rods acting as capacitive elements C. Moreover, capacitance can also be generated between the silver rods and the waveguide wall. Maybe because of this capacitance the electromagnetic resonance occurs near the higher frequencies than those in Ref. [10,11,13,15].

 

Fig. 2. Fig. 2. (a) Simulated S parameters for the unit cell in Fig. 1(b); (b) retrieved refractive index; (c) retrieved impedance; (d) retrieved permittivity; (e) retrieved permeability. (f) Distributions of the condition Γ and the Re(n).

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Fig. 3. Distribution of FOM in the negative-index band in Fig. 2(b).

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It is to be noted that an LHM with high transmission is to be expected. In other words, its figure of merit (FOM=-Re(n)/Im(n)) should be as large as possible, i.e., the higher the FOM is, the higher the transmission is. From Fig. 3, we can find that the maximum of FOM arrives at 1.12 near the wavelength of 543.5 nm, which means the highest transmission occurs at this wavelength.

 

Fig. 4. (a) Simulated S parameters for the unit cell with geometric dimensions L=700 nm, W=640 nm, a=200 nm, b=400 nm, g=40nm, t=30 nm, and s=15 nm; (b) retrieved refractive index; (c) retrieved permittivity; (d) retrieved permeability.

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Fig. 5. istribution of FOM in the negative-index band in Fig. 4(b).

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In addition, we investigate the influence on the refractive index when the geometric dimensions of the unit cell are changed (the changed parameters are displayed beneath Fig. 4). From Fig. 4(b), we obtain that the negative-index band ranges between 660 nm and 770 nm. The strong electromagnetic resonance shifts toward the wavelengths of 725 nm. Meanwhile, figure 4(d) exhibits a negative permeability band at 717–728 nm, implying the smaller scattering loss than the above case [10]. This is verified in Fig. 5. Namely, the maximum of FOM equals 1.41 (higher than 1.12) near 721 nm. This FOM value is quite high. Importantly, it occurs in visible wavelengths and this wavelength is shortest thus far. It is well known that researchers have experimentally and theoretically confirmed the LHMs in the optical range.

However, their FOMs are low (often below 1) [10,11,13]. Although the LHMs were demonstrated at 1400 nm with an FOM of 3 [26], at 1800 nm with an FOM above 1[27], and at 813 nm with an FOM of 1.3 [15], they still range in the infrared wavelengths. Our additional large numbers of simulations testify that different negative-index bands with high FOMs in visible wavelengths can be obtained by tuning the geometric dimensions of the unit cell.

4. Conclusions

In conclusion, a type of metamaterial composed of a metal waveguide with discrete rod resonators, has been reported in our work. Simulating the S parameters of its unit cell, we have retrieved the complex refractive index n, wave impedance z, effective permittivity ε and effective permeability µ. Our retrieved results have shown that the maximum of FOM reaches 1.12 at the 543.5 nm. For another set of dimensions of the unit cell, the maximum of FOM arrives at 1.41 at the wavelength of 721 nm. This FOM value is quite high, indicating that this metamaterial possesses high transmission. Importantly, it occurs in visible wavelengths and this wavelength is shortest thus far. Our additional large numbers of simulations testify that different negative-index bands in visible wavelengths can be obtained by tuning the geometric dimensions of the unit cell. This approach is greatly effective to the realization of negative refraction at visible wavelengths.

References and links

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

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

3. R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001). [CrossRef]  

4. A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92, 5930–5935 (2002). [CrossRef]  

5. N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161–163 (2003). [CrossRef]  

6. Z. W. Liu, N. Fang, T. J. Yen, and X. Zhang, “Rapid growth of evanescent wave by a silver superlens,” Appl. Phys. Lett. 83, 5184–5186 (2003). [CrossRef]  

7. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science , 314, 977–979 (2006). [CrossRef]   [PubMed]  

8. 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]  

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

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

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. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial,” Science 312, 892–894 (2006). [CrossRef]   [PubMed]  

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

14. G. Dolling, M. Wegener, and S. Linden, “Realization of a three-functional-layer negative-index photonic metamaterial,” Opt. Lett. 32, 551–553 (2007). [CrossRef]   [PubMed]  

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

16. H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316, 430–432 (2007). [CrossRef]   [PubMed]  

17. C. M. Krowne, “Multi-species two-level atomic media displaying electromagnetic left handedness,” Phys. Lett. A 372, 2304–2310 (2008). [CrossRef]  

18. J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, “Tunable negative refraction without absorption via electromagnetically induced chirality,” Phys. Rev. Lett. 99, 073602 (2007). [CrossRef]   [PubMed]  

19. T. OkamotoS. Kawata, M. Ohtsu, and M. Irie (Springer, New York, 2001), Chap. 6, p.97.

20. 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 π-shaped metallic metamaterial,” Phys. Rev. B 75, 075117 (2007). [CrossRef]  

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

22. S. G. Mao, S. L. Chen, and C. W. Huang, “Effective electromagnetic parameters of novel distributed left-handed microstrip lines,” IEEE Trans. Microwave Theory Tech. 53, 1515–1521 (2005). [CrossRef]  

23. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. E 71, 036617 (2005). [CrossRef]  

24. R. A. Depine and A. Lakhtakia, “A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity,” Microwave Opt. Tech. Lett. 41, 315–316 (2004). [CrossRef]  

25. F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, “Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime,” Phys. Rev. E 75, 016604 (2007). [CrossRef]  

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

27. S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies,” J. Opt. Soc. Am. B 23, 434–438 (2006). [CrossRef]  

References

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  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  3. R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
    [CrossRef]
  4. A. Grbic and G. V. Eleftheriades, "Experimental verification of backward-wave radiation from a negative refractive index metamaterial," J. Appl. Phys. 92, 5930-5935 (2002).
    [CrossRef]
  5. N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163 (2003).
    [CrossRef]
  6. Z. W. Liu, N. Fang, T. J. Yen, and X. Zhang, "Rapid growth of evanescent wave by a silver superlens," Appl. Phys. Lett. 83, 5184-5186 (2003).
    [CrossRef]
  7. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science,  314, 977-979 (2006).
    [CrossRef] [PubMed]
  8. 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]
  9. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  10. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404 (2005).
    [CrossRef] [PubMed]
  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. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial," Science 312, 892-894 (2006).
    [CrossRef] [PubMed]
  13. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007).
    [CrossRef]
  14. G. Dolling, M. Wegener, and S. Linden, "Realization of a three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, 551-553 (2007).
    [CrossRef] [PubMed]
  15. U. K. Chettiar, A. V. Kildishev, H. K. Yuan, W. Cai, S. M. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-band negative index metamaterial: double negative at 813nm and single negative at 772nm," Opt. Lett. 32, 1671-1673 (2007).
    [CrossRef] [PubMed]
  16. H. J. Lezec, J. A. Dionne, and H. A. Atwater, "Negative refraction at visible frequencies," Science 316, 430-432 (2007).
    [CrossRef] [PubMed]
  17. C. M. Krowne, "Multi-species two-level atomic media displaying electromagnetic left handedness," Phys. Lett. A 372, 2304-2310 (2008).
    [CrossRef]
  18. J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, "Tunable negative refraction without absorption via electromagnetically induced chirality," Phys. Rev. Lett. 99, 073602 (2007).
    [CrossRef] [PubMed]
  19. T. Okamoto, In Near-field Optics and Surface Plasmon Polariton, S. Kawata, M. Ohtsu, and M. Irie, eds., (Springer, New York, 2001), Chap. 6, p.97.
  20. 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]
  21. D. R. Smith, S. Schultz, P. Marko, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
    [CrossRef]
  22. S. G. Mao, S. L. Chen, and C. W. Huang, "Effective electromagnetic parameters of novel distributed left-handed microstrip lines," IEEE Trans. Microwave Theory Tech. 53, 1515-1521 (2005).
    [CrossRef]
  23. D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
    [CrossRef]
  24. R. A. Depine, and A. Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Tech. Lett. 41, 315-316 (2004).
    [CrossRef]
  25. F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, "Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime," Phys. Rev. E 75, 016604 (2007).
    [CrossRef]
  26. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at communication wavelengths," Opt. Lett. 31, 1800-1802 (2006).
    [CrossRef] [PubMed]
  27. S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
    [CrossRef]

2008 (1)

C. M. Krowne, "Multi-species two-level atomic media displaying electromagnetic left handedness," Phys. Lett. A 372, 2304-2310 (2008).
[CrossRef]

2007 (7)

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, "Tunable negative refraction without absorption via electromagnetically induced chirality," Phys. Rev. Lett. 99, 073602 (2007).
[CrossRef] [PubMed]

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]

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, "Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime," Phys. Rev. E 75, 016604 (2007).
[CrossRef]

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

G. Dolling, M. Wegener, and S. Linden, "Realization of a three-functional-layer negative-index photonic metamaterial," Opt. Lett. 32, 551-553 (2007).
[CrossRef] [PubMed]

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

H. J. Lezec, J. A. Dionne, and H. A. Atwater, "Negative refraction at visible frequencies," Science 316, 430-432 (2007).
[CrossRef] [PubMed]

2006 (4)

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science,  314, 977-979 (2006).
[CrossRef] [PubMed]

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

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

2005 (4)

S. G. Mao, S. L. Chen, and C. W. Huang, "Effective electromagnetic parameters of novel distributed left-handed microstrip lines," IEEE Trans. Microwave Theory Tech. 53, 1515-1521 (2005).
[CrossRef]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

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

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]

2004 (1)

R. A. Depine, and A. Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Tech. Lett. 41, 315-316 (2004).
[CrossRef]

2003 (2)

N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163 (2003).
[CrossRef]

Z. W. Liu, N. Fang, T. J. Yen, and X. Zhang, "Rapid growth of evanescent wave by a silver superlens," Appl. Phys. Lett. 83, 5184-5186 (2003).
[CrossRef]

2002 (2)

A. Grbic and G. V. Eleftheriades, "Experimental verification of backward-wave radiation from a negative refractive index metamaterial," J. Appl. Phys. 92, 5930-5935 (2002).
[CrossRef]

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

2001 (2)

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

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

2000 (2)

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

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]

1968 (1)

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

Atwater, H. A.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, "Negative refraction at visible frequencies," Science 316, 430-432 (2007).
[CrossRef] [PubMed]

Brueck, S. R. J.

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

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

Cai, W.

Chen, S. L.

S. G. Mao, S. L. Chen, and C. W. Huang, "Effective electromagnetic parameters of novel distributed left-handed microstrip lines," IEEE Trans. Microwave Theory Tech. 53, 1515-1521 (2005).
[CrossRef]

Chettiar, U. K.

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science,  314, 977-979 (2006).
[CrossRef] [PubMed]

Depine, R. A.

R. A. Depine, and A. Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Tech. Lett. 41, 315-316 (2004).
[CrossRef]

Dionne, J. A.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, "Negative refraction at visible frequencies," Science 316, 430-432 (2007).
[CrossRef] [PubMed]

Dolling, G.

Dong, Z. G.

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]

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, "Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime," Phys. Rev. E 75, 016604 (2007).
[CrossRef]

Drachev, V. P.

Eleftheriades, G. V.

A. Grbic and G. V. Eleftheriades, "Experimental verification of backward-wave radiation from a negative refractive index metamaterial," J. Appl. Phys. 92, 5930-5935 (2002).
[CrossRef]

Enkrich, C.

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

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Fan, W.

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

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

Fang, N.

Z. W. Liu, N. Fang, T. J. Yen, and X. Zhang, "Rapid growth of evanescent wave by a silver superlens," Appl. Phys. Lett. 83, 5184-5186 (2003).
[CrossRef]

N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163 (2003).
[CrossRef]

Fleischhauer, M.

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, "Tunable negative refraction without absorption via electromagnetically induced chirality," Phys. Rev. Lett. 99, 073602 (2007).
[CrossRef] [PubMed]

Grbic, A.

A. Grbic and G. V. Eleftheriades, "Experimental verification of backward-wave radiation from a negative refractive index metamaterial," J. Appl. Phys. 92, 5930-5935 (2002).
[CrossRef]

Heyman, E.

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Huang, C. W.

S. G. Mao, S. L. Chen, and C. W. Huang, "Effective electromagnetic parameters of novel distributed left-handed microstrip lines," IEEE Trans. Microwave Theory Tech. 53, 1515-1521 (2005).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science,  314, 977-979 (2006).
[CrossRef] [PubMed]

Kästel, J.

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, "Tunable negative refraction without absorption via electromagnetically induced chirality," Phys. Rev. Lett. 99, 073602 (2007).
[CrossRef] [PubMed]

Kildishev, A. V.

Koschny, T.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Krowne, C. M.

C. M. Krowne, "Multi-species two-level atomic media displaying electromagnetic left handedness," Phys. Lett. A 372, 2304-2310 (2008).
[CrossRef]

Lakhtakia, A.

R. A. Depine, and A. Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Tech. Lett. 41, 315-316 (2004).
[CrossRef]

Lei, S. Y.

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]

Lezec, H. J.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, "Negative refraction at visible frequencies," Science 316, 430-432 (2007).
[CrossRef] [PubMed]

Li, Q.

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]

Li, T.

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]

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, "Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime," Phys. Rev. E 75, 016604 (2007).
[CrossRef]

Linden, S.

Liu, H.

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]

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, "Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime," Phys. Rev. E 75, 016604 (2007).
[CrossRef]

Liu, Z. W.

Z. W. Liu, N. Fang, T. J. Yen, and X. Zhang, "Rapid growth of evanescent wave by a silver superlens," Appl. Phys. Lett. 83, 5184-5186 (2003).
[CrossRef]

Malloy, K. J.

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

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

Mao, S. G.

S. G. Mao, S. L. Chen, and C. W. Huang, "Effective electromagnetic parameters of novel distributed left-handed microstrip lines," IEEE Trans. Microwave Theory Tech. 53, 1515-1521 (2005).
[CrossRef]

Marko, P.

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

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science,  314, 977-979 (2006).
[CrossRef] [PubMed]

Nemat-Nasser, S. C.

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]

Osgood, R. M.

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

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

Padilla, W. J.

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]

Panoiu, N. C.

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

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

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science,  314, 977-979 (2006).
[CrossRef] [PubMed]

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

Sarychev, A. K.

Schultz, S.

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

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

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]

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science,  314, 977-979 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

Shelby, R. A.

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

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science,  314, 977-979 (2006).
[CrossRef] [PubMed]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

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

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

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]

Soukoulis, C. M.

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

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

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

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

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science,  314, 977-979 (2006).
[CrossRef] [PubMed]

Veselago, V. G.

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

Vier, D. C.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

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]

Walsworth, R. L.

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, "Tunable negative refraction without absorption via electromagnetically induced chirality," Phys. Rev. Lett. 99, 073602 (2007).
[CrossRef] [PubMed]

Wang, F. M.

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, "Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime," Phys. Rev. E 75, 016604 (2007).
[CrossRef]

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]

Wegener, M.

Xiao, S. M.

Xu, M. X.

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]

Yelin, S. F.

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, "Tunable negative refraction without absorption via electromagnetically induced chirality," Phys. Rev. Lett. 99, 073602 (2007).
[CrossRef] [PubMed]

Yen, T. J.

Z. W. Liu, N. Fang, T. J. Yen, and X. Zhang, "Rapid growth of evanescent wave by a silver superlens," Appl. Phys. Lett. 83, 5184-5186 (2003).
[CrossRef]

Yuan, H. K.

Zhang, S.

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

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

Zhang, X.

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, "Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime," Phys. Rev. E 75, 016604 (2007).
[CrossRef]

Z. W. Liu, N. Fang, T. J. Yen, and X. Zhang, "Rapid growth of evanescent wave by a silver superlens," Appl. Phys. Lett. 83, 5184-5186 (2003).
[CrossRef]

N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163 (2003).
[CrossRef]

Zhu, S. N.

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]

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, "Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime," Phys. Rev. E 75, 016604 (2007).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Appl. Phys. Lett. (2)

N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163 (2003).
[CrossRef]

Z. W. Liu, N. Fang, T. J. Yen, and X. Zhang, "Rapid growth of evanescent wave by a silver superlens," Appl. Phys. Lett. 83, 5184-5186 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

S. G. Mao, S. L. Chen, and C. W. Huang, "Effective electromagnetic parameters of novel distributed left-handed microstrip lines," IEEE Trans. Microwave Theory Tech. 53, 1515-1521 (2005).
[CrossRef]

J. Appl. Phys. (1)

A. Grbic and G. V. Eleftheriades, "Experimental verification of backward-wave radiation from a negative refractive index metamaterial," J. Appl. Phys. 92, 5930-5935 (2002).
[CrossRef]

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

Microwave Opt. Tech. Lett. (1)

R. A. Depine, and A. Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Tech. Lett. 41, 315-316 (2004).
[CrossRef]

Opt. Lett. (5)

Phys. Lett. A (1)

C. M. Krowne, "Multi-species two-level atomic media displaying electromagnetic left handedness," Phys. Lett. A 372, 2304-2310 (2008).
[CrossRef]

Phys. Rev. B (2)

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

Phys. Rev. E (3)

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, "Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime," Phys. Rev. E 75, 016604 (2007).
[CrossRef]

Phys. Rev. Lett. (4)

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

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]

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, "Tunable negative refraction without absorption via electromagnetically induced chirality," Phys. Rev. Lett. 99, 073602 (2007).
[CrossRef] [PubMed]

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

Science (4)

H. J. Lezec, J. A. Dionne, and H. A. Atwater, "Negative refraction at visible frequencies," Science 316, 430-432 (2007).
[CrossRef] [PubMed]

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science,  314, 977-979 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

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

Other (1)

T. Okamoto, In Near-field Optics and Surface Plasmon Polariton, S. Kawata, M. Ohtsu, and M. Irie, eds., (Springer, New York, 2001), Chap. 6, p.97.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic for a metal waveguide with array of H shape within it. (b) A unit cell with geometric dimensions L=600 nm, W=500 nm, a=120 nm, b=300 nm, g=40 nm, t=24 nm, and s=12 nm. The glass substrate is much thicker than the silver layer. The propagation of the polarized electromagnetic wave is along the z axis, and the electric field and the magnetic field are respectively in the x and y directions.

Fig. 2.
Fig. 2.

Fig. 2. (a) Simulated S parameters for the unit cell in Fig. 1(b); (b) retrieved refractive index; (c) retrieved impedance; (d) retrieved permittivity; (e) retrieved permeability. (f) Distributions of the condition Γ and the Re(n).

Fig. 3.
Fig. 3.

Distribution of FOM in the negative-index band in Fig. 2(b).

Fig. 4.
Fig. 4.

(a) Simulated S parameters for the unit cell with geometric dimensions L=700 nm, W=640 nm, a=200 nm, b=400 nm, g=40nm, t=30 nm, and s=15 nm; (b) retrieved refractive index; (c) retrieved permittivity; (d) retrieved permeability.

Fig. 5.
Fig. 5.

istribution of FOM in the negative-index band in Fig. 4(b).

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