## Near-infrared double negative metamaterials

Optics Express, Vol. 13, Issue 13, pp. 4922-4930 (2005)

http://dx.doi.org/10.1364/OPEX.13.004922

Acrobat PDF (191 KB)

### Abstract

We numerically demonstrate a metamaterial with both negative ε and negative µ over an overlapping near-infrared wavelength range resulting in a low loss negative-index material. Parametric studies optimizing this negative index are presented. This structure can be easily fabricated with standard semiconductor processing techniques.

© 2005 Optical Society of America

## 1. Introduction

1. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science **292**, 77–79 (2002). [CrossRef]

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

3. N. C. Panoiu and R. M. Osgood, “Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials,” Phys. Rev. E **68**, 016611(2003). [CrossRef]

4. N. C. Panoiu and R. M. Osgood, “Numerical investigation of negative refractive index metamaterials at infrared and optical frequencies,” Opt. Commun. **233**, 331 (2003). [CrossRef]

5. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science **303**, 1494–1496 (2004) [CrossRef] [PubMed]

7. Shuang Zhang, Wenjun Fan, A. Frauenglass, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Demonstration of Mid-Infrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,” Phys. Rev. Lett. **94**, 037402 (2005). [CrossRef] [PubMed]

8. Shuang Zhang, Wenjun fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Demonstration of Near-Infrared Negative-Index Materials,” Postdeadline Paper at OSA Topical Meeting on NanoPhotonics for Information Systems (April 15, 2005), at IQEC (May 26, 2005) and submitted to Phys. Rev. Lett. Also available at: http://arxiv.org/ftp/physics/papers/0504/0504208.pdf (2005)

9. Vladimir M. Shalaev, Wenshan Cai, Uday Chettiar, Hsiao-Kuan Yuan, Andrey K. Sarychev, Vladimir P. Drachev, and Alexander V. Kildishev, “Negative Index of Refraction in Optical Metamaterials,” http://arxiv.org/ftp/physics/papers/0504/0504091.pdf. (2005)

8. Shuang Zhang, Wenjun fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Demonstration of Near-Infrared Negative-Index Materials,” Postdeadline Paper at OSA Topical Meeting on NanoPhotonics for Information Systems (April 15, 2005), at IQEC (May 26, 2005) and submitted to Phys. Rev. Lett. Also available at: http://arxiv.org/ftp/physics/papers/0504/0504208.pdf (2005)

9. Vladimir M. Shalaev, Wenshan Cai, Uday Chettiar, Hsiao-Kuan Yuan, Andrey K. Sarychev, Vladimir P. Drachev, and Alexander V. Kildishev, “Negative Index of Refraction in Optical Metamaterials,” http://arxiv.org/ftp/physics/papers/0504/0504091.pdf. (2005)

*ε*=

*ε*

_{1}+

*iε*

_{2}and

*µ*=

*µ*

_{1}+

*iµ*

_{2}. To achieve a negative

*n*

_{1}, the imaginary part inside the square root needs to be <0, which can be satisfied for a sufficiently large imaginary term without requiring both

*ε*

_{1}and

*µ*

_{1}to be negative. In Ref. [8

8. Shuang Zhang, Wenjun fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Demonstration of Near-Infrared Negative-Index Materials,” Postdeadline Paper at OSA Topical Meeting on NanoPhotonics for Information Systems (April 15, 2005), at IQEC (May 26, 2005) and submitted to Phys. Rev. Lett. Also available at: http://arxiv.org/ftp/physics/papers/0504/0504208.pdf (2005)

*ε*

_{1}is negative and large,

*ε*

_{1}≫

*ε*

_{2}, giving,

*µ*

_{2}>0, which indicates that the real part of

*n*is negative even if

*µ*

_{1}>0. However, the sign of

*µ*

_{1}determines the relative magnitudes of the imaginary and real parts of the refractive index, with

*n*

_{1}>

*n*

_{2}for

*µ*

_{1}<0, and the opposite for

*µ*

_{1}<0. Thus, to achieve a negative index with a small imaginary part of the index, a negative permeability is required. In this paper, we numerically study a structure similar to that in Ref. [8

*ε*

_{1}and

*µ*

_{1}, and thus a reduced loss.

## 2. Proposed structure and simulation method

7. Shuang Zhang, Wenjun Fan, A. Frauenglass, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Demonstration of Mid-Infrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,” Phys. Rev. Lett. **94**, 037402 (2005). [CrossRef] [PubMed]

10. M. G. Moharam and T.K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. **71**, 811–818 (1981). [CrossRef]

11. B. K. Minhas, W. Fan, K. Agi, S. R. J. Brueck, and K. J. Malloy, “Metallic Inductive and Capacitive Grids: Theory and Experiment,” J. Opt. Soc. Am. A **19**, 1352–1359 (2002). [CrossRef]

*a*and

_{x}*a*are both fixed to 801 nm, less than the resonance wavelength of about 2 µm. The refractive index of the dielectric layer between the gold films is taken to be 1.5. The thicknesses of the Au/dielectric/Au layers are fixed at 30/60/30 nm, respectively. We systematically vary the linewidth of the gratings

_{y}*d*and

_{x}*d*in the simulation to study the magnetic and electric response of the structure. After the complex coefficients of transmission and reflection are obtained by RCWA, the effective refractive index and impedance can be extracted following the methods in Ref. [12, 13

_{y}13. S. O’Brien and J. B. Pendry, “Magnetic activity at infrared frequencies in structured metallic photonic crystals,” J. Phys. Condens. Matter **14**, 6383–6394 (2002). [CrossRef]

*z*), the use of an effective-medium model is justified [14

14. M. Qui, “Effective Index Method for Heterostructure-Slab-Waveguide-Based Two-Dimensional Photonic Crystals,” Appl. Phys. Lett. **81**, 1163–1165 (2002). [CrossRef]

*x*-

*y*plane with scales comparable to the wavelength. In our evaluations, the period of 801 nm is significantly smaller than the resonance wavelength of 2 µm. The present calculations are for a single three-layer structure and the dimension of the metamaterial in the z-direction is just the physical thickness of the three layers. In future work, this will be extended to thicker, more complex structures.

## 3. Simulation results for bulk gold parameters

*d*=0). Structures with three different Au grating linewidths (

_{y}*d*=400

_{x}*nm*, 500

*nm*, 600

*nm*) were modeled to investigate the effect of the linewidth on the position and strength of the magnetic resonance. Bulk gold dispersion parameters were used in the simulation [15]. As shown in Fig. 3, the resonance wavelength increases with the linewidth of Au gratings. This trend can be qualitatively explained by tracking the resonance of an equivalent L-C circuit; a wider grating corresponds to larger inductance and capacitance, which in turn leads to a larger resonance wavelength. As shown in the inset of Fig. 3, the resonance wavelength is linearly dependent on the Au linewidth

*d*. An Au linewidth of 500

_{x}*nm*(

*d*) was used in the simulation of the 2D negative index structures.

_{x}*d*was varied from 100- to 500-nm and transmission and reflection were calculated. Fig. 4 shows the simulated transmission spectra. With an increase of

_{y}*d*, the resonance shifts to shorter wavelength, indicating an interaction between the electric and magnetic structures. The transmission decreases (reflection increases) as

_{y}*d*becomes larger, due to metal polarizer effects. When

_{y}*d*is small, the resonance is characterized by dip in the transmission, for increasing

_{y}*d*a peak is clearly formed. The transmission phase exhibits a dip around the resonance, indicating that the light is advanced in phase at the resonance, characteristic of a negative index material.

_{y}*d*parameters, the minimum values of the real part of the refractive index range from about -4 to -6, initially increasing with linewidth, peaking at

_{y}*d*=300

_{y}*nm*, and then decreasing. From Figs. 4 and 5(a), for the sample with

*d*=100 nm, over 80% transmission is obtained over the negative index wavelength range, while for the sample with the largest

_{y}*d*, only <10% of the light is transmitted. The impedance of the structure, shown in Fig. 5(b), explains the high transmission for small

_{y}*d*; the real part of the impedance is closer to the condition for impedance matching (~1).

_{y}*n*, which is a good indicator of the “quality” of the negative refraction. For thin metal lines along the electric field, the ratio is ~6, as

*d*is increased, this quantity is shifted and reduced.

_{y}*µ*and permittivity

*ε*can be simply calculated as

*µ*=

*n*ζ and

*ε*=

*n*/ζ, the real parts of which are shown in Fig.7. The maximum negative permeability decreases with the increase of the line width, which is due in part to the shrinking fill factor of the magnetic resonant structure; the absolute value of the effective permittivity increases with line width as the screening by the metal lines increases. The increasing -

*ε*compensates the decreasing -

*µ*, explaining the comparative stability of the maximum of -

*n*. However, the impedance of the metamaterial is more mismatched to that of air with increasing

*d*leading to a much smaller transmission.

_{y}*d*is barely negative over the range of negative refraction. This is very similar to the case in reference [8

_{y}*d*=100

_{y}*nm*, over most of the range of negative refraction, both the real part of permeability and permittivity are negative, thus a double negative material with a dramatically lower loss is realized.

13. S. O’Brien and J. B. Pendry, “Magnetic activity at infrared frequencies in structured metallic photonic crystals,” J. Phys. Condens. Matter **14**, 6383–6394 (2002). [CrossRef]

*f*is a fill factor and

*µ*

_{∞}is the effective permeability for wavelengths far above the resonance. As shown in Ref. [17

17. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science **305**, 847–848 (2004). [CrossRef] [PubMed]

*µ*

_{∞}≠ 0, thus this parameter is estimated from the simulation results, and found to be around 0.6 for all the

*d*parameters. As an example, in Fig. 9 we show the excellent fit of to the simulated permeability for

_{y}*d*=100

_{y}*nm*, which has the strongest magnetic resonance.

*d*. The fill factor f decreases from 0.2 to 0.045 as

_{y}*d*is from 100- to 500-nm. The resonance frequency

_{y}*ω*

_{∞}increases slightly with

*d*(resonance wavelength

_{y}*λ*

_{0}decreases), while the dissipation term

*γ*increases by ~2. From Eq. (1), the strength of resonance is proportional to

*fω*

_{0}/

*γ*, thus, the decreasing resonance strength with increasing

*d*shown in Fig. 7 results from the decreasing fill factor and the increasing

_{y}*γ*.

## 4. Simulation with varying Au scattering loss

*d*=500

_{x}*nm*and

*d*=100

_{y}*nm*, and change the scattering loss of the Au film to 1-, 2- and 3-times that of bulk Au. Figure 9 (a) shows the real and imaginary parts of the effective index for the three different Au scattering parameters. On the short wavelength side of the resonance, which has the smaller imaginary part, the real part of the index decreases and the imaginary part increases. We plot again the quality factor, the ratio of the (-

*n*

_{1}) to

*n*

_{2}, in Fig. 9(b). The extremum of the ratio occurs at the same wavelength for the three scattering parameters, dropping from 6 to 2 as the scattering loss trebles. Nonetheless, for a considerable wavelength range, the ratio is larger than one.

## 5. Summary

9. Vladimir M. Shalaev, Wenshan Cai, Uday Chettiar, Hsiao-Kuan Yuan, Andrey K. Sarychev, Vladimir P. Drachev, and Alexander V. Kildishev, “Negative Index of Refraction in Optical Metamaterials,” http://arxiv.org/ftp/physics/papers/0504/0504091.pdf. (2005)

## Acknowledgments

## Reference and links

1. | R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science |

2. | J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. |

3. | N. C. Panoiu and R. M. Osgood, “Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials,” Phys. Rev. E |

4. | N. C. Panoiu and R. M. Osgood, “Numerical investigation of negative refractive index metamaterials at infrared and optical frequencies,” Opt. Commun. |

5. | T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science |

6. | Stefan Linden, Christian Enkrich, Martin Wegener, Jiangfeng Zhou, Thomas Koschny, and Costas M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science |

7. | Shuang Zhang, Wenjun Fan, A. Frauenglass, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Demonstration of Mid-Infrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,” Phys. Rev. Lett. |

8. | Shuang Zhang, Wenjun fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Demonstration of Near-Infrared Negative-Index Materials,” Postdeadline Paper at OSA Topical Meeting on NanoPhotonics for Information Systems (April 15, 2005), at IQEC (May 26, 2005) and submitted to Phys. Rev. Lett. Also available at: http://arxiv.org/ftp/physics/papers/0504/0504208.pdf (2005) |

9. | Vladimir M. Shalaev, Wenshan Cai, Uday Chettiar, Hsiao-Kuan Yuan, Andrey K. Sarychev, Vladimir P. Drachev, and Alexander V. Kildishev, “Negative Index of Refraction in Optical Metamaterials,” http://arxiv.org/ftp/physics/papers/0504/0504091.pdf. (2005) |

10. | M. G. Moharam and T.K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. |

11. | B. K. Minhas, W. Fan, K. Agi, S. R. J. Brueck, and K. J. Malloy, “Metallic Inductive and Capacitive Grids: Theory and Experiment,” J. Opt. Soc. Am. A |

12. | D. R. Smith and S. Schultz, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. |

13. | S. O’Brien and J. B. Pendry, “Magnetic activity at infrared frequencies in structured metallic photonic crystals,” J. Phys. Condens. Matter |

14. | M. Qui, “Effective Index Method for Heterostructure-Slab-Waveguide-Based Two-Dimensional Photonic Crystals,” Appl. Phys. Lett. |

15. | J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, |

16. | M.K. Karkkainen, “Numerical study of wave propagation in uniaxially anisotropic Lorentzian backward-wave slabs,” Phys. Rev. |

17. | J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science |

18. | Xiaolan Chen, Saleem H. Zaidi, S. R. J. Brueck, and D. J. Devine, “Interferometric Lithography of Sub- Micrometer Sparse Hole Arrays for Field-Emission Display Applications,” J. Vac. Sci. Technol. |

**OCIS Codes**

(260.2030) Physical optics : Dispersion

(290.3030) Scattering : Index measurements

(310.6860) Thin films : Thin films, optical properties

**ToC Category:**

Research Papers

**History**

Original Manuscript: April 29, 2005

Revised Manuscript: June 10, 2005

Published: June 27, 2005

**Citation**

Shuang Zhang, Wenjun Fan, K. J. Malloy, S.R. Brueck, N. C. Panoiu, and R. M. Osgood, "Near-infrared double negative metamaterials," Opt. Express **13**, 4922-4930 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-13-4922

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### References

- R. A. Shelby, D. R. Smith, S. Schultz, �??Experimental Verification of a Negative Index of Refraction,�?? Science 292, 77-79 (2002). [CrossRef]
- J. B. Pendry, �??Negative refraction makes a perfect lens,�?? Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
- N. C. Panoiu and R. M. Osgood, �??Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials,�?? Phys. Rev. E 68, 016611(2003). [CrossRef]
- N. C. Panoiu and R. M. Osgood, �??Numerical investigation of negative refractive index metamaterials at infrared and optical frequencies,�?? Opt. Commun. 233, 331 (2003). [CrossRef]
- T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, �??Terahertz Magnetic Response from Artificial Materials,�?? Science 303, 1494-1496 (2004). [CrossRef] [PubMed]
- Stefan Linden, Christian Enkrich, Martin Wegener, Jiangfeng Zhou, Thomas Koschny, and Costas M. Soukoulis, �??Magnetic Response of Metamaterials at 100 Terahertz,�?? Science 306, 1351-1353 (2004). [CrossRef] [PubMed]
- Shuang Zhang, Wenjun Fan, A. Frauenglass, B. Minhas, K. J. Malloy and S. R. J. Brueck, �??Demonstration of Mid-Infrared Resonant Magnetic Nanostructures Exhibiting a Negative Permeability,�?? Phys. Rev. Lett. 94, 037402 (2005). [CrossRef] [PubMed]
- Shuang Zhang, Wenjun fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, S. R. J. Brueck, �??Demonstration of Near-Infrared Negative-Index Materials,�?? Postdeadline Paper at OSA Topical Meeting on NanoPhotonics for Information Systems (April 15, 2005), at IQEC (May 26, 2005) and submitted to Phys. Rev. Lett. Also available at: <a href= "http://arxiv.org/ftp/physics/papers/0504/0504208.pdf"> http://arxiv.org/ftp/physics/papers/0504/0504208.pdf</a> (2005)
- Vladimir M. Shalaev, Wenshan Cai, Uday Chettiar, Hsiao-Kuan Yuan, Andrey K. Sarychev, Vladimir P. Drachev, Alexander V. Kildishev, �??Negative Index of Refraction in Optical Metamaterials,�?? <a href= "http://arxiv.org/ftp/physics/papers/0504/0504091.pdf.">http://arxiv.org/ftp/physics/papers/0504/0504091.pdf.</a> (2005)
- M. G. Moharam and T.K. Gaylord, �??Rigorous coupled-wave analysis of planar-grating diffraction,�?? J. Opt. Soc. Am. 71, 811-818 (1981). [CrossRef]
- B. K. Minhas, W. Fan, K. Agi, S. R. J. Brueck and K. J. Malloy, �??Metallic Inductive and Capacitive Grids: Theory and Experiment,�?? J. Opt. Soc. Am. A19, 1352-1359 (2002). [CrossRef]
- D. R. Smith and S. Schultz, �??Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,�?? Phys. Rev. B65, 195104. (2002)
- S. O'Brien and J. B. Pendry, �??Magnetic activity at infrared frequencies in structured metallic photonic crystals,�?? J. Phys. Condens. Matter 14, 6383-6394 (2002). [CrossRef]
- M. Qui, �??Effective Index Method for Heterostructure-Slab-Waveguide-Based Two-Dimensional Photonic Crystals,�?? Appl. Phys. Lett. 81, 1163-1165 (2002). [CrossRef]
- J. H. Weaver, C. Krafka, D. W. Lynch and E. E. Koch, Optical Properties of Metals, Physics Data Vols. I and II (Fachinformationzentrum, Karlsrube, Germany, 1981), Vol. 18-2.
- M.K. Karkkainen, �??Numerical study of wave propagation in uniaxially anisotropic Lorentzian backwardwave slabs,�?? Phys. Rev. E68, 026602 (2003).
- J. B. Pendry, L. Martin-Moreno and F. J. Garcia-Vidal, �??Mimicking Surface Plasmons with Structured Surfaces,�?? Science 305, 847-848 (2004). [CrossRef] [PubMed]
- Xiaolan Chen, Saleem H. Zaidi, S. R. J. Brueck and D. J. Devine, "Interferometric Lithography of Sub- Micrometer Sparse Hole Arrays for Field-Emission Display Applications," J. Vac. Sci. Technol. B14, 3339-3349 (1996).

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