## Modeling and experimental verification of optical materials formed by stacked nanostrips |

Optics Express, Vol. 18, Issue 14, pp. 14842-14849 (2010)

http://dx.doi.org/10.1364/OE.18.014842

Acrobat PDF (1054 KB)

### Abstract

The effective plasma frequency *f _{p}
* of periodic metallic wires whose characteristic dimensions are comparable to their skin depth has been analyzed. And a relevant analytic model is constructed by considering the skin effect and making a reasonable shape approximation, which is suitable for the case that the cross section of the wire is noncircular. To verify this model, a wires array with rectangle cross section is designed and the corresponding stacked Au-SiO

_{2}nanostrips are fabricated. The experimental and simulational transmittances of the metamaterial have been evaluated with a good agreement, although the presence of quartz substrate and structural imperfections in experiment will have an impact, which validates that the multilayer Au-SiO

_{2}nanostrips could function similarly to a natural bulk metal with discrepancies of

*f*values less than 8%. It could be confirmed that the theoretic formula is trustworthy in predicting

_{p}*f*for designing and realizing a controllable artificial metal in optical region.

_{p}© 2010 OSA

## 1. Introduction

1. W. Rotman, “Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media,” IRE Trans. Antennas Propag. **10**(1), 82–95 (1962). [CrossRef]

*f*) depends on the structural parameters of the wire system. The early relevant work was proposed by Pendry

_{p}*et al*., they demonstrated that the metallic wire-mesh structures have a low frequency stop band from zero frequency up to a cut-off frequency, which was attributed to the motion of electrons in the metal wires [2

2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs I, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. **76**(25), 4773–4776 (1996). [CrossRef] [PubMed]

3. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter **10**(22), 4785–4809 (1998). [CrossRef]

*f*was depressed into GHz region. The metamaterial of Pendry was composed of very thin wires (namely r<<

_{p}*δ*,

*r*and

*δ*is the radius and skin depth of the metal wire, respectively), and the cross section of wire is specifically required to be circular. All electrons would equally participate in the modulation of

*f*. Thus the skin effect could be ignored, and Pendry’s model was given bywhere

_{p}*c*

_{0}is the velocity of light in vacuum, and

*a*is the lattice constant of the wire array. Since then several alternative theories have been proposed [4

4. S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, “Wire media with negative effective permittivity: A quasi-static model,” Microw. Opt. Technol. Lett. **35**(1), 47–51 (2002). [CrossRef]

6. S. Brand, R. A. Abram, and M. A. Kaliteevski, “Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods,” Phys. Rev. B **75**(3), 035102 (2007). [CrossRef]

*δ*, it has been verified that only the effective active electrons near the wire surface will work and take part in the modulation of

*f*[7

_{p}7. X. Wei, H. Shi, Q. Deng, X. Dong, C. Liu, Y. Lu, and C. Du, “Artificial metal with effective plasma frequency in near-infrared region,” Opt. Express **18**(4), 3370–3378 (2010). [CrossRef] [PubMed]

*f*were studied for the case of rods with circular cross-section [8

_{p}8. M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of epsilon-negative rods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **73**(4), 046612 (2006). [CrossRef] [PubMed]

9. M. G. Silveirinha, “Artificial plasma formed by connected metallic wires at infrared frequencies,” Phys. Rev. B **79**(3), 035118 (2009). [CrossRef]

*f*of the optical structured material with above requirement.

_{p}*f*of the structured material in optical region with a noncircular cross section being comparable to the skin depth

_{p}*δ*. Accordingly, an improved model is deduced by considering the skin effect and making a reasonable shape approximation. The noncircular wires could be approximated into circular ones by keeping the total amount of the electrons invariable which determines

*f*. For instance, the design is given for wires array with rectangle cross section. According to the theoretic investigation of

_{p}*f*, we report a successful fabrication of an elementary artificial metal composed of multilayer Au-SiO2 nanostrips whose

_{p}*f*is in optical region. The experimental and simulational transmittance results have been evaluated with a good agreement. It is validated that the multilayer Au-SiO

_{p}_{2}nanostrips could function similarly to a natural bulk metal based on the model. This metamaterial may lead to various plasmonics-based applications such as subwavelength waveguides and antennas [10

10. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. **89**(21), 213902 (2002). [CrossRef] [PubMed]

11. R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. **100**(2), 023903–023907 (2008). [CrossRef] [PubMed]

12. 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]

13. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science **308**(5721), 534–537 (2005). [CrossRef] [PubMed]

14. Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. **7**(2), 403–408 (2007). [CrossRef] [PubMed]

15. G. Dolling, M. Wegener, and S. Linden, “Realization of a three-functional-layer negative-index photonic metamaterial,” Opt. Lett. **32**(5), 551–553 (2007). [CrossRef] [PubMed]

## 2. Modeling of effective plasma frequency

*a.*The electric field is applied parallel to the wires (along the

*y*axis). When the waves impinge this system, the electrons are confined to move within the wires. Thus, two vital consequences are brought: the first is the decrease of the average electrons density due to diluting of the metal by the air space; the second is the distinct enhancement of the effective mass of the electrons caused by magnetic effects [2

2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs I, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. **76**(25), 4773–4776 (1996). [CrossRef] [PubMed]

*ω*is given in terms of the effective electron density

_{p}*e*.We first consider the dilution of the effective electrons density. Supposing the average density of the electrons in the cross section of the noncircular wire is

*n*', then the total amount of the electrons participating in the modulation of

*f*, can be expressed approximately aswhere

_{p}*d*is the decaying distance. By keeping

*N*' unchangeable, we make an approximation as shown in Fig. 1. The noncircular wire has been replaced by a newer wire with an effective radius

*r*, in which the active electrons can uniformly participate in the

_{eff}*f*modulation process.The effective electrons density in the effective structure as a whole is given by the fraction of space occupied by the effective wire,In addition, the distinct enhancement of the effective mass of the electrons could be well expressed through the above approximation. The effective mass of the electrons can be achieved with the same principle as in Pendry’ work [2

_{p}2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs I, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. **76**(25), 4773–4776 (1996). [CrossRef] [PubMed]

*f*of the arranged metal wires, whose characteristic dimensions are comparable to

_{p}*δ*, could be expressed asIn above consideration, the wire is surrounded by the vacuum. However, when the dielectric such as SiO

_{2}is used to act as the filling layer, a modulation factor

*ε*called relative permittivity of the relevant dielectric must be added which have been verified in our previous report [7

_{r}7. X. Wei, H. Shi, Q. Deng, X. Dong, C. Liu, Y. Lu, and C. Du, “Artificial metal with effective plasma frequency in near-infrared region,” Opt. Express **18**(4), 3370–3378 (2010). [CrossRef] [PubMed]

*f*can be expressed asThe final expression for

_{p}*f*in Eq. (8) is independent of the microscopic quantities such as the electron density and the mean drift velocity. It only depends on the spacing

_{p}*a*and the effective radius of the wire

*r*. And

_{eff}*r*could be obtained through solving Eqs. (3) and (4), which is determined by the structural parameters of the wire and the skin depth

_{eff}*δ*.

16. 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**(5775), 892–894 (2006). [CrossRef] [PubMed]

*ω*= 1.32 × 10

_{pl}^{16}s

^{−1}and collision frequency

*ω*= 1.2 × 10

_{col}^{14}s

^{−1}. Note that the skin depth of Au is frequency dependent, whereas the change is not obvious. Therefore, we consider it as an invariable parameter with the value of 20 nm in the visible and near-infrared region [17

17. V. Shrotriya, E. H. Wu, G. Li, Y. Yao, and Y. Yang, “Efficient light harvesting in multiple-device stacked structure for polymer solar cells,” Appl. Phys. Lett. **88**(6), 064104 (2006). [CrossRef]

*r*is the radius of the original circular wire, which is comparable to

*δ*. When

*r*= 25 nm,

*r*can be obtained to be 20.7 nm through solving Eqs. (4) and (9). To obtain

_{eff}*f*through simulation, we applied the well known retrieval procedure [18

_{p}18. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B **65**(19), 195104 (2002). [CrossRef]

*ε*from the simulated reflection and transmission data. And

_{eff}*f*can be determined at the frequency where

_{p}*ε*= 0. Figure 2 shows the comparisons of

_{eff}*f*values, which are derived by the FDTD simulation and our analytic model, separately. The discrepancies between the simulation and our model are small, and the maximum value is less than 8%.

_{p}*w*and

*t*, respectively. For this case,

*N*' can be formulated as the following expression corresponding to the Eq. (3). Here

*t*is comparable to

*δ*and much smaller than

*w*,By solving Eqs. (4) and (10), the rectangular cross section with

*w*= 70 nm and

*t*= 30 nm can be replaced by an equivalent circle with

*r*= 21.7 nm. In Fig. 3, the simulation results by FDTD as the criterion are compared with the predicting ones by model which indicates the validity of the improved model for the rectangle wire. Similarly, this model could be suitable for many other shapes, such as ellipse, square and irregular shape through above reasonable approximation.

_{eff}## 3. Experiment

*f*is in optical region by using Au strip surrounded by SiO2. An elementary bulk metamaterial composed of triple Au strips has been designed, as shown in Fig. 4(a) . We have actualized an etching-based procedure [19

_{p}19. A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: Recent advances and outlook,” Metamaterials (Amst.) **2**(1), 1–17 (2008). [CrossRef]

_{2}layer by layer (Au-SiO

_{2}-Au-SiO

_{2}-Au) onto the SiO

_{2}substrate at pressures about 4 mTorr by magnetron sputtering (LAB-18, Kutt. J. Lesker). The depths of Au and SiO

_{2}were 20 nm and 40 nm, respectively. Subsequently, 200 nm thick poly(methy lmethacrylate) (PMMA) was spun on the top of the upper Au film. And then, lithography was performed by using standard electron beam exposure apparatus (JBX5500ZA), followed by an appropriate development for 90 s in a solution of methyl isobutyl ketone (MIBK) diluted 1:3 by volume with isopropyl alcohol (IPA) at 21°C. For achieving the artificial metal with excellent performance, the results of electron beam lithography were examined using field emission scanning electron microscope (Quanta 400 FEG) to confirm the fine quality. Although the sample of 40nm minimum lateral feature size and 200 nm thickness were fabricated, some parts of the PMMA patterns collapsed as shown in Fig. 5(a) because of the high aspect ratio (i.e., height/width). Obviously, this result would not meet the requirement for the following etching step. However, the unwanted effect could be avoided by extending the strip width

*w*to 70 nm. Next, the PMMA pattern was transferred into the multilayer Au and SiO

_{2}film using deep anisotropic etching in LKJ-1C-150 IBE system with Ar at pressures below 2 × 10

^{−2}Pa. The samples were rotated to achieve uniform etching rate in various directions. The cooling system of etching device could help to control working temperature to avoid the PMMA deformation caused by ion bombardment. The etching rates of Au, SiO

_{2}, and PMMA were beforehand stabilized at 30 nm/min, 15 nm/min, and 23 nm/min, respectively, with 80 mA ion beam, 300 eV ion energy, 180 V acceleration voltage, and 2 mA neutralization current. After 8 min etching, the pre-patterned PMMA topography could be perfectly transferred into the alternating Au-SiO2 layers. The electron micrograph of the best sample (500 μm × 500 μm footprint) shown in Fig. 5(b) reveals a good large-scale homogeneity with the feature dimension about 70 nm line width and 250 nm period, and the sidewall roughness is about 10 nm. With these experimental parameters, the effective plasma wavelength can be estimated by our model. We can obtain

*r*= 18.7 nm through solving Eqs. (4) and (10) and

_{eff}*a*can be appropriately decided to be

_{2}, the modulation factor could be effectively decided to be

*g*represents the ratio of the area of SiO

_{2}to the whole filling layer,

## 4. Results and discussion

20. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. **94**(19), 197401 (2005). [CrossRef] [PubMed]

21. 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]

22. 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]

*λ*= 524 nm as shown in Fig. 6(b). And the discrepancy of the effective plasma wavelength between above-mentioned prediction by model and the experiment is below 8%. Above the interested plasma wavelength, the real part of effective permittivity is regularly negative. Note that only the modes whose electric fields are parallel to the strips will play a great role in the modulation of

_{p}*f*.

_{p}## 5. Conclusion

*f*, which is suitable for the case that the characteristic dimension of the metal wire is comparable to

_{p}*δ*. The dependence of

*f*on the geometric parameters, which can be predicted by the model, provides us with a general recipe for designing and fabricating such artificial metal at desired frequency. This new artificial material may open new possibilities for many plasmonics-based applications in much wider regime, and the fascinating electrodynamic effects of such metamaterials are expected to be investigated further.

_{p}## Acknowledgment

## References and links

1. | W. Rotman, “Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media,” IRE Trans. Antennas Propag. |

2. | J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs I, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. |

3. | J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter |

4. | S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, “Wire media with negative effective permittivity: A quasi-static model,” Microw. Opt. Technol. Lett. |

5. | M. Silveirinha and C. Fernandes, “A Hybrid Method for the Efficient Calculation of the Band Structure of 3-D Metallic Crystals,” IEEE Trans. Microw. Theory Tech. |

6. | S. Brand, R. A. Abram, and M. A. Kaliteevski, “Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods,” Phys. Rev. B |

7. | X. Wei, H. Shi, Q. Deng, X. Dong, C. Liu, Y. Lu, and C. Du, “Artificial metal with effective plasma frequency in near-infrared region,” Opt. Express |

8. | M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of epsilon-negative rods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

9. | M. G. Silveirinha, “Artificial plasma formed by connected metallic wires at infrared frequencies,” Phys. Rev. B |

10. | S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. |

11. | R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. |

12. | 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. |

13. | N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science |

14. | Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. |

15. | G. Dolling, M. Wegener, and S. Linden, “Realization of a three-functional-layer negative-index photonic metamaterial,” Opt. Lett. |

16. | G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science |

17. | V. Shrotriya, E. H. Wu, G. Li, Y. Yao, and Y. Yang, “Efficient light harvesting in multiple-device stacked structure for polymer solar cells,” Appl. Phys. Lett. |

18. | D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B |

19. | A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: Recent advances and outlook,” Metamaterials (Amst.) |

20. | J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. |

21. | J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. |

22. | 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. |

**OCIS Codes**

(160.4670) Materials : Optical materials

(160.4760) Materials : Optical properties

(260.5740) Physical optics : Resonance

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

**ToC Category:**

Metamaterials

**History**

Original Manuscript: April 27, 2010

Revised Manuscript: June 5, 2010

Manuscript Accepted: June 16, 2010

Published: June 28, 2010

**Citation**

Xingzhan Wei, Haofei Shi, Guoxing Zheng, Xiaochun Dong, and Chunlei Du, "Modeling and experimental verification of optical materials formed by stacked nanostrips," Opt. Express **18**, 14842-14849 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-14-14842

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### References

- W. Rotman, “Plasma Simulation by Artificial Dielectrics and Parallel-Plate Media,” IRE Trans. Antennas Propag. 10(1), 82–95 (1962). [CrossRef]
- J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]
- J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys. Condens. Matter 10(22), 4785–4809 (1998). [CrossRef]
- S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, “Wire media with negative effective permittivity: A quasi-static model,” Microw. Opt. Technol. Lett. 35(1), 47–51 (2002). [CrossRef]
- M. Silveirinha and C. Fernandes, “A Hybrid Method for the Efficient Calculation of the Band Structure of 3-D Metallic Crystals,” IEEE Trans. Microw. Theory Tech. 52(3), 889–902 (2004). [CrossRef]
- S. Brand, R. A. Abram, and M. A. Kaliteevski, “Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods,” Phys. Rev. B 75(3), 035102 (2007). [CrossRef]
- X. Wei, H. Shi, Q. Deng, X. Dong, C. Liu, Y. Lu, and C. Du, “Artificial metal with effective plasma frequency in near-infrared region,” Opt. Express 18(4), 3370–3378 (2010). [CrossRef] [PubMed]
- M. G. Silveirinha, “Nonlocal homogenization model for a periodic array of epsilon-negative rods,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046612 (2006). [CrossRef] [PubMed]
- M. G. Silveirinha, “Artificial plasma formed by connected metallic wires at infrared frequencies,” Phys. Rev. B 79(3), 035118 (2009). [CrossRef]
- S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002). [CrossRef] [PubMed]
- R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100(2), 023903–023907 (2008). [CrossRef] [PubMed]
- 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]
- N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]
- Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007). [CrossRef] [PubMed]
- G. Dolling, M. Wegener, and S. Linden, “Realization of a three-functional-layer negative-index photonic metamaterial,” Opt. Lett. 32(5), 551–553 (2007). [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(5775), 892–894 (2006). [CrossRef] [PubMed]
- V. Shrotriya, E. H. Wu, G. Li, Y. Yao, and Y. Yang, “Efficient light harvesting in multiple-device stacked structure for polymer solar cells,” Appl. Phys. Lett. 88(6), 064104 (2006). [CrossRef]
- D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002). [CrossRef]
- A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: Recent advances and outlook,” Metamaterials (Amst.) 2(1), 1–17 (2008). [CrossRef]
- J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005). [CrossRef] [PubMed]
- 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]
- 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]

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