## Novel hybrid plasmonic waveguide consisting of two identical dielectric nanowires symmetrically placed on each side of a thin metal film |

Optics Express, Vol. 20, Issue 18, pp. 20535-20544 (2012)

http://dx.doi.org/10.1364/OE.20.020535

Acrobat PDF (1484 KB)

### Abstract

It is well-known that, a dielectric cylinder on a metal surface offers the advantage of not yielding singular field, which would effectively reduce the propagation loss as opposed to a rectangle-shaped waveguide on a metal surface. In this article, a novel hybrid plasmonic waveguide consisting of two identical dielectric nanowires symmetrically placed on each side of a thin metal film is presented. With the strong interaction between the dielectric cylindrical waveguide mode and long-range surface plasmon polaritons (LRSPP) mode of a thin metal film, deep-subwavelength mode confinement can be achieved. Compared with the hybrid plasmonic mode guided in only one dielectric nanowire above a metal film, a much larger propagation length as well as improved figure of merit (FoM) can be simultaneously realized. A typical propagation length is 434μm, and optical field is confined into an ultra-small area of approximately 0.0096μm^{2} at 1.55μm. This structure could enable various applications such as nanophotonic waveguides, high-quality nanolasers, and optical trapping and transportation of nanoparticles and biomolecules.

© 2012 OSA

## 1. Introduction

1. M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science **292**(5523), 1897–1899 (2001). [CrossRef] [PubMed]

4. R. Yan, D. Gargas, and P. D. Yang, “Nanowire photonics,” Nat. Photonics **3**(10), 569–576 (2009). [CrossRef]

5. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface Plasmon subwavelength optics,” Nature **424**(6950), 824–830 (2003). [CrossRef] [PubMed]

6. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science **311**(5758), 189–193 (2006). [CrossRef] [PubMed]

7. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics **2**(8), 496–500 (2008). [CrossRef]

24. J. T. Kim and S. Choi, “Hybrid plasmonic slot waveguides with sidewall slope,” IEEE Photon. Technol. Lett. **24**(3), 170–172 (2012). [CrossRef]

16. R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature **461**(7264), 629–632 (2009). [CrossRef] [PubMed]

25. P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon. **1**(3), 484–588 (2009). [CrossRef]

26. Y. Bian, Z. Zheng, X. Zhao, J. Zhu, and T. Zhou, “Symmetric hybrid surface plasmon polariton waveguides for 3D photonic integration,” Opt. Express **17**(23), 21320–21325 (2009). [CrossRef] [PubMed]

28. L. Chen, X. Li, G. Wang, W. Li, S. Chen, L. Xiao, and D. Gao, “A silicon-based 3-D hybrid long-range plasmonic waveguide for nanophotonic integration,” J. Lightwave Technol. **30**(1), 163–168 (2012). [CrossRef]

11. M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. **21**(6), 362–364 (2009). [CrossRef]

7. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics **2**(8), 496–500 (2008). [CrossRef]

18. X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. **11**(2), 321–328 (2011). [CrossRef] [PubMed]

## 2. Geometry and modal properties of the proposed hybrid plasmonic waveguide

_{2}and the metallic film is silver with thickness of t = 20nm and permittivity of

29. P. B. Johnson and R. W. Christy, “optical constants of the noble metals,” Phys. Rev. B **6**(12), 4370–4379 (1972). [CrossRef]

*d*, and the dielectric gap width, h, to adjust the mode field distribution, and propagation length,

7. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics **2**(8), 496–500 (2008). [CrossRef]

_{m}, is defined as the ratio of the total mode energy and the peak energy density:where W

_{m}and W(

**r**) are the electromagnetic energy and energy density respectively (per unit length along the direction of propagation). The normalized modal area is defined as A

_{m}/A

_{0}, where A

_{0}represents the diffraction-limited area in free space, A

_{0}= λ

^{2}/4.

_{m}/A

_{0}, on

_{2}-Ag-SiO

_{2}model. As the gap distance increases, the hybrid mode tends to confine light energy both in the gaps and dielectric nanowires [Fig. 2(d)]. For a large cylinder diameter and gap distance, the hybrid waveguide supports a cylinder-like dielectric guided mode that the electromagnetic energy is confined in the two dielectric nanowires [Fig. 2(e)]. In this case, the propagation length is much bigger than that of the LRSPP mode in a pure SiO

_{2}-Ag- SiO

_{2}, but at the cost of much larger modal area as opposed to that in Figs. 2(b) and 2(c), where a small gap distance is employed. To balance the modal area and propagation length, an optimum combination of the gap distance and cylinder diameter is required. We can also see from Fig. 2(a) and Fig. 3 that there exists a point with

26. Y. Bian, Z. Zheng, X. Zhao, J. Zhu, and T. Zhou, “Symmetric hybrid surface plasmon polariton waveguides for 3D photonic integration,” Opt. Express **17**(23), 21320–21325 (2009). [CrossRef] [PubMed]

28. L. Chen, X. Li, G. Wang, W. Li, S. Chen, L. Xiao, and D. Gao, “A silicon-based 3-D hybrid long-range plasmonic waveguide for nanophotonic integration,” J. Lightwave Technol. **30**(1), 163–168 (2012). [CrossRef]

## 3. Mode character and coupling strength

_{2}-Ag- SiO

_{2}model. This is because that the LRSPP mode is coupled with the dielectric cylinder waveguide mode, which induces a much higher effective index [7

**2**(8), 496–500 (2008). [CrossRef]

28. L. Chen, X. Li, G. Wang, W. Li, S. Chen, L. Xiao, and D. Gao, “A silicon-based 3-D hybrid long-range plasmonic waveguide for nanophotonic integration,” J. Lightwave Technol. **30**(1), 163–168 (2012). [CrossRef]

**2**(8), 496–500 (2008). [CrossRef]

_{2}-Ag-SiO

_{2}model, respectively .

**2**(8), 496–500 (2008). [CrossRef]

**2**(8), 496–500 (2008). [CrossRef]

18. X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. **11**(2), 321–328 (2011). [CrossRef] [PubMed]

18. X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. **11**(2), 321–328 (2011). [CrossRef] [PubMed]

**11**(2), 321–328 (2011). [CrossRef] [PubMed]

## 4. Figure of merit

_{m}[30

30. R. Buckley and P. Berini, “Figures of merit for 2D surface plasmon waveguides and application to metal stripes,” Opt. Express **15**(19), 12174–12182 (2007). [CrossRef] [PubMed]

_{e}, defined as the area bounded by the closed 1/e field magnitude contour relative to the global field maximum, has been widely used to measure the mode area of plasmonic waveguide [30

30. R. Buckley and P. Berini, “Figures of merit for 2D surface plasmon waveguides and application to metal stripes,” Opt. Express **15**(19), 12174–12182 (2007). [CrossRef] [PubMed]

_{e}, for the two waveguides on the cylindrical diameter

_{e}is always larger than that for the previous hybrid plasmonic mode. This is because the electromagnetic field is located on both sides of metal film for the hybrid LRSPP waveguide. When the cylindrical diameter is very small, the confinement for both structures is relatively weak as a large portion of light field expands into the cladding. We can get an optimum mode confinement at around

_{e}can be smaller than A

_{m}as

_{e}is larger than A

_{m}when

_{e}becomes smaller than A

_{m}.

*d*for h = 5nm, and 10nm. The mode size used to evaluate FoM in Fig. 7(a) is A

_{m}, while that for Fig. 7(b) is A

_{e}. It can be seen that, the FoM for the hybrid LRSPP mode is always larger than that for the previous hybrid plasmonic mode in the whole range of nanowire diameter

*d*. For both of hybrid waveguides, the minimum FoM occurs at approximately

*d*= 250nm, at which the FoM for the hybrid LRSPP mode is 7 times as large as that for the previous hybrid plasmonic mode in Fig. 7(a), while this value is approximately 7.8 times in Fig. 7(b). We can see that, the present hybrid LRSPP waveguide is superior to the previous plasmonic waveguides since it shows a much longer propagation distance for similar degrees of confinement.

31. T. Kuykendall, P. J. Pauzauskie, Y. Zhang, J. Goldberger, D. Sirbuly, J. Denlinger, and P. Yang, “Crystallographic alignment of high-density gallium nitride nanowire arrays,” Nat. Mater. **3**(8), 524–528 (2004). [CrossRef] [PubMed]

_{2}substrate and cover the nanowire with a SiO

_{2}cladding. The silver film will later be deposited using sputtering and/or E-beam evaporation with a high precision. Using the same method, we can form the upper SiO

_{2}layer, Si nanowire, and SiO

_{2}cladding in succession. We believe that, at least in principle, the present structure can be fabricated by current nano-fabrication technology. However, compared with the rectangular-shaped waveguides, the fabrication process for the present hybrid plasmonic waveguide is by no means easy since placing nanowires precisely to implement an integrated nanophotonic circuit is very challenging by current nanofabrication technology.

## 5. Conclusion

## Acknowledgment

## References and links

1. | M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science |

2. | H. Kind, H. Q. Yan, B. Messer, M. Law, and P. D. Yang, “Nanowire ultraviolet photodetectors and optical switches,” Adv. Mater. (Deerfield Beach Fla.) |

3. | X. F. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature |

4. | R. Yan, D. Gargas, and P. D. Yang, “Nanowire photonics,” Nat. Photonics |

5. | W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface Plasmon subwavelength optics,” Nature |

6. | E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science |

7. | R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics |

8. | M. Z. Alam, J Meier, J S. Aitchison, and M Mojahedi, “Super mode propagation in low index medium,” CLEO/QELS, Paper ID JThD112, 2007. |

9. | R. Salvador, R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top. Quantum Electron. |

10. | R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys. |

11. | M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett. |

12. | D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express |

13. | Y. Zhao and L. Zhu, “Coaxial hybrid plasmonic nanowire waveguides,” J. Opt. Soc. Am. B |

14. | H. Benisty and M. Besbes, “Plasmonic inverse rib waveguiding for tight confinement and smooth interface definition,” J. Appl. Phys. |

15. | X. Y. Zhang, A. Hu, J. Z. Wen, T. Zhang, X. J. Xue, Y. Zhou, and W. W. Duley, “Numerical analysis of deep sub-wavelength integrated plasmonic devices based on Semiconductor-Insulator-Metal strip waveguides,” Opt. Express |

16. | R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature |

17. | D. Chen, “Cylindrical hybrid plasmonic waveguide for subwavelength confinement of light,” Appl. Opt. |

18. | X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. |

19. | Y. Bian, Z. Zheng, Y. Liu, J. Liu, J. Zhu, and T. Zhou, “Hybrid wedge plasmon polariton waveguide with good fabrication-error-tolerance for ultra-deep-subwavelength mode confinement,” Opt. Express |

20. | V. D. Ta, R. Chen, and H. D. Sun, “Wide-range coupling between surface plasmon polariton and cylindrical dielectric waveguide mode,” Opt. Express |

21. | Y. Bian, Z. Zheng, Y. Liu, J. Zhu, and T. Zhou, “Coplanar plasmonic nanolasers based on edge-coupled hybrid plasmonic waveguides,” IEEE Photon. Technol. Lett. |

22. | M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “Compact and silicon-on-insulator-compatible hybrid plasmonic TE-pass polarizer,” Opt. Lett. |

23. | V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, “Experimental demonstration of low-loss optical waveguiding at deep sub-wavelength scales,” Nat. Commun. |

24. | J. T. Kim and S. Choi, “Hybrid plasmonic slot waveguides with sidewall slope,” IEEE Photon. Technol. Lett. |

25. | P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon. |

26. | Y. Bian, Z. Zheng, X. Zhao, J. Zhu, and T. Zhou, “Symmetric hybrid surface plasmon polariton waveguides for 3D photonic integration,” Opt. Express |

27. | B. Yun, G. Hu, Y. Ji, and Y. Cui, “Characteristics analysis of a hybrid surface plasmonic waveguide with nanometric confinement and high optical intensity,” J. Opt. Soc. Am. B |

28. | L. Chen, X. Li, G. Wang, W. Li, S. Chen, L. Xiao, and D. Gao, “A silicon-based 3-D hybrid long-range plasmonic waveguide for nanophotonic integration,” J. Lightwave Technol. |

29. | P. B. Johnson and R. W. Christy, “optical constants of the noble metals,” Phys. Rev. B |

30. | R. Buckley and P. Berini, “Figures of merit for 2D surface plasmon waveguides and application to metal stripes,” Opt. Express |

31. | T. Kuykendall, P. J. Pauzauskie, Y. Zhang, J. Goldberger, D. Sirbuly, J. Denlinger, and P. Yang, “Crystallographic alignment of high-density gallium nitride nanowire arrays,” Nat. Mater. |

**OCIS Codes**

(130.2790) Integrated optics : Guided waves

(240.6680) Optics at surfaces : Surface plasmons

(250.5300) Optoelectronics : Photonic integrated circuits

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: June 18, 2012

Revised Manuscript: August 3, 2012

Manuscript Accepted: August 3, 2012

Published: August 22, 2012

**Citation**

Lin Chen, Tian Zhang, Xun Li, and Weiping Huang, "Novel hybrid plasmonic waveguide consisting of two identical dielectric nanowires symmetrically placed on each side of a thin metal film," Opt. Express **20**, 20535-20544 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-18-20535

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### References

- M. H. Huang, S. Mao, H. Feick, H. Yan, Y. Wu, H. Kind, E. Weber, R. Russo, and P. D. Yang, “Room-temperature ultraviolet nanowire nanolasers,” Science292(5523), 1897–1899 (2001). [CrossRef] [PubMed]
- H. Kind, H. Q. Yan, B. Messer, M. Law, and P. D. Yang, “Nanowire ultraviolet photodetectors and optical switches,” Adv. Mater. (Deerfield Beach Fla.)14(2), 158–160 (2002). [CrossRef]
- X. F. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature421(6920), 241–245 (2003). [CrossRef] [PubMed]
- R. Yan, D. Gargas, and P. D. Yang, “Nanowire photonics,” Nat. Photonics3(10), 569–576 (2009). [CrossRef]
- W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface Plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]
- E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006). [CrossRef] [PubMed]
- R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008). [CrossRef]
- M. Z. Alam, J Meier, J S. Aitchison, and M Mojahedi, “Super mode propagation in low index medium,” CLEO/QELS, Paper ID JThD112, 2007.
- R. Salvador, R. Salvador, A. Martinez, C. Garcia-Meca, R. Ortuno, and J. Marti, “Analysis of hybrid dielectric plasmonic waveguides,” IEEE J. Sel. Top. Quantum Electron.14(6), 1496–1501 (2008). [CrossRef]
- R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” New J. Phys.10(10), 105018 (2008). [CrossRef]
- M. Fujii, J. Leuthold, and W. Freude, “Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides,” IEEE Photon. Technol. Lett.21(6), 362–364 (2009). [CrossRef]
- D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express17(19), 16646–16653 (2009). [CrossRef] [PubMed]
- Y. Zhao and L. Zhu, “Coaxial hybrid plasmonic nanowire waveguides,” J. Opt. Soc. Am. B27(6), 1260–1265 (2010). [CrossRef]
- H. Benisty and M. Besbes, “Plasmonic inverse rib waveguiding for tight confinement and smooth interface definition,” J. Appl. Phys.108(6), 063108 (2010). [CrossRef]
- X. Y. Zhang, A. Hu, J. Z. Wen, T. Zhang, X. J. Xue, Y. Zhou, and W. W. Duley, “Numerical analysis of deep sub-wavelength integrated plasmonic devices based on Semiconductor-Insulator-Metal strip waveguides,” Opt. Express18(18), 18945–18959 (2010). [CrossRef] [PubMed]
- R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature461(7264), 629–632 (2009). [CrossRef] [PubMed]
- D. Chen, “Cylindrical hybrid plasmonic waveguide for subwavelength confinement of light,” Appl. Opt.49(36), 6868–6871 (2010). [CrossRef] [PubMed]
- X. Yang, Y. Liu, R. F. Oulton, X. Yin, and X. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett.11(2), 321–328 (2011). [CrossRef] [PubMed]
- Y. Bian, Z. Zheng, Y. Liu, J. Liu, J. Zhu, and T. Zhou, “Hybrid wedge plasmon polariton waveguide with good fabrication-error-tolerance for ultra-deep-subwavelength mode confinement,” Opt. Express19(23), 22417–22422 (2011). [CrossRef] [PubMed]
- V. D. Ta, R. Chen, and H. D. Sun, “Wide-range coupling between surface plasmon polariton and cylindrical dielectric waveguide mode,” Opt. Express19(14), 13598–13603 (2011). [CrossRef] [PubMed]
- Y. Bian, Z. Zheng, Y. Liu, J. Zhu, and T. Zhou, “Coplanar plasmonic nanolasers based on edge-coupled hybrid plasmonic waveguides,” IEEE Photon. Technol. Lett.23(13), 884–886 (2011). [CrossRef]
- M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “Compact and silicon-on-insulator-compatible hybrid plasmonic TE-pass polarizer,” Opt. Lett.37(1), 55–57 (2012). [CrossRef] [PubMed]
- V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, “Experimental demonstration of low-loss optical waveguiding at deep sub-wavelength scales,” Nat. Commun.2, 331 (2011). [CrossRef]
- J. T. Kim and S. Choi, “Hybrid plasmonic slot waveguides with sidewall slope,” IEEE Photon. Technol. Lett.24(3), 170–172 (2012). [CrossRef]
- P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon.1(3), 484–588 (2009). [CrossRef]
- Y. Bian, Z. Zheng, X. Zhao, J. Zhu, and T. Zhou, “Symmetric hybrid surface plasmon polariton waveguides for 3D photonic integration,” Opt. Express17(23), 21320–21325 (2009). [CrossRef] [PubMed]
- B. Yun, G. Hu, Y. Ji, and Y. Cui, “Characteristics analysis of a hybrid surface plasmonic waveguide with nanometric confinement and high optical intensity,” J. Opt. Soc. Am. B26(10), 1924–1929 (2009). [CrossRef]
- L. Chen, X. Li, G. Wang, W. Li, S. Chen, L. Xiao, and D. Gao, “A silicon-based 3-D hybrid long-range plasmonic waveguide for nanophotonic integration,” J. Lightwave Technol.30(1), 163–168 (2012). [CrossRef]
- P. B. Johnson and R. W. Christy, “optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
- R. Buckley and P. Berini, “Figures of merit for 2D surface plasmon waveguides and application to metal stripes,” Opt. Express15(19), 12174–12182 (2007). [CrossRef] [PubMed]
- T. Kuykendall, P. J. Pauzauskie, Y. Zhang, J. Goldberger, D. Sirbuly, J. Denlinger, and P. Yang, “Crystallographic alignment of high-density gallium nitride nanowire arrays,” Nat. Mater.3(8), 524–528 (2004). [CrossRef] [PubMed]

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