## Electromagnetic wave propagation in a Ag nanoparticle-based plasmonic power divider

Optics Express, Vol. 17, Issue 1, pp. 337-345 (2009)

http://dx.doi.org/10.1364/OE.17.000337

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### Abstract

In this paper a new silver (Ag) nanoparticle-based structure is presented which shows potential as a device for front end applications, in nano-interconnects or power dividers. A novel oxide bar ensures waveguiding and control of the signal strength with promising results. The structure is simulated by the two dimensional finite difference time domain (FDTD) method considering TM polarization and the Drude model. The effect of different wavelengths, material loss, gaps and particle sizes on the overall performance is discussed. It is found that the maximum signal strength remains along the Ag metallic nanoparticles and can be guided to targeted end points.

© 2009 Optical Society of America

## 1. Introduction

6. Z. Y. Zhang and Y. P. Zhao, “Tuning the optical absorption properties of Ag nanorods by their topologic shapes: A discrete dipole approximation calculation,” Appl. Phys. Lett. **89**, 023110–023113 (2006). [CrossRef]

8. D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, and R. Botet, “Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters,” Phys. Rev. Lett. **72**, 4149–4152 (1994). [CrossRef] [PubMed]

17. R. Sainidou and F. J. García de Abajo, “Plasmon guided modes in nanoparticle metamaterials,” Opt. Express **16**, 4499–4506 (2008). [CrossRef] [PubMed]

5. S. A. Maier and H. A. J. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. **98**, 011101–011110 (2005). [CrossRef]

18. N.C. Panoiu and R. M. Osgood, “Subwavelength nonlinear plasmonic nanowire,” Nano Lett. **4**, 2427–2430 (2004). [CrossRef]

21. H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. **81**, 1762–1764 (2002). [CrossRef]

## 2. Methodology

*ω*is the plasma frequency and Γ is the collision frequency. The values of

_{p}*ω*= 9.39×10

_{p}^{15}Hz and Γ = 0.3×10

^{15}Hz. Under consideration of the Drude model Maxwell’s equations are written as:

*D*-field in the FDTD formulation can be read as

_{x}*α*=

*e*

^{-ΓΔt}

27. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. **114**, 185–200 (1994). [CrossRef]

## 3. Modeling the device under consideration

## 4. Results and discussion

*I*, and the signal at center ‘C’ of the divider,

_{in}*I*. This ratio is shown with respect to different nanoparticles size and gaps “d” in between its nanoparticles.

_{O}_{o}=785 nm) and gap size (5 nm) is kept constant. The results are shown in Fig. 6, where Fig. 6(a) shows the normalized electric field for particle diameters ranging from 8-15 nm. Also here the signal delay is increasing with increasing particle diameter, which is due to the fact that for the chosen wavelength and particle diameters the resonance effect becomes less pronounced. These results are similar to the case with increasing gap size and are thus not further investigated.

_{reference}is the value of the field intensity without material loss and A

_{measured}is the value of the field intensity with material loss of the structure. These measurements are taken at point C (Fig. 1). The relative loss with respect to particle size and with gap size is shown in Fig. 7. It can be observed from these results that the relative loss is highly dependent on size of the nanoparticles and the gap in between them. For example when the gap size in between nanoparticles is 3 nm, the relative loss is around 17%. This loss increases with the increase in gap size and reaches to 50% when the gap size is 10 nm (particle size for different gap size measurements is fixed at 10 nm). Similarly, when the particle size is 8 nm, the relative loss is around 13%. This loss increases with an increase in the size of nanoparticles and it reaches to 58% when the particle size is 15 nm (gap size in these measurements is fixed at 5 nm).

## 5. Conclusions

## Acknowledgments

## References and links

1. | M. L. Brongersma and G. Kik, |

2. | M. Gerken, N. K. Dhar, A. K. Dutta, and M. S. Islam, |

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

4. | J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non- diffraction-limited light transport by gold nanowires,” Europhys. Lett. |

5. | S. A. Maier and H. A. J. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. |

6. | Z. Y. Zhang and Y. P. Zhao, “Tuning the optical absorption properties of Ag nanorods by their topologic shapes: A discrete dipole approximation calculation,” Appl. Phys. Lett. |

7. | Y. Xia and N. J. Halas, “Shape-controlled synthesis and surface plasmonic properties of metallic nanostructures,” MRS Bulletin |

8. | D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, and R. Botet, “Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters,” Phys. Rev. Lett. |

9. | D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner,, “Gap-dependent optical coupling of single “bowtie” nanoantennas resonant in the visible,” Nano Lett. |

10. | P. J. Kottmann and O. J. F. Martin, “Retardation-induced plasmon resonances in coupled nanoparticles,” Opt. Lett. |

11. | S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, “Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy,” Phys. Rev. B |

12. | K. Song and P. Mazmuder, “Surface plasmon dynamics of a metallic nano-particle,” IEEE Inter. Conf. on Nanotecchnology , August 2-5, Hong Kong, 637–643 (2007). |

13. | E. Hao and G. J. Schatz, “Electromagnetic fields around silver nanoparticles and dimmers,” J. Chem. Phys. |

14. | S. A. Maier and H. A. J. Atwater, “Energy transport in metal nanoparticle plasmon waveguides,” Mat. Res. Soc. Symp. Proc. |

15. | J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, “Plasmon polaritons of metallic nanowires for controlling submicron propagation of light,” Phys. Rev. B |

16. | H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, “Surface plasmon polariton propagation and combination in Y-shaped metallic channels,” Opt. Express |

17. | R. Sainidou and F. J. García de Abajo, “Plasmon guided modes in nanoparticle metamaterials,” Opt. Express |

18. | N.C. Panoiu and R. M. Osgood, “Subwavelength nonlinear plasmonic nanowire,” Nano Lett. |

19. | S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss,” Appl. Phys. Lett. |

20. | D. S. Citrin, “Coherent excitation transport in metal-nanoparticle chains,” Nano Lett. |

21. | H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, “Two-dimensional optics with surface plasmon polaritons,” Appl. Phys. Lett. |

22. | W. Namura, M. Ohtsu, and T. Yatusi, “Nanodot coupler wih a surface plasmon polariton condenser for optical far/near-field conversion,” App Phys Lett. |

23. | R. Zia and M. L. Brongersma, “Surface plasmon polariton analogue to Young’s double-slit experiment,” Nature Nanotech. |

24. | A. Taflove and S. G. Hagness, |

25. | W. M. Saj, “FDTD simulation of 2D Plasmon waveguide on silver nanorods in hexagonal lattice,” Opt. Express , |

26. | T. Grosges, A. Vial, and D. Barchiesi, “Models of near-field spectroscopic studies: comparison between Finite-Element and Finite-Difference methods,” Opt. Express , |

27. | J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. |

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(130.2790) Integrated optics : Guided waves

(230.7370) Optical devices : Waveguides

(240.6680) Optics at surfaces : Surface plasmons

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: November 11, 2008

Revised Manuscript: December 19, 2008

Manuscript Accepted: December 19, 2008

Published: January 2, 2009

**Citation**

Iftikhar Ahmed, Ching Eng PNG, Er-Ping Li, and Rüdiger Vahldieck, "Electromagnetic wave propagation in a Ag nanoparticle-based plasmonic power divider," Opt. Express **17**, 337-345 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-1-337

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### References

- M. L. Brongersma and G. Kik, Surface Plasmon Nanophotonics; Springer series in optical science, (2007).
- M. Gerken, N. K. Dhar, A. K. Dutta, and M. S. Islam, Nanophotonics for Communication: Materials, Devices, and Systems III, SPIE Society (2006).
- M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, "Electromagnetic energy transport via linear chains of silver nanoparticles," Opt. Lett. 23, 1331-1333, (1998). [CrossRef]
- J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, "Non-diffraction-limited light transport by gold nanowires," Europhys. Lett. 60, 663-669 (2002). [CrossRef]
- S. A. Maier and H. A. J. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys. 98, 011101-011110 (2005). [CrossRef]
- Z. Y. Zhang and Y. P. Zhao, "Tuning the optical absorption properties of Ag nanorods by their topologic shapes: A discrete dipole approximation calculation," Appl. Phys. Lett. 89, 023110 - 023113 (2006). [CrossRef]
- Y. Xia and N. J. Halas, "Shape-controlled synthesis and surface plasmonic properties of metallic nanostructures," MRS Bulletin 30, 338 - 348 (2005). [CrossRef]
- D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, and R. Botet, "Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters," Phys. Rev. Lett. 72, 4149 - 4152 (1994). [CrossRef] [PubMed]
- D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, "Gap-dependent optical coupling of single "bowtie" nanoantennas resonant in the visible," Nano Lett. 4, 957-961 (2004). [CrossRef]
- P. J. Kottmann and O. J. F. Martin, "Retardation-induced plasmon resonances in coupled nanoparticles," Opt. Lett. 26, 1096-1098 (2001). [CrossRef]
- S. A. Maier, M. L. Brongersma, P. G. Kik, and H. A. Atwater, "Observation of near-field coupling in metal nanoparticle chains using far-field polarization spectroscopy," Phys. Rev. B 65, 193408- 193411 (2002). [CrossRef]
- K. Song and P. Mazmuder, "Surface plasmon dynamics of a metallic nano-particle," IEEE Inter. Conf. on Nanotecchnology, August 2-5, Hong Kong, 637-643 (2007).
- E. Hao and G. J. Schatz, "Electromagnetic fields around silver nanoparticles and dimmers," J. Chem. Phys. 120, 357-366 (2004). [CrossRef] [PubMed]
- S. A. Maier and H. A. J. Atwater, "Energy transport in metal nanoparticle plasmon waveguides," Mat. Res. Soc. Symp. Proc. 777. T7.1.1- T7.1.12 (2003).
- J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, "Plasmon polaritons of metallic nanowires for controlling submicron propagation of light," Phys. Rev. B 60, 9061-9068(1999). [CrossRef]
- H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, "Surface plasmon polariton propagation and combination in Y-shaped metallic channels," Opt. Express 13, 10795-10800 (2005). [CrossRef] [PubMed]
- R. Sainidou and F. J. García de Abajo, "Plasmon guided modes in nanoparticle metamaterials," Opt. Express 16, 4499-4506 (2008). [CrossRef] [PubMed]
- N.C. Panoiu and R. M. Osgood, "Subwavelength nonlinear plasmonic nanowire," Nano Lett. 4, 2427-2430 (2004). [CrossRef]
- S. A. Maier, P. G. Kik, and H. A. Atwater, "Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss," Appl. Phys. Lett. 81, 1714-1716 (2002). [CrossRef]
- D. S. Citrin, "Coherent excitation transport in metal-nanoparticle chains," Nano Lett. 4, 1562- 1565 (2004). [CrossRef]
- H. Ditlbacher, J. R. Krenn, G. Schider, A. Leitner, and F. R. Aussenegg, "Two-dimensional optics with surface plasmon polaritons,"Appl. Phys. Lett. 81, 1762 - 1764 (2002). [CrossRef]
- W. Namura, M. Ohtsu, T. and Yatusi, "Nanodot coupler wih a surface plasmon polariton condenser for optical far/near-field conversion," App Phys Lett. 86, 181108 -181110 (2005). [CrossRef]
- R. Zia, and M. L. Brongersma, "Surface plasmon polariton analogue to Young’s double-slit experiment," Nature Nanotech. 2, 426- 429 (2007). [CrossRef]
- A. Taflove and S. G. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Boston, Artech House, 2005).
- W. M. Saj, "FDTD simulation of 2D Plasmon waveguide on silver nanorods in hexagonal lattice," Opt. Express, 13, 4818-4827 (2006) [CrossRef]
- T. Grosges, A. Vial, and D. Barchiesi, "Models of near-field spectroscopic studies: comparison between Finite-Element and Finite-Difference methods," Opt. Express, 13, 8483-8497 (2005). [CrossRef] [PubMed]
- J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 - 200 (1994). [CrossRef]

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