## Hybrid wedge plasmon polariton waveguide with good fabrication-error-tolerance for ultra-deep-subwavelength mode confinement |

Optics Express, Vol. 19, Issue 23, pp. 22417-22422 (2011)

http://dx.doi.org/10.1364/OE.19.022417

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### Abstract

A novel hybrid plasmonic waveguide consisting of a high-index dielectric nanowire placed above a triangular metal wedge substrate is proposed and analyzed theoretically. The strong coupling between the wedge plasmon polariton and the dielectric nanowire mode results in both the ultra-tight confinement and low propagation loss. Compared to the previous studied hybrid surface plasmon polariton structures without the metal wedge substrate, stronger field enhancement in the low-index gap region as well as improved figure of merit (FOM) could be realized simultaneously. Results of the modal properties considering certain fabrication imperfections show that the proposed structure is also quite tolerant to these errors.

© 2011 OSA

## 1. Introduction

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

2. G. Veronis and S. H. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. **30**(24), 3359–3361 (2005). [CrossRef] [PubMed]

5. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B **73**(3), 035407 (2006). [CrossRef]

6. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature **440**(7083), 508–511 (2006). [CrossRef] [PubMed]

7. E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. **31**(23), 3447–3449 (2006). [CrossRef] [PubMed]

8. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. **87**(6), 061106 (2005). [CrossRef]

11. T. Ogawa, D. F. P. Pile, T. Okamoto, M. Haraguchi, M. Fukui, and D. K. Gramotnev, “Numerical and experimental investigation of wedge tip radius effect on wedge plasmons,” J. Appl. Phys. **104**(3), 033102 (2008). [CrossRef]

12. 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]

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

18. 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]

19. Y. S. Bian, Z. Zheng, Y. Liu, J. S. Zhu, and T. Zhou, “Coplanar plasmonic nanolasers based on edge-coupled hybrid plasmonic waveguides,” IEEE Photon. Technol. Lett. **23**(13), 884–886 (2011). [CrossRef]

20. H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett. **96**(22), 221103 (2010). [CrossRef]

21. 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]

22. M. Wu, Z. H. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components at subwavelength scale,” Opt. Express **18**(11), 11728–11736 (2010). [CrossRef] [PubMed]

21. 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]

12. 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]

12. 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]

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

16. Y. S. Bian, Z. Zheng, Y. Liu, J. S. Zhu, and T. Zhou, “Dielectric-loaded surface plasmon polariton waveguide with a holey ridge for propagation-loss reduction and subwavelength mode confinement,” Opt. Express **18**(23), 23756–23762 (2010). [CrossRef] [PubMed]

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

15. I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express **18**(1), 348–363 (2010). [CrossRef] [PubMed]

19. Y. S. Bian, Z. Zheng, Y. Liu, J. S. Zhu, and T. Zhou, “Coplanar plasmonic nanolasers based on edge-coupled hybrid plasmonic waveguides,” IEEE Photon. Technol. Lett. **23**(13), 884–886 (2011). [CrossRef]

23. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B **61**(15), 10484–10503 (2000). [CrossRef]

**2**(8), 496–500 (2008). [CrossRef]

8. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. **87**(6), 061106 (2005). [CrossRef]

11. T. Ogawa, D. F. P. Pile, T. Okamoto, M. Haraguchi, M. Fukui, and D. K. Gramotnev, “Numerical and experimental investigation of wedge tip radius effect on wedge plasmons,” J. Appl. Phys. **104**(3), 033102 (2008). [CrossRef]

**2**(8), 496–500 (2008). [CrossRef]

24. X. D. Yang, Y. M. Liu, R. F. Oulton, X. B. Yin, and X. A. 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 WPP waveguides

*h*away from the top edge of the wedge. The metal wedge tip has an angle of

*θ*and a curvature radius of

*r*, while the wedge height is

*h*. The diameter of the nanowire is

_{w}*d*. The characteristics of the hybrid WPP waveguides are investigated at λ = 1550nm. The metallic substrate is assumed to be silver (Ag), the high-index dielectric is silicon (Si), and the cladding is silica (SiO

_{2}). The permittivities of SiO

_{2}, Si and Ag are ε

_{c}= 2.25, ε

_{d}= 12.25 and ε

_{m}= −129 + 3.3i [25

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

^{TM}. The eigenmode solver is used with the scattering boundary condition. Convergence tests are done to ensure that the numerical boundaries and meshing do not interfere with the solutions.

*h*→∞).To avoid singularities in simulations, the tip of the top corner are rounded with a 10nm curvature [26

_{w}26. M. Yan and M. Qiu, “Guided plasmon polariton at 2D metal corners,” J. Opt. Soc. Am. B **24**(9), 2333–2342 (2007). [CrossRef]

*h*is set at 5nm. The metal wedge tip-angle is chosen at 20deg, 60deg, 100deg, 140deg and 180deg, respectively. We note that the extreme case of 180deg corresponds to the hybrid plasmonic waveguide with flat metallic substrate as investigated in [12

**2**(8), 496–500 (2008). [CrossRef]

**2**(8), 496–500 (2008). [CrossRef]

16. Y. S. Bian, Z. Zheng, Y. Liu, J. S. Zhu, and T. Zhou, “Dielectric-loaded surface plasmon polariton waveguide with a holey ridge for propagation-loss reduction and subwavelength mode confinement,” Opt. Express **18**(23), 23756–23762 (2010). [CrossRef] [PubMed]

27. V. R. Almeida, Q. F. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. **29**(11), 1209–1211 (2004). [CrossRef] [PubMed]

*θ*would result in stronger field enhancement in the gap region, especially near the wedge tip. At larger

*θ*, the field enhancement is less obvious, and more electric field is distributed along the metal surface, leading to an increased mode area. These phenomena suggest that in order to suppress the mode area and enhance the mode confinement, a metal wedge with a sharper tip is preferred.

*N*), propagation length (

_{eff}*L*), normalized mode area (

_{p}*A*) and figure of merit (FOM) of the SPP mode of our proposed structures with different tip-angles are shown in Fig. 3 as

_{eff}/A_{0}*θ*varies from 20deg to 180deg. The propagation length is given by

*L*=

_{p}*λ*/[4

*π*Im(

*n*)].

_{eff}*A*is the diffraction-limited mode area and defined as λ

_{0}^{2}/4. The effective mode area (

*A*) is calculated using

_{eff}*W(*

*r**)*is defined as [5

5. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B **73**(3), 035407 (2006). [CrossRef]

28. R. F. Oulton, G. Bartal, D. F. P. Pile, and X. Zhang, “Confinement and propagation characteristics of subwavelength plasmonic modes,” N. J. Phys. **10**(10), 105018 (2008). [CrossRef]

*E(*

*r**)*and

*H(*

*r**)*are the electric and magnetic fields,

*ε(*

*r**)*is the electric permittivity and

*μ*is the vacuum magnetic permeability. FOM is defined as the ratio of

_{0}*L*to

_{p}*D*[29

_{eff}29. 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]

*D*is the effective mode size defined as the diameter of

_{eff}*A*.

_{eff}*θ*, which is consistent with the trend of increased effective mode area as shown in Fig. 3(b). While the propagation length is shown to increase first before it decreases when the metal wedge shifts towards flat metallic surface, which indicates the existence of an optimized tip angle (~140 deg) with respect to

*L*. When

_{p}*θ*is around 140 deg, the corresponding hybrid WPP waveguide could achieve longer propagation length with much smaller mode area compared to the previous hybrid plasmonic waveguide [12

**2**(8), 496–500 (2008). [CrossRef]

**2**(8), 496–500 (2008). [CrossRef]

*N*decreases while

_{eff}*L*and

_{p}*A*increase at larger gap width. The propagation lengths in Fig. 3 are comparable to those of the dielectric-loaded plasmonic waveguides but with much stronger confinement, which could be used to realize various devices such as plasmonic Bragg grating and other wavelength-selective structures, as well as active devices including nanolasers. We also note

_{eff}*L*could be increased to even hundreds of microns by further increasing the gap widths at the expense of weaker field confinement. Our results indicate that between 20 to 40% of the total power resides in the high-index nanowire for the geometrical parameters in Fig. 3, indicating sufficient modal overlap for possible applications like nanolasers [18

_{p}18. 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]

19. Y. S. Bian, Z. Zheng, Y. Liu, J. S. Zhu, and T. Zhou, “Coplanar plasmonic nanolasers based on edge-coupled hybrid plasmonic waveguides,” IEEE Photon. Technol. Lett. **23**(13), 884–886 (2011). [CrossRef]

9. E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. **100**(2), 023901 (2008). [CrossRef] [PubMed]

*h*(e.g. >300nm), the modal properties of the hybrid WPP waveguides quickly reach those under infinitely large

_{w}*h*as shown in Fig. 3. Thus, the waveguide’s characteristics are robust against the variation of the metal wedge height when the wedge is not too shallow. On the other hand, when

_{w}*h*is very small, the coupling between the dielectric nanowire and the bottom flat metal substrate becomes more obvious. This results in more complex mode properties, such as the non-monotonical changes of the curves shown in Fig. 4. The mode eventually approaches that from a flat metal surface [12

_{w}**2**(8), 496–500 (2008). [CrossRef]

_{2}layer on the wedge. Another approach might be using a reverse step by positioning the Si nanowire on a SiO

_{2}substrate and then covering the nanowire with a SiO

_{2}cladding first. The metal will later be deposited after milling a V-shape groove in the upper silica layer, similar as the fabrication process for the WPP waveguide in [10

10. A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express **16**(8), 5252–5260 (2008). [CrossRef] [PubMed]

*h*could be controlled with high precision [18

18. 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]

8. D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. **87**(6), 061106 (2005). [CrossRef]

11. T. Ogawa, D. F. P. Pile, T. Okamoto, M. Haraguchi, M. Fukui, and D. K. Gramotnev, “Numerical and experimental investigation of wedge tip radius effect on wedge plasmons,” J. Appl. Phys. **104**(3), 033102 (2008). [CrossRef]

*r*causes little changes in

*L*and

_{p}*A*. When

_{eff}*r*increases from 10nm to 20nm, the changes in

*L*and

_{p}*A*are only ~2% and ~5%, respectively. However, when

_{eff}*θ*is small (e.g. 20deg), the difference of the modal properties at various

*r*becomes more obvious, especially when the radius is very small (e.g.<5nm). Figure 5(b) shows that, for all the considered tip-angles, a ± 10nm misalignment in the horizontal direction only result in a less than 3% fluctuation for

*L*and a no more than 5% variation for

_{p}*A*. The modifications in the mode profile are also negligible. The above results clearly indicate that the proposed hybrid WPP waveguide is quite tolerant to fabrication errors, especially at larger tip-angles, which is beneficial for its implementations.

_{eff}9. E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. **100**(2), 023901 (2008). [CrossRef] [PubMed]

**2**(8), 496–500 (2008). [CrossRef]

## 3. Conclusions

## Acknowledgments

## References and links

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

2. | G. Veronis and S. H. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. |

3. | D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett. |

4. | L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express |

5. | J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B |

6. | S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature |

7. | E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. |

8. | D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett. |

9. | E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. |

10. | A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express |

11. | T. Ogawa, D. F. P. Pile, T. Okamoto, M. Haraguchi, M. Fukui, and D. K. Gramotnev, “Numerical and experimental investigation of wedge tip radius effect on wedge plasmons,” J. Appl. Phys. |

12. | 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 |

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

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

15. | I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express |

16. | Y. S. Bian, Z. Zheng, Y. Liu, J. S. Zhu, and T. Zhou, “Dielectric-loaded surface plasmon polariton waveguide with a holey ridge for propagation-loss reduction and subwavelength mode confinement,” Opt. Express |

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

18. | 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 |

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

20. | H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett. |

21. | 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 |

22. | M. Wu, Z. H. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components at subwavelength scale,” Opt. Express |

23. | P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B |

24. | X. D. Yang, Y. M. Liu, R. F. Oulton, X. B. Yin, and X. A. Zhang, “Optical forces in hybrid plasmonic waveguides,” Nano Lett. |

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

26. | M. Yan and M. Qiu, “Guided plasmon polariton at 2D metal corners,” J. Opt. Soc. Am. B |

27. | V. R. Almeida, Q. F. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. |

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

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

**OCIS Codes**

(130.2790) Integrated optics : Guided waves

(240.6680) Optics at surfaces : Surface plasmons

(250.5300) Optoelectronics : Photonic integrated circuits

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: April 22, 2011

Revised Manuscript: June 11, 2011

Manuscript Accepted: June 14, 2011

Published: October 24, 2011

**Citation**

Yusheng Bian, Zheng Zheng, Ya Liu, Jiansheng Liu, Jinsong Zhu, and Tao Zhou, "Hybrid wedge plasmon polariton waveguide with good fabrication-error-tolerance for ultra-deep-subwavelength mode confinement," Opt. Express **19**, 22417-22422 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-23-22417

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### References

- W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]
- G. Veronis and S. H. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett.30(24), 3359–3361 (2005). [CrossRef] [PubMed]
- D. F. P. Pile, T. Ogawa, D. K. Gramotnev, Y. Matsuzaki, K. C. Vernon, K. Yamaguchi, T. Okamoto, M. Haraguchi, and M. Fukui, “Two-dimensionally localized modes of a nanoscale gap plasmon waveguide,” Appl. Phys. Lett.87(26), 261114 (2005). [CrossRef]
- L. Liu, Z. Han, and S. He, “Novel surface plasmon waveguide for high integration,” Opt. Express13(17), 6645–6650 (2005). [CrossRef] [PubMed]
- J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006). [CrossRef]
- S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006). [CrossRef] [PubMed]
- E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett.31(23), 3447–3449 (2006). [CrossRef] [PubMed]
- D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, “Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding,” Appl. Phys. Lett.87(6), 061106 (2005). [CrossRef]
- E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett.100(2), 023901 (2008). [CrossRef] [PubMed]
- A. Boltasseva, V. S. Volkov, R. B. Nielsen, E. Moreno, S. G. Rodrigo, and S. I. Bozhevolnyi, “Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths,” Opt. Express16(8), 5252–5260 (2008). [CrossRef] [PubMed]
- T. Ogawa, D. F. P. Pile, T. Okamoto, M. Haraguchi, M. Fukui, and D. K. Gramotnev, “Numerical and experimental investigation of wedge tip radius effect on wedge plasmons,” J. Appl. Phys.104(3), 033102 (2008). [CrossRef]
- 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]
- D. X. Dai and S. L. 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. S. Bian, Z. Zheng, X. Zhao, J. S. Zhu, and T. Zhou, “Symmetric hybrid surface plasmon polariton waveguides for 3D photonic integration,” Opt. Express17(23), 21320–21325 (2009). [CrossRef] [PubMed]
- I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express18(1), 348–363 (2010). [CrossRef] [PubMed]
- Y. S. Bian, Z. Zheng, Y. Liu, J. S. Zhu, and T. Zhou, “Dielectric-loaded surface plasmon polariton waveguide with a holey ridge for propagation-loss reduction and subwavelength mode confinement,” Opt. Express18(23), 23756–23762 (2010). [CrossRef] [PubMed]
- Y. S. Zhao and L. Zhu, “Coaxial hybrid plasmonic nanowire waveguides,” J. Opt. Soc. Am. B27(6), 1260–1265 (2010). [CrossRef]
- 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]
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