## Low-loss single-layer metamaterial with negative index of refraction at visible wavelengths

Optics Express, Vol. 15, Issue 15, pp. 9320-9325 (2007)

http://dx.doi.org/10.1364/OE.15.009320

Acrobat PDF (483 KB)

### Abstract

We present a structure exhibiting a negative index of refraction at visible or near infrared frequencies using a single metal layer. This contrasts with recently developed structures based on metal-dielectric-metal composites. The proposed metamaterial consists of periodically arranged thick stripes interacting with each other to give rise to a negative permeability. Improved designs that allow for a negative index for both polarizations are also presented. The structures are numerically analyzed and it is shown that the dimensions can be engineered to shift the negative index band within a region ranging from telecommunication wavelengths down to blue light.

© 2007 Optical Society of America

## 1. Introduction

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

2. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Technol. **47**, 2075–2084 (1999). [CrossRef]

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

4. Costas M. Soukoulis, Stefan Linden, and Martin Wegener, “Negative refractive index at optical wavelengths,” Science **315**, 47–49 (2007). [CrossRef] [PubMed]

5. 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**, 223902 (2005). [CrossRef] [PubMed]

6. Michael Scalora et al., “Negative refraction and sub-wavelength focusing in the visible range using transparent metallodielectric stacks,” Opt. Express **15**, 508–529 (2007). [CrossRef] [PubMed]

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

8. U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, “Dual-band negative index metamaterial: Double-negative at 813 nm and single-negative at 772 nm,” http://arxiv.org/ftp/physics/papers/0612/0612247.pdf.

## 2. Negative index metamaterial

9. Zhiming Huang, Jianqiang Xue, Yun Hou, Junhao Chu, and D.H. Zhang, “Optical magnetic response from parallel plate metamaterials,” Phys. Rev. B **74**, 193105 (2006). [CrossRef]

10. Vladimir M. Shalaev, Wenshan Cai, Hsiao-Kuan Chettiar, Andrey K. Yuan, Vladimir P. Sarychev, Alexander V. Drachev, and Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. **30**, 3356–3358 (2005). [CrossRef]

*t*and width

*w*. The stripes are interrupted periodically by gaps of length

*s*. The incidence is normal to the structure (see Fig. 1(e)) with the

*E*field along the stripes and the

*H*field perpendicular to them. As far as the electric response is concerned, the metamaterial acts as a dilute plasmonic medium, i. e., a metal with a lower plasma frequency than that in bulk. In addition, the cuts in the stripes give rise to a resonance in the permittivity. According to Faraday’s law, the incident magnetic field induces an emf, which accounts for a current flow (thanks to a large thickness

*t*of the stripes) in an open loop normal to the

*H*field with opposite directions at each side of the gap. Since the current is interrupted by the gaps, we can consider the structure as an equivalent circuit which consists of an inductance in series with two capacitors, resulting in a resonant permeability that becomes negative in a certain band. This anti-symmetric mode generates a magnetic field that opposes the incident one above the resonance frequency, where the current phase is reversed, as Fig. 2 shows. Moreover, the permittivity is still negative in the magnetic resonance region giving rise to a negative index of refraction. Obviously, the metamaterial is sensible to polarization, in fact, it is almost transparent if we swap

*E*and

*H*. We can make it polarization independent by adding cut stripes normal to the original ones as in Fig. 1(d). The result is a symmetric medium made up of crosses very close to each other. We can go a step further and replicate the stripes (Fig. 1(b)). By doing so, we reinforce the magnetic resonance and shift it slightly. Note that the gap between the upper and lower stripes is of the same length as the one between horizontal stripes. Finally, we add double stripes parallel to

*H*and obtain square rings exhibiting negative refraction in both polarizations.

## 3. Numerical analysis

11. P.B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B **6**, 4370–4379 (1972). [CrossRef]

*ω*=1.37×10

_{p}^{16}s

^{-1}and the collision frequency is chosen to match data from [11

11. P.B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B **6**, 4370–4379 (1972). [CrossRef]

*n*and

*z*from the calculated S11 and S21, the traditional retrieval method [12

12. 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**, 195104 (2002). [CrossRef]

13. Xudong Chen, Tomasz M. Grzegorczyk, Bae-Ian Wu, Joe Pacheco Jr., and Jin Au Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E **70**, 016608 (2004). [CrossRef]

*ε*and

*µ*are obtained as

*n*=(

*εµ*)

^{1/2}and

*z*=(

*µ*/

*ε*)

^{1/2}. As an example, we simulate all structures with

*t*=150 nm,

*l*=106 nm,

*w*=54 nm and

*s*=30 nm (in designs 1(a) and 1(b) the length of the stripes is 2

*l*+2

*w*and their periodicity in the direction parallel to

*H*is chosen to be the same as in their symmetric counterparts). The results are depicted in Fig. 3. The use of an effective-medium model is justified since the structures dimension in the propagation direction is, depending on the design, from four to six times smaller than the wavelength. Moreover, the amplitude of high-order modes is negligible compared to the plane-wave one.

*ε*and

*µ*are very similar for all designs verifying that the stripes parallel to the electric field are the ones responsible for the negative index behavior. There is a dip in S21 around 0.95 µm (no transmission) due to the resonance in

*ε*, which is a consequence of the stripes not being continuous. The real part of the permeability has a strong resonance around 0.64 µm in all structures. At that frequency, the permittivity shows a characteristic antiresonant behavior [14

14. T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E **68**, 065602 (2003). [CrossRef]

*n*’ is negative). However, it is possible to adjust the geometrical parameters of this structure to make

*ε*’ and

*µ*’ negative in the same region as shown below. For the double stripe metamaterials (Figs. 1(b) and 1(c)), the permittivity becomes more negative, or equivalently, the effective plasma frequency gets higher. This can be ascribed to the higher metal filling factor in the direction normal to the electric field since the larger the filling factor is, the more the material resembles bulk metal. At this point, it is interesting to know how the negative index band shifts in frequency with dimensions scaling, being the most important variables the magnetic resonance frequency (

*f*) and the effective plasma frequency (

_{res}*f*). Since all structures have a very similar response, we will focus on the simplest one (structure in Fig. 1(a)). It is appropriate to note that fabrication of the designs presented above is not straightforward due to the high ratio between thickness

_{p}*t*and width

*w*, which is of the order of 3:1. To overcome this difficulty we can increase the width

*w*of the stripes and make it comparable to the thickness. Thus, we will scale the structure 1(a) with

*t*=

*w*and depict the evolution of

*f*and

_{res}*f*with a geometrical scaling factor (

_{p}*S*). As shown,

*f*does not vary linearly with

_{res}*S*as would occur with ideal metals or any metal at low frequencies. On the contrary, there exists saturation because the magnetic energy no longer dominates the kinetic one and both become comparable [5

5. 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**, 223902 (2005). [CrossRef] [PubMed]

*S*within this frequency range.

*S*

^{-1}<0.8) where

*f*is larger than

_{res}*f*and therefore the refractive index is not negative. In Fig. 4(b) we can see that

_{p}*f*increases when the spacing

_{res}*s*grows whilst

*f*remains almost unchanged. Hence, we have a way to invert the previous situation and make

_{p}*f*<

_{res}*f*by decreasing

_{p}*s*. The thickness

*t*and width

*w*also have influence in these two parameters and could be adjusted in order to tune the negative index band. As we scale down the structure

*s*becomes too small, complicating its fabrication. To avoid this, we can make s larger and compensate the resonance shift by scaling up the metamaterial. For instance, if we take the configuration of Fig. 4(b) with

*s*=30 nm, increase it to 50 nm and then apply

*S*≈ 1.1,

*f*remains in the same location. Regarding losses, the factor of merit (FOM) defined as FOM=|

_{res}*n*’/

*n*”| is usually taken as a measure of how good the metamaterial behaves. We show in Fig. 5 the extracted

*n*’,

*ε*’, µ’ and FOM for structure 1(a) with

*t*=

*w*=110 nm,

*s*=60 nm and a stripe length equal to 220 nm. In this case, the FOM is larger than 6 at the wavelength where

*n*’=-1 (464 nm). To our knowledge, this is the first metamaterial exhibiting negative refractive index at such high frequencies with only one metal layer.

## 4. Conclusion

## Acknowledgments

## References and Links

1. | A. Ricardo, Akhlesh Depine, and Lakhtakia, “A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity,” Microwave Opt. Technol. Lett. |

2. | J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Technol. |

3. | R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science |

4. | Costas M. Soukoulis, Stefan Linden, and Martin Wegener, “Negative refractive index at optical wavelengths,” Science |

5. | 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. |

6. | Michael Scalora et al., “Negative refraction and sub-wavelength focusing in the visible range using transparent metallodielectric stacks,” Opt. Express |

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

8. | U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, “Dual-band negative index metamaterial: Double-negative at 813 nm and single-negative at 772 nm,” http://arxiv.org/ftp/physics/papers/0612/0612247.pdf. |

9. | Zhiming Huang, Jianqiang Xue, Yun Hou, Junhao Chu, and D.H. Zhang, “Optical magnetic response from parallel plate metamaterials,” Phys. Rev. B |

10. | Vladimir M. Shalaev, Wenshan Cai, Hsiao-Kuan Chettiar, Andrey K. Yuan, Vladimir P. Sarychev, Alexander V. Drachev, and Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. |

11. | P.B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B |

12. | 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 |

13. | Xudong Chen, Tomasz M. Grzegorczyk, Bae-Ian Wu, Joe Pacheco Jr., and Jin Au Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E |

14. | T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E |

**OCIS Codes**

(160.4760) Materials : Optical properties

(260.2110) Physical optics : Electromagnetic optics

**ToC Category:**

Metamaterials

**History**

Original Manuscript: April 26, 2007

Revised Manuscript: June 18, 2007

Manuscript Accepted: June 19, 2007

Published: July 13, 2007

**Citation**

C. García-Meca, R. Ortuño, R. Salvador, A. Martínez, and J. Martí, "Low-loss single-layer metamaterial with negative index of refraction at visible wavelengths," Opt. Express **15**, 9320-9325 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-15-9320

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### References

- RicardoA. Depine and Akhlesh Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Technol. Lett. 41, 315-316 (2004). [CrossRef]
- J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Technol. 47, 2075-2084 (1999). [CrossRef]
- R. A. Shelby, D. R. Smith, S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001). [CrossRef] [PubMed]
- CostasM. Soukoulis, Stefan Linden, Martin Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007). [CrossRef] [PubMed]
- 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. 95,223902 (2005). [CrossRef] [PubMed]
- Michael Scalora et al., "Negative refraction and sub-wavelength focusing in the visible range using transparent metallodielectric stacks," Opt. Express 15, 508-529 (2007). [CrossRef] [PubMed]
- G. Dolling, M. Wegener, C. M. Soukoulis, S. Linden, "Negative-index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007). [CrossRef]
- U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-band negative index metamaterial: Double-negative at 813 nm and single-negative at 772 nm," http://arxiv.org/ftp/physics/papers/0612/0612247.pdf.
- Zhiming Huang, Jianqiang Xue, Yun Hou, Junhao Chu, and D.H. Zhang, "Optical magnetic response from parallel plate metamaterials," Phys. Rev. B 74, 193105 (2006). [CrossRef]
- VladimirM. Shalaev, Wenshan Cai, Uday K. Chettiar, Hsiao-Kuan Yuan, Andrey K. Sarychev, Vladimir P. Drachev, and Alexander V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005). [CrossRef]
- P.B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972). [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, 195104 (2002). [CrossRef]
- Xudong Chen, Tomasz M. Grzegorczyk, Bae-Ian Wu, Joe Pacheco, Jr., and Jin Au Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004). [CrossRef]
- T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602 (2003). [CrossRef]

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