## Experimental verification of spoof surface plasmons in wire metamaterials |

Optics Express, Vol. 20, Issue 16, pp. 18238-18247 (2012)

http://dx.doi.org/10.1364/OE.20.018238

Acrobat PDF (1716 KB)

### Abstract

In this paper, we experimentally demonstrate the excitation of spoof surface plasmon polaritons (SPPs) on a wire-medium metamaterial slab in the microwave region. The spoof SPPs are excited on the opposite side of the slab from the source, which is desirable for applications such as sensing devices. Using the prism coupling method, we verify the excitation of spoof SPPs by measuring the reflection spectrum and near-field enhancement. The excitation of spoof SPPs is also verified by using the grating coupling method, where we demonstrate transmission enhancement through the metamaterial slab by placing diffraction gratings on both sides of the slab. Numerical investigation shows that the enhanced transmission can be attributed to the dispersion relations of the spoof SPPs and the periodicity of the diffraction grating. These properties can be used to realize extraordinary transmission and directional beaming.

© 2012 OSA

## 1. Introduction

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

2. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature **391**, 667–669 (1998). [CrossRef]

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

2. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature **391**, 667–669 (1998). [CrossRef]

3. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science **305**, 847–848 (2004). [CrossRef] [PubMed]

3. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science **305**, 847–848 (2004). [CrossRef] [PubMed]

4. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science **308**, 670–672 (2005). [CrossRef] [PubMed]

5. M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. **102**, 073901 (2009). [CrossRef] [PubMed]

6. D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. **47**, 2059–2074 (1999). [CrossRef]

7. M. Navarro-Cía, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express **17**, 18184–18195 (2009). [CrossRef] [PubMed]

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

9. M. A. Shapiro, G. Shvets, J. R. Sirigiri, and R. J. Temkin, “Spatial dispersion in metamaterials with negative dielectric permittivity and its effect on surface waves,” Opt. Lett. **31**, 2051–2053 (2006). [CrossRef] [PubMed]

10. A. Demetriadou and J. B. Pendry, “Taming spatial dispersion in wire metamaterial,” J. Phys.: Condens. Matter **20**, 295222 (2008). [CrossRef]

11. Y. Kushiyama, T. Uno, and T. Arima, “Novel negative permittivity structure and its application to excitation of surface plasmon in microwave frequency range,” IEICE Trans. Commun. **E93-B**, 2629–2635 (2010). [CrossRef]

11. Y. Kushiyama, T. Uno, and T. Arima, “Novel negative permittivity structure and its application to excitation of surface plasmon in microwave frequency range,” IEICE Trans. Commun. **E93-B**, 2629–2635 (2010). [CrossRef]

## 2. Principle

11. Y. Kushiyama, T. Uno, and T. Arima, “Novel negative permittivity structure and its application to excitation of surface plasmon in microwave frequency range,” IEICE Trans. Commun. **E93-B**, 2629–2635 (2010). [CrossRef]

*r*= 0.3 mm, and the radius of the sphere is

_{w}*r*= 1.73 mm. The dispersion relation of the structure is also shown in Fig. 1. In the calculation of the dispersion diagram, we employed a three-dimensional finite difference frequency domain (FDFD) method [13

_{s}13. K. Beilenhoff, W. Heinrich, and H. Hartnagel, “Improved finite-difference formulation in frequency domain for three-dimensional scattering problems,” IEEE Trans. Microwave Theory Tech. **40**, 540–546 (1992). [CrossRef]

14. V. Hernandez, J. E. Roman, and V. Vidal, “SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems,” ACM Trans. Math. Software **31**, 351–362 (2005). [CrossRef]

*ω*(

**k**), where

**k**represents the Bloch wavevector. As we can see in Fig. 1, the two degenerate modes due to the interaction of waves on both sides of the slab will be excited, which is also shown in the inset. It can be also seen that the parallel momentum of the spoof SPPs exceeds any wavenumber that radiative waves can have in the air at the same frequency. This requires momentum-matching methods for coupling the external plane wave to the surface state.

*k*

_{0}is the wavenumber in free space and

*n*is the refractive index of the dielectric prism. Therefore, if

*n*is sufficiently large, the left-hand side of the equation matches the dispersion relation of the SPPs. The parallel component of the wavevector is also controlled by diffraction gratings, as given by where

*k*=

_{x}*k*

_{0}sin

*θ*,

_{inc}*m*is a diffraction order, and Λ is the grating period. The diffraction grating is placed near the surface of the metamaterial. This grating layer can be considered as an additional surface structure of the metamaterial. We computed the dispersion relation of the surface with such a grating layer in Section 4.

## 3. Prism coupling

## 4. Grating coupling and plasmon-induced transmission

*ωa*/2

*πc*= 0.55 for normal incidence.

*a*= 23 mm. The gratings are made of a 23-mm-wide aluminum sheet put on a 3.5-mm-thick foam board. The foam boards are placed tight against the metamaterial face. Figure 8 shows the transmission for the metamaterial and the grating–metamaterial–grating configuration installed in the PPW. A large transmission is found around 2.45 GHz in the measured result and around 2.35 GHz in the simulated result. An enhanced transmission of 12 dB, achieved by inserting the gratings on both sides of the slab, is observed in the experiment. In the simulated result, four distinct peaks and two band gaps can be seen, while no such distinctions are found in the measured result. As we have seen, these distinctive peaks involve highly symmetrical spatial distributions. The experimental observation of such details requires more careful fabrication of the metamaterial. It is worth noting that the spatial symmetry can be exploited; the even symmetric modes can be reproduced by placing the PEC plane in the middle of the metamaterial. This can provide another means of experimentally verifying the numerical results and more opportunities for practical applications like frequency dependent beam steering.

## 5. Conclusions

## References and links

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

2. | T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature |

3. | J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science |

4. | A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science |

5. | M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett. |

6. | D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech. |

7. | M. Navarro-Cía, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express |

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

9. | M. A. Shapiro, G. Shvets, J. R. Sirigiri, and R. J. Temkin, “Spatial dispersion in metamaterials with negative dielectric permittivity and its effect on surface waves,” Opt. Lett. |

10. | A. Demetriadou and J. B. Pendry, “Taming spatial dispersion in wire metamaterial,” J. Phys.: Condens. Matter |

11. | Y. Kushiyama, T. Uno, and T. Arima, “Novel negative permittivity structure and its application to excitation of surface plasmon in microwave frequency range,” IEICE Trans. Commun. |

12. | R. Raether, |

13. | K. Beilenhoff, W. Heinrich, and H. Hartnagel, “Improved finite-difference formulation in frequency domain for three-dimensional scattering problems,” IEEE Trans. Microwave Theory Tech. |

14. | V. Hernandez, J. E. Roman, and V. Vidal, “SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems,” ACM Trans. Math. Software |

15. | A. Taflove and S. C. Hagness, |

**OCIS Codes**

(050.1950) Diffraction and gratings : Diffraction gratings

(240.6680) Optics at surfaces : Surface plasmons

(240.6690) Optics at surfaces : Surface waves

(160.1245) Materials : Artificially engineered materials

(160.3918) Materials : Metamaterials

(050.6624) Diffraction and gratings : Subwavelength structures

**ToC Category:**

Metamaterials

**History**

Original Manuscript: April 11, 2012

Revised Manuscript: July 14, 2012

Manuscript Accepted: July 15, 2012

Published: July 25, 2012

**Citation**

Yujiro Kushiyama, Takuji Arima, and Toru Uno, "Experimental verification of spoof surface plasmons in wire metamaterials," Opt. Express **20**, 18238-18247 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-18238

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### References

- J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85, 3966–3969 (2000). [CrossRef] [PubMed]
- T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391, 667–669 (1998). [CrossRef]
- J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305, 847–848 (2004). [CrossRef] [PubMed]
- A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science308, 670–672 (2005). [CrossRef] [PubMed]
- M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, “Microwave surface-plasmon-like modes on thin metamaterials,” Phys. Rev. Lett.102, 073901 (2009). [CrossRef] [PubMed]
- D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microwave Theory Tech.47, 2059–2074 (1999). [CrossRef]
- M. Navarro-Cía, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express17, 18184–18195 (2009). [CrossRef] [PubMed]
- J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely-low-frequency plasmons in metallic mesostructures,” Phys. Rev. Lett.76, 4773–4776 (1996). [CrossRef] [PubMed]
- M. A. Shapiro, G. Shvets, J. R. Sirigiri, and R. J. Temkin, “Spatial dispersion in metamaterials with negative dielectric permittivity and its effect on surface waves,” Opt. Lett.31, 2051–2053 (2006). [CrossRef] [PubMed]
- A. Demetriadou and J. B. Pendry, “Taming spatial dispersion in wire metamaterial,” J. Phys.: Condens. Matter20, 295222 (2008). [CrossRef]
- Y. Kushiyama, T. Uno, and T. Arima, “Novel negative permittivity structure and its application to excitation of surface plasmon in microwave frequency range,” IEICE Trans. Commun.E93-B, 2629–2635 (2010). [CrossRef]
- R. Raether, Surface Plasmons (Springer–Verlag, Berlin, 1988).
- K. Beilenhoff, W. Heinrich, and H. Hartnagel, “Improved finite-difference formulation in frequency domain for three-dimensional scattering problems,” IEEE Trans. Microwave Theory Tech.40, 540–546 (1992). [CrossRef]
- V. Hernandez, J. E. Roman, and V. Vidal, “SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems,” ACM Trans. Math. Software31, 351–362 (2005). [CrossRef]
- A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Third Edition (Artech House Publishers, 2000).

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