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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 18 — Aug. 27, 2012
  • pp: 20535–20544
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Novel hybrid plasmonic waveguide consisting of two identical dielectric nanowires symmetrically placed on each side of a thin metal film

Lin Chen, Tian Zhang, Xun Li, and Weiping Huang  »View Author Affiliations


Optics Express, Vol. 20, Issue 18, pp. 20535-20544 (2012)
http://dx.doi.org/10.1364/OE.20.020535


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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 0.0096μm2 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

Semiconductor nanowires offer tremendous applications in nanophotonics, such as waveguides, sensors, photodetectors, and lasers [1

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

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

]. The use of current nanofabrication techniques enables us to easily control the sizes and dimensions of nanowires. However, the optical modes are very weakly confined due to the limited index-contrast when the diameters of nanowires are much smaller than the operation wavelength. This makes it difficult to achieve deep subwavelength optical scale, which would limit their practical applications in nanophotonics, such as nanolasers, where small mode volumes and wire radius are highly required. Furthermore, strong optical confinement is highly required for enhanced optical field strength and gradient of light field, which will highly enhance the optical force in the nanoscale region.

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

Figure 1
Fig. 1 Schematic of a hybrid long-range plasmonic waveguide, where two identical cylindrical Si nanowires of permittivity εn and diameter d are placed on each side of a thin metallic film with a gap distance of h. The surrounding dielectric layer is SiO2 of permittivity εd. εn and εd are 12.25 and 2.25 at λ = 1.55μm. The metallic film is silver with a permittivity of εm = −129 + 3.3i and thickness of t = 20nm.
schematically shows the proposed hybrid plasmonic waveguide, where two identical cylindrical Si nanowires are placed on each side of a thin metallic film with a small gap distance h. The surrounding dielectric layer is SiO2 and the metallic film is silver with thickness of t = 20nm and permittivity of εm = −129 + 3.3i at λ = 1.55μm [29

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

]. Here we consider an intrinsic Si nanowire which has a negligible material loss at the window around 1550nm. For a thin metal film surrounded by uniform dielectric medium, there exists a symmetric mode and an anti-symmetric mode. The symmetric one is the so-called LRSPP mode, which is able to support long-rang propagation length but with a weak mode confinement. On the contrary, the propagation length of the anti-symmetric mode can become several orders of magnitude shorter than that of LRSPP mode. The dielectric cylindrical mode couples with both of the two modes. However, in this work only the symmetric mode is of our interest because it supports much longer propagation length.

3. Mode character and coupling strength

Figure 5(a)
Fig. 5 (a) The dependence of the mode effective index of the hybrid LRSPP mode, nhyb, on d for different gap distance h. As a comparison, the mode effective index of a pure cylindrical dielectric waveguides, nd, versus d is depicted in the solid black line. The dependence of the effective index of the pure LRSPP mode at SiO2-silver-SiO2 waveguides is shown in the dashed black line. (b) The mode character derived from Eq. (2). (c) The dependence of coupling strength κ on d and h.
shows the effective refractive index of the hybrid mode on d for different gap distance h. The guided hybrid mode is beyond the dielectric cylinder mode or pure LRSPP mode in a pure SiO2-Ag- SiO2 model. This is because that the LRSPP mode is coupled with the dielectric cylinder waveguide mode, which induces a much higher effective index [7

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]

, 28

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]

]. The mode’s effective index can be increased by reducing the gap distance for a fixed d, or enhancing the diameter of the cylinder nanowire, d, for a fixed gap distance, h. This can be explained that the LRSPP mode couples with the dielectric cylinder mode more effectively as d increases or h reduces.

In order to describe the mode characteristics of the hybrid mode, a mode character, |a+(d,h)|2, is employed to represent the superposition of the cylinder waveguide mode and the LRSPP mode based on the coupled-mode theory [7

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]

]
|a+(d,h)|2=nhyb(d,h)nL[nhyb(d,h)nc(d)]+[nhyb(d,h)nL]
(2)
where nhyb(d,h), nL are the mode effective indices of hybrid LRSPP mode and pure LRSPP mode in a pure SiO2-Ag-SiO2 model, respectively . nc(d) is the mode effective index of the dielectric cylinder waveguide mode.

4. Figure of merit

The figure of merit (FoM) can be applied to quantitatively measure plasmonic waveguides, and help trade-off mode confinement against attenuation. Here the FoM is defined as the ratio of the propagation length to the effective mode size defined as the diameter of Am [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]

]

FoM=Lm2Amπ=λ4Im(neff)πAm
(4)

For future experimental fabrication of the present hybrid LRSPP waveguide, we can use ‘vapour-liquid-solid’ method to produce Si nanowires with precise sizes and dimensions [31

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]

]. We can then position the Si nanowire on a SiO2 substrate and cover the nanowire with a SiO2 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 SiO2 layer, Si nanowire, and SiO2 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

This work is supported by NSFC (Grant No. 11104093), and ‘the Fundamental Research Funds for the Central Universities,’ HUST: 2011QN041.

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 292(5523), 1897–1899 (2001). [CrossRef] [PubMed]

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.) 14(2), 158–160 (2002). [CrossRef]

3.

X. F. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature 421(6920), 241–245 (2003). [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]

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. 14(6), 1496–1501 (2008). [CrossRef]

10.

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]

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]

12.

D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express 17(19), 16646–16653 (2009). [CrossRef] [PubMed]

13.

Y. Zhao and L. Zhu, “Coaxial hybrid plasmonic nanowire waveguides,” J. Opt. Soc. Am. B 27(6), 1260–1265 (2010). [CrossRef]

14.

H. Benisty and M. Besbes, “Plasmonic inverse rib waveguiding for tight confinement and smooth interface definition,” J. Appl. Phys. 108(6), 063108 (2010). [CrossRef]

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 18(18), 18945–18959 (2010). [CrossRef] [PubMed]

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]

17.

D. Chen, “Cylindrical hybrid plasmonic waveguide for subwavelength confinement of light,” Appl. Opt. 49(36), 6868–6871 (2010). [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]

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 19(23), 22417–22422 (2011). [CrossRef] [PubMed]

20.

V. D. Ta, R. Chen, and H. D. Sun, “Wide-range coupling between surface plasmon polariton and cylindrical dielectric waveguide mode,” Opt. Express 19(14), 13598–13603 (2011). [CrossRef] [PubMed]

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. 23(13), 884–886 (2011). [CrossRef]

22.

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]

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. 2, 331 (2011). [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]

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]

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 26(10), 1924–1929 (2009). [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]

29.

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

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]

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]

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

  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,” Science292(5523), 1897–1899 (2001). [CrossRef] [PubMed]
  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.)14(2), 158–160 (2002). [CrossRef]
  3. X. F. Duan, Y. Huang, R. Agarwal, and C. M. Lieber, “Single-nanowire electrically driven lasers,” Nature421(6920), 241–245 (2003). [CrossRef] [PubMed]
  4. R. Yan, D. Gargas, and P. D. Yang, “Nanowire photonics,” Nat. Photonics3(10), 569–576 (2009). [CrossRef]
  5. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface Plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]
  6. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(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. Photonics2(8), 496–500 (2008). [CrossRef]
  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.14(6), 1496–1501 (2008). [CrossRef]
  10. 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]
  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]
  12. 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]
  13. Y. Zhao and L. Zhu, “Coaxial hybrid plasmonic nanowire waveguides,” J. Opt. Soc. Am. B27(6), 1260–1265 (2010). [CrossRef]
  14. H. Benisty and M. Besbes, “Plasmonic inverse rib waveguiding for tight confinement and smooth interface definition,” J. Appl. Phys.108(6), 063108 (2010). [CrossRef]
  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. Express18(18), 18945–18959 (2010). [CrossRef] [PubMed]
  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,” Nature461(7264), 629–632 (2009). [CrossRef] [PubMed]
  17. D. Chen, “Cylindrical hybrid plasmonic waveguide for subwavelength confinement of light,” Appl. Opt.49(36), 6868–6871 (2010). [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]
  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. Express19(23), 22417–22422 (2011). [CrossRef] [PubMed]
  20. 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]
  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.23(13), 884–886 (2011). [CrossRef]
  22. 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]
  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.2, 331 (2011). [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]
  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. Express17(23), 21320–21325 (2009). [CrossRef] [PubMed]
  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. B26(10), 1924–1929 (2009). [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]
  29. P. B. Johnson and R. W. Christy, “optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  30. 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]
  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]

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