## Experimental characterization of the dispersive behavior in a uniaxial metamaterial around plasma frequency |

Optics Express, Vol. 18, Issue 22, pp. 22631-22636 (2010)

http://dx.doi.org/10.1364/OE.18.022631

Acrobat PDF (922 KB)

### Abstract

In this paper, the dispersive behavior around the plasma frequency in a magnetically uniaxial metamaterial is experimentally investigated. We show by theoretical analysis, parameter retrieval and experiment that when material loss is considered, while the plasma frequency is defined by the frequency where the real part of permeability approaches zero, ultra fast phase velocity actually appears at a slightly lower frequency, due to the change of the dispersion diagram. Both parameter retrieval and experimental data show that within a narrow frequency band to the left of the plasma frequency, the inherent loss keeps finite and is much less than that in the corresponding resonant region. In a real metamaterial sample, an ultra fast phase velocity of 24,440 times the speed of light in free space is measured, and negative phase propagation due to the only negative permeability is observed. The existence of such ultra fast phase velocity with finite loss perfectly explains how the highly directivity antennas based on near-zero refractive index metamaterial work, and can be further used in other applications such as in-phase wave divider and coherent wave sources.

© 2010 OSA

## 1. Introduction

*c*in naturally occurring media that possess refractive indices greater than unity, we also know that it can be faster than

*c*without violating any known physical laws, for example, in a plasma medium with a relative permittivity of

2. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. **10**(4), 509–514 (1968). [CrossRef]

3. 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**(18), 4184–4187 (2000). [CrossRef] [PubMed]

4. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **70**(4), 046608 (2004). [CrossRef] [PubMed]

9. T. Jiang, Y. Luo, Z. Wang, L. Peng, J. Huangfu, W. Cui, W. Ma, H. Chen, and L. Ran, “Rainbow-like radiation from an omni-directional source placed in a uniaxial metamaterial slab,” Opt. Express **17**(9), 7068–7073 (2009). [CrossRef] [PubMed]

10. M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. **97**(15), 157403 (2006). [CrossRef] [PubMed]

## 2. Theoretical analysis

*x, y, z*) Cartesian coordinates ofAssume

*y*direction and a wave vector

*x*direction, which means

*x*direction at frequencies where

*k*-surface of

12. G. A. Zheng, “Abrupt change of reflectivity from the strongly anisotropic metamaterial,” Opt. Commun. **281**(8), 1941–1944 (2008). [CrossRef]

14. S. Qiao, G. A. Zheng, W. Ren, and L. X. Ran, “Possible abnormal group velocity in the normal dispersive anisotropic media,” J. Electromagn. Waves Appl. **22**(10), 1309–1317 (2008). [CrossRef]

## 3. Parameter retrieval

9. T. Jiang, Y. Luo, Z. Wang, L. Peng, J. Huangfu, W. Cui, W. Ma, H. Chen, and L. Ran, “Rainbow-like radiation from an omni-directional source placed in a uniaxial metamaterial slab,” Opt. Express **17**(9), 7068–7073 (2009). [CrossRef] [PubMed]

15. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. **47**(11), 2075–2084 (1999). [CrossRef]

*x*direction with a periodicity of 6 mm and 15 unit cells in the

*y*direction with a periodicity of 10 mm. Eight layers of such PCBs are aligned along the z direction spaced by 16 mm to form a slab-shaped sample with a width of 500 mm along the

*x*direction and a thickness of 105 mm in the

*z*direction. In such a slab, for an incidence with z-polarized magnetic field, magnetic resonances can be induced at X-band microwave frequencies inside the metallic rings, yielding a complex dispersion with a negative band of permeability along the

*z*direction. Meanwhile, there is no magnetic response in the

*x*and

*y*directions, allowing

16. D. R. Smith, S. Schultz, P. Markoš, 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]

17. X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco Jr, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **70**(1), 016608 (2004). [CrossRef] [PubMed]

## 4. Experimental investigation

*x*direction (such that

*x*-axis, are chosen. The phase at each point is measured using an Agilent 8722ES vector network analyzer, and the phase velocity along the

*x*direction is calculated by

*y*-axis represents

*c*, where

*c*is the speed of light in free space is experimentally obtained, and with the frequency moves to higher frequencies, the PV drastically falls. This variation trend of the PV versus frequency clearly reflects a plasma-like dispersion. As predicted before, when frequency moves from 9.3235 GHz toward lower frequencies, while the PV also drastically decreases, its direction is negative, meaning that in such lossy area, negative phase propagation, and therefore negative refraction, can be expected to occur without requiring simultaneously negative permittivity and permeability. Although the loss is substantial, the negative refraction at this frequency band is of interest and needs to be further investigated.

## 5. Conclusion

*c*is observed and the PV can be negative in an adjacent band. In the mean time, the loss is inherent but is also finite. Experimental results fit quite well with theoretically analysis and parameter retrieval. The ultra fast phase velocity along the x direction can be used to perfectly explain how the highly directivity antennas based on such uniaxial metamaterial work, and can be used in other applications such as in-phase wave divider and coherent wave sources. Moreover, at optical frequencies, similar dispersive behaviors can be found in the band diagrams of photonic crystals, indicating that ultra fast PV can also be found in optics, and therefore can be used in optical applications.

## Acknowledgements

## References and links

1. | L. Brillouin, |

2. | V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. |

3. | 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. |

4. | R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

5. | F. Zhang, S. Potet, and J. Caobonell, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE Trans. Microw. Theory Tech. |

6. | A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of epsilon -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

7. | B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. |

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

9. | T. Jiang, Y. Luo, Z. Wang, L. Peng, J. Huangfu, W. Cui, W. Ma, H. Chen, and L. Ran, “Rainbow-like radiation from an omni-directional source placed in a uniaxial metamaterial slab,” Opt. Express |

10. | M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. |

11. | M. Bozzi, L. Perregrini, D. Deslandes, K. Wu, and G. Conciaurol, “A compact, wideband, phase-equalized waveguide divider/combiner for power amplification,” Microwave Conference, 33rd European (2003). |

12. | G. A. Zheng, “Abrupt change of reflectivity from the strongly anisotropic metamaterial,” Opt. Commun. |

13. | S. Qiao, G. A. Zheng, H. Zhang, and L. X. Ran, “Transition behavior of k-surface: from hyperbola to ellipse,” Prog. Electromagn. Res. |

14. | S. Qiao, G. A. Zheng, W. Ren, and L. X. Ran, “Possible abnormal group velocity in the normal dispersive anisotropic media,” J. Electromagn. Waves Appl. |

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

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

17. | X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco Jr, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

**OCIS Codes**

(160.1190) Materials : Anisotropic optical materials

(160.3918) Materials : Metamaterials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: August 2, 2010

Revised Manuscript: September 27, 2010

Manuscript Accepted: October 1, 2010

Published: October 11, 2010

**Citation**

Dexin Ye, Shan Qiao, Jiangtao Huangfu, and Lixin Ran, "Experimental characterization of the dispersive behavior in a uniaxial metamaterial around plasma frequency," Opt. Express **18**, 22631-22636 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-22-22631

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### References

- L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).
- V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968). [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(18), 4184–4187 (2000). [CrossRef] [PubMed]
- R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004). [CrossRef] [PubMed]
- F. Zhang, S. Potet, and J. Caobonell, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE Trans. Microw. Theory Tech. 56(11), 2566–2573 (2008). [CrossRef]
- A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of epsilon -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(1), 016604 (2008). [CrossRef] [PubMed]
- B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008). [CrossRef] [PubMed]
- 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]
- T. Jiang, Y. Luo, Z. Wang, L. Peng, J. Huangfu, W. Cui, W. Ma, H. Chen, and L. Ran, “Rainbow-like radiation from an omni-directional source placed in a uniaxial metamaterial slab,” Opt. Express 17(9), 7068–7073 (2009). [CrossRef] [PubMed]
- M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006). [CrossRef] [PubMed]
- M. Bozzi, L. Perregrini, D. Deslandes, K. Wu, and G. Conciaurol, “A compact, wideband, phase-equalized waveguide divider/combiner for power amplification,” Microwave Conference, 33rd European (2003).
- G. A. Zheng, “Abrupt change of reflectivity from the strongly anisotropic metamaterial,” Opt. Commun. 281(8), 1941–1944 (2008). [CrossRef]
- S. Qiao, G. A. Zheng, H. Zhang, and L. X. Ran, “Transition behavior of k-surface: from hyperbola to ellipse,” Prog. Electromagn. Res. 81, 267–277 (2008). [CrossRef]
- S. Qiao, G. A. Zheng, W. Ren, and L. X. Ran, “Possible abnormal group velocity in the normal dispersive anisotropic media,” J. Electromagn. Waves Appl. 22(10), 1309–1317 (2008). [CrossRef]
- J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]
- D. R. Smith, S. Schultz, P. Markoš, 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]
- X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004). [CrossRef] [PubMed]

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