## Coherent magnetic plasmon modes in a contacting gold nano-sphere chain on a gold Slab |

Optics Express, Vol. 19, Issue 24, pp. 23782-23789 (2011)

http://dx.doi.org/10.1364/OE.19.023782

Acrobat PDF (2171 KB)

### Abstract

A coupled magnetic resonator waveguide, composed of a contacting gold nanosphere chain on a gold slab, is proposed and investigated. A broadband coherent magnetic plasmon mode can be excited in this one dimensional nanostructure. By employing the Lagrangian formalism and the Fourier transform method, the dispersion properties of the wave vector and group velocity of the magnetic plasmon mode are investigated. Small group velocity can be obtained from this system which can be applied as subwavelength slow wave waveguides.

© 2011 OSA

## 1. Introduction

1. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science **302**(5644), 419–422 (2003). [CrossRef] [PubMed]

2. N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. **111**(6), 3913–3961 (2011). [CrossRef] [PubMed]

3. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. **23**(17), 1331–1333 (1998). [CrossRef] [PubMed]

8. K. B. Crozier, E. Togan, E. Simsek, and T. Yang, “Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains,” Opt. Express **15**(26), 17482–17493 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-26-17482. [CrossRef] [PubMed]

9. K. H. Fung and C. T. Chan, “Plasmonic modes in periodic metal nanoparticle chains: a direct dynamic eigenmode analysis,” Opt. Lett. **32**(8), 973–975 (2007). [CrossRef] [PubMed]

12. K. H. Fung, R. C. Tang, and C. T. Chan, “Analytical properties of the plasmon decay profile in a periodic metal-nanoparticle chain,” Opt. Lett. **36**(12), 2206–2208 (2011). [CrossRef] [PubMed]

13. 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]

14. E. Shamonina, V. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. **92**(10), 6252–6261 (2002). [CrossRef]

15. O. Sydoruk, A. Radkovskaya, O. Zhuromskyy, E. Shamonina, M. Shamonin, C. J. Stevens, G. Faulkner, D. J. Edwards, and L. Solymar, “Tailoring the near-field guiding properties of magnetic metamaterials with two resonant elements per unit cell,” Phys. Rev. B **73**(22), 224406 (2006). [CrossRef]

16. H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. **97**(24), 243902 (2006). [CrossRef] [PubMed]

17. H. Liu, Y. M. Liu, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Coupled magnetic plasmons in metamaterials,” Physica Status Solidi B **246**(7), 1397–1406 (2009). [CrossRef]

18. H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B **79**(2), 024304 (2009). [CrossRef]

19. C. Zhu, H. Liu, S. M. Wang, T. Li, J. X. Cao, Y. J. Zheng, L. Li, Y. Wang, S. N. Zhu, and X. Zhang, “Electric and magnetic excitation of coherent magnetic plasmon waves in a one-dimensional meta-chain,” Opt. Express **18**(25), 26268–26273 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-18-25-26268. [CrossRef] [PubMed]

## 2. One magnetic resonator

*= 1.37*

_{p}*×*10

^{16}rad/s and γ = 12.24

*×*10

^{13}rad/s for infrared light. The dielectric is assumed to be glass with ε = 2.28 and μ = 1. The single unit structure is excited by a dipole source located at a distance of 120 nm in front of the first sphere. To obtain the EM resonance of the single unit, a set of finite-difference time-domain calculations using a commercial software package CST Microwave Studio is employed. The local magnetic field in the gap between the two spheres is recorded during simulations. A resonance peak is detected at 92.9 THz. The obtained distribution of current density inside the gold spheres and slab at this resonance frequency is demonstrated in Fig. 1(b). The two spheres are shown to exchange current at the contact point. The excitation also simultaneously induces current on the slab surface. The entire structure can be considered as a closed equivalent LC circuit [Fig. 1(d)]. The two spheres and the slab can be regarded as inductors in series. The middle dielectric layer works as a capacitor. However, the resonant current around the closed circuit can induce a strong magnetic field in the area surrounded by the two spheres and the slab. This phenomenon makes the structure behave like a magnetic dipole

## 3. Two coupled magnetic resonators

## 4. One chain of coupled magnetic resonators

*m*-th unit, and considering the coupling between magnetic resonators, the Lagrangian can be expressed as

^{7}The Fourier transform follows the formula,

## 5. Conclusion

## Acknowledgment

## References and links

1. | E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science |

2. | N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. |

3. | M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett. |

4. | M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B |

5. | S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B |

6. | J. R. Krenn, “Nanoparticle waveguides: Watching energy transfer,” Nat. Mater. |

7. | C. Girard and R. Quidant, “Near-field optical transmittance of metal particle chain waveguides,” Opt. Express |

8. | K. B. Crozier, E. Togan, E. Simsek, and T. Yang, “Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains,” Opt. Express |

9. | K. H. Fung and C. T. Chan, “Plasmonic modes in periodic metal nanoparticle chains: a direct dynamic eigenmode analysis,” Opt. Lett. |

10. | X. M. Bendana and F. J. García de Abajo, “Confined collective excitations of self-standing and supported planar periodic particle arrays,” Opt. Express |

11. | A. Alù, P. A. Belov, and N. Engheta, “Coupling and guided propagation along parallel chains of plasmonic nanoparticles,” New J. Phys. |

12. | K. H. Fung, R. C. Tang, and C. T. Chan, “Analytical properties of the plasmon decay profile in a periodic metal-nanoparticle chain,” Opt. Lett. |

13. | 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. |

14. | E. Shamonina, V. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. |

15. | O. Sydoruk, A. Radkovskaya, O. Zhuromskyy, E. Shamonina, M. Shamonin, C. J. Stevens, G. Faulkner, D. J. Edwards, and L. Solymar, “Tailoring the near-field guiding properties of magnetic metamaterials with two resonant elements per unit cell,” Phys. Rev. B |

16. | H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. |

17. | H. Liu, Y. M. Liu, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Coupled magnetic plasmons in metamaterials,” Physica Status Solidi B |

18. | H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B |

19. | C. Zhu, H. Liu, S. M. Wang, T. Li, J. X. Cao, Y. J. Zheng, L. Li, Y. Wang, S. N. Zhu, and X. Zhang, “Electric and magnetic excitation of coherent magnetic plasmon waves in a one-dimensional meta-chain,” Opt. Express |

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

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

(250.5403) Optoelectronics : Plasmonics

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: August 31, 2011

Revised Manuscript: September 26, 2011

Manuscript Accepted: October 10, 2011

Published: November 8, 2011

**Virtual Issues**

Vol. 7, Iss. 1 *Virtual Journal for Biomedical Optics*

**Citation**

K. N. Chen, H. Liu, S. M. Wang, Y. J. Zheng, C. Zhu, Y. Wang, and S. N. Zhu, "Coherent magnetic plasmon modes in a contacting gold nano-sphere chain on a gold Slab," Opt. Express **19**, 23782-23789 (2011)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-24-23782

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### References

- E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302(5644), 419–422 (2003). [CrossRef] [PubMed]
- N. J. Halas, S. Lal, W. S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev.111(6), 3913–3961 (2011). [CrossRef] [PubMed]
- M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic energy transport via linear chains of silver nanoparticles,” Opt. Lett.23(17), 1331–1333 (1998). [CrossRef] [PubMed]
- M. L. Brongersma, J. W. Hartman, and H. A. Atwater, “Electromagnetic energy transfer and switching in nanoparticle chain arrays below the diffraction limit,” Phys. Rev. B62(24), R16356 (2000). [CrossRef]
- S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal nanoparticle chain waveguides,” Phys. Rev. B67(20), 205402 (2003). [CrossRef]
- J. R. Krenn, “Nanoparticle waveguides: Watching energy transfer,” Nat. Mater.2(4), 210–211 (2003). [CrossRef] [PubMed]
- C. Girard and R. Quidant, “Near-field optical transmittance of metal particle chain waveguides,” Opt. Express12(25), 6141–6146 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-25-6141 . [CrossRef] [PubMed]
- K. B. Crozier, E. Togan, E. Simsek, and T. Yang, “Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains,” Opt. Express15(26), 17482–17493 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-26-17482 . [CrossRef] [PubMed]
- K. H. Fung and C. T. Chan, “Plasmonic modes in periodic metal nanoparticle chains: a direct dynamic eigenmode analysis,” Opt. Lett.32(8), 973–975 (2007). [CrossRef] [PubMed]
- X. M. Bendana and F. J. García de Abajo, “Confined collective excitations of self-standing and supported planar periodic particle arrays,” Opt. Express17(21), 18826–18835 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-21-18826 . [CrossRef] [PubMed]
- A. Alù, P. A. Belov, and N. Engheta, “Coupling and guided propagation along parallel chains of plasmonic nanoparticles,” New J. Phys.13(3), 033026 (2011). [CrossRef]
- K. H. Fung, R. C. Tang, and C. T. Chan, “Analytical properties of the plasmon decay profile in a periodic metal-nanoparticle chain,” Opt. Lett.36(12), 2206–2208 (2011). [CrossRef] [PubMed]
- 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]
- E. Shamonina, V. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys.92(10), 6252–6261 (2002). [CrossRef]
- O. Sydoruk, A. Radkovskaya, O. Zhuromskyy, E. Shamonina, M. Shamonin, C. J. Stevens, G. Faulkner, D. J. Edwards, and L. Solymar, “Tailoring the near-field guiding properties of magnetic metamaterials with two resonant elements per unit cell,” Phys. Rev. B73(22), 224406 (2006). [CrossRef]
- H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett.97(24), 243902 (2006). [CrossRef] [PubMed]
- H. Liu, Y. M. Liu, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Coupled magnetic plasmons in metamaterials,” Physica Status Solidi B246(7), 1397–1406 (2009). [CrossRef]
- H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B79(2), 024304 (2009). [CrossRef]
- C. Zhu, H. Liu, S. M. Wang, T. Li, J. X. Cao, Y. J. Zheng, L. Li, Y. Wang, S. N. Zhu, and X. Zhang, “Electric and magnetic excitation of coherent magnetic plasmon waves in a one-dimensional meta-chain,” Opt. Express18(25), 26268–26273 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-18-25-26268 . [CrossRef] [PubMed]

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