## Study on scattering coefficient of Surface Plasmon Polariton waves at interface of two metal-dielectric waveguides by using G-GFSIEM method

Optics Express, Vol. 18, Issue 8, pp. 8574-8586 (2010)

http://dx.doi.org/10.1364/OE.18.008574

Acrobat PDF (1290 KB)

### Abstract

Generalized Green’s Function Surface Integral Equation Method (G-GFSIEM) is used to study propagation of surface plasmon polariton waves at interface of two semi-infinite metal-dielectric waveguides. Reflection, transmission, and scattering coefficients for structures with different dielectric constants are calculated by using this method and by using energy conservation law. Conditions where scattering coefficient is maximized or minimized are studied. It is found that by using appropriate materials with specified dielectric constants, structures with required reflection, transmission, and scattering coefficients can be designed.

© 2010 OSA

## Introduction

2. R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip- scale technology,” Mater. Today **9**(7-8), 20–27 (2006). [CrossRef]

3. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface- plasmon circuitry,” Phys. Today **61**(5), 44–50 (2008). [CrossRef]

5. R. F. Oulton, D. F. Pile, Y. Liu, and X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implication for nanoscale cavities,” Phys. Rev. B **76**(3), 035408 (2007). [CrossRef]

6. G. I. Stegeman, A. A. Maradudin, and T. S. Rahman, “Refraction of a surface polariton by an interface,” Phys. Rev. B **23**(6), 2576–2585 (1981). [CrossRef]

5. R. F. Oulton, D. F. Pile, Y. Liu, and X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implication for nanoscale cavities,” Phys. Rev. B **76**(3), 035408 (2007). [CrossRef]

7. M. Zhong-Tuan, W. Pei, C. Yong, T. Hong-Gao, and M. Hai, “Pure reflection and refraction of a surface polariton by a matched waveguide structure,” Chin. Phys. Lett. **23**(9), 2545–2548 (2006). [CrossRef]

8. J. Elser and V. A. Podolskiy, “Scattering-free plasmonic optics with anisotropic metamaterials,” Phys. Rev. Lett. **100**(6), 066402 (2008). [CrossRef] [PubMed]

9. J. Jung and T. Søndergaard, “Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B **77**(24), 245310 (2008). [CrossRef]

11. J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B **79**(3), 035401 (2009). [CrossRef]

5. R. F. Oulton, D. F. Pile, Y. Liu, and X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implication for nanoscale cavities,” Phys. Rev. B **76**(3), 035408 (2007). [CrossRef]

## Review of theory

9. J. Jung and T. Søndergaard, “Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B **77**(24), 245310 (2008). [CrossRef]

*ω*and

**76**(3), 035408 (2007). [CrossRef]

## Numerical results

**76**(3), 035408 (2007). [CrossRef]

**76**(3), 035408 (2007). [CrossRef]

**76**(3), 035408 (2007). [CrossRef]

**76**(3), 035408 (2007). [CrossRef]

**76**(3), 035408 (2007). [CrossRef]

15. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. **23**(1), 413–422 (2005). [CrossRef]

## Conclusion

## Appendix A

9. J. Jung and T. Søndergaard, “Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B **77**(24), 245310 (2008). [CrossRef]

## Appendix B

**76**(3), 035408 (2007). [CrossRef]

## References and Links

1. | H. Raether, |

2. | R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip- scale technology,” Mater. Today |

3. | T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface- plasmon circuitry,” Phys. Today |

4. | S. I. Bozhevolnyi, ed., |

5. | R. F. Oulton, D. F. Pile, Y. Liu, and X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implication for nanoscale cavities,” Phys. Rev. B |

6. | G. I. Stegeman, A. A. Maradudin, and T. S. Rahman, “Refraction of a surface polariton by an interface,” Phys. Rev. B |

7. | M. Zhong-Tuan, W. Pei, C. Yong, T. Hong-Gao, and M. Hai, “Pure reflection and refraction of a surface polariton by a matched waveguide structure,” Chin. Phys. Lett. |

8. | J. Elser and V. A. Podolskiy, “Scattering-free plasmonic optics with anisotropic metamaterials,” Phys. Rev. Lett. |

9. | J. Jung and T. Søndergaard, “Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B |

10. | T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi |

11. | J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B |

12. | J. D. Jackson, |

13. | F. Paris, and J. Canas, |

14. | E. D. Palik, ed., |

15. | A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. |

**OCIS Codes**

(230.7370) Optical devices : Waveguides

(240.0240) Optics at surfaces : Optics at surfaces

(240.6680) Optics at surfaces : Surface plasmons

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: February 17, 2010

Revised Manuscript: March 17, 2010

Manuscript Accepted: March 31, 2010

Published: April 8, 2010

**Citation**

Nafiseh Zavareian and Reza Massudi, "Study on scattering coefficient of Surface Plasmon Polariton waves at interface of two metal-dielectric waveguides by using G-GFSIEM method," Opt. Express **18**, 8574-8586 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-8-8574

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### References

- H. Raether, Surface plasmons on smooth and rough surfaces and on grating (Springer-Verlag, Berlin, 1988).
- R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip- scale technology,” Mater. Today 9(7-8), 20–27 (2006). [CrossRef]
- T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface- plasmon circuitry,” Phys. Today 61(5), 44–50 (2008). [CrossRef]
- S. I. Bozhevolnyi, ed., Plasmonic Nanoguides and Circuits (Pan Stanford, Singapore, 2009).
- R. F. Oulton, D. F. Pile, Y. Liu, and X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implication for nanoscale cavities,” Phys. Rev. B 76(3), 035408 (2007). [CrossRef]
- G. I. Stegeman, A. A. Maradudin, and T. S. Rahman, “Refraction of a surface polariton by an interface,” Phys. Rev. B 23(6), 2576–2585 (1981). [CrossRef]
- M. Zhong-Tuan, W. Pei, C. Yong, T. Hong-Gao, and M. Hai, “Pure reflection and refraction of a surface polariton by a matched waveguide structure,” Chin. Phys. Lett. 23(9), 2545–2548 (2006). [CrossRef]
- J. Elser and V. A. Podolskiy, “Scattering-free plasmonic optics with anisotropic metamaterials,” Phys. Rev. Lett. 100(6), 066402 (2008). [CrossRef] [PubMed]
- J. Jung and T. Søndergaard, “Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B 77(24), 245310 (2008). [CrossRef]
- T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi 244(10), 3448–3462 (2007) (b). [CrossRef]
- J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B 79(3), 035401 (2009). [CrossRef]
- J. D. Jackson, Classical electrodynamics, (John Wiley & Sons, New York, 1999), p. 479.
- F. Paris, and J. Canas, Boundary element method-fundamentals and applications (Oxford University Press, 1997).
- E. D. Palik, ed., The Handbook of optical constants of solids (Academic Press, New York, NY 1997)
- A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005). [CrossRef]

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