OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 14 — Jul. 15, 2013
  • pp: 17404–17412
« Show journal navigation

Circular hybrid plasmonic waveguide with ultra-long propagation distance

Chang Yeong Jeong, Myunghwan Kim, and Sangin Kim  »View Author Affiliations


Optics Express, Vol. 21, Issue 14, pp. 17404-17412 (2013)
http://dx.doi.org/10.1364/OE.21.017404


View Full Text Article

Acrobat PDF (1506 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We propose a novel plasmonic waveguide structure, which is referred to as a circular hybrid plasmonic waveguide (HPW) and consists of a metal wire covered with low- and high-index dielectric layers. The circular HPW exhibits two distinctly different modes, namely, the strongly localized mode and the extremely low-loss mode. Our numerical calculation demonstrates that the strongly localized mode exhibits 10−4 order scale in normalized mode area and can be performed even in tens of nanometer sizes of waveguide geometry. In the extremely low-loss mode, the HPW exhibits ultra-long propagation distance of more than 103μm that can be achieved by forming the dipole-like hybrid mode and properly adjusting the radius of the metal wire. It is also shown that, even with this long-range propagation, the mode area of the dipole-like hybrid mode can be maintained at subwavelength scale. The simultaneous achievement of a small mode area and ultra-long propagation distance contributes to the ultra-high propagation distance to mode size ratio of the waveguide. The HPW results are very helpful for plasmonic device applications in the fields of low-threshold nanolasers, ultrafast modulators, and optical switches.

© 2013 OSA

1. Introduction

2. Various plasmonic waveguide structures

A dielectric wire HPW depicted in Fig. 1(d) is an extension of the planar HPW into a two-dimensional waveguide by replacing the semi-infinite dielectric layer with a dielectric wire [26

26. 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]

,27

27. R. Hao, E. Li, and X. Wei, “Two-dimensional light confinement in cross-index-modulation plasmonic waveguides,” Opt. Lett. 37(14), 2934–2936 (2012). [CrossRef] [PubMed]

], which exhibits the best plasmonic waveguide performance reported thus far. In this structure, the hybrid plasmonic mode property provides low-loss characteristics, thereby leading to a propagation distance of tens of microns. From our point of view, it is necessary to further increase the range of the feasible propagation distance for proper waveguiding. For this, an alternative approach of the extension of the planar HPW into a two-dimensional waveguide is proposed in this work, which is depicted in Fig. 1(e). The proposed structure is formed by rolling-up the planar HPW in a similar way to get the metal wire structure from the planar MD structure.

3. Definition of mode area and propagation distance

In all calculation, the permittivities of dielectrics are assumed to be εH = 13.84 (InGaAs), εL = 2.1025 (SiO2), and εA = 1 (air). The permittivity of metal (Au) is chosen as εM = −125.03 + 4.23i at λ = 1.55 μm [28

28. S. Lee and S. Kim, “Plasmonic mode-gap waveguides using hetero-metal films,” Opt. Express 18(3), 2197–2208 (2010). [CrossRef] [PubMed]

].

4. Modal analysis of a circular hybrid plasmonic waveguide

In the proposed circular hybrid plasmonic waveguide, it has been found that there are two types of guided mode: one is a strongly confined mode which shows circular symmetry (the first mode) and the other is a mode of dipole-like shaped profile which shows an ultra-long propagation distance (the second mode). The characteristics of those modes are discussed in this section.

4.1 Mode with extremely enhanced confinement

4.2 Mode with ultra-long propagation distance

Figure 3(g) shows the effective index, neff, as a function of thigh. The effective indices of the 1st mode substantially increase with decreasing the low-index dielectric thickness from 5 nm to 1 nm, and it implies that the 1st mode is highly affected by metal. However, the behavior of the 2nd mode is somewhat different, and it is similar to that of the dielectric wire HPW [26

26. 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]

]. Because it is less influenced by metal, the effective indices of the 2nd mode show much lower values than those of the 1st mode for the same thigh.

So far, the effect of the thicknesses of the dielectric layers on the characteristics of the 2nd mode with a fixed metal wire radius has been investigated. Now, we investigate the effect of the metal wire radius. The mode area and the propagation distance are calculated and plotted for various r with tlow = 1 nm. One can see that as the metal wire radius decreases, the loss can be further reduced while the mode area becomes larger. An important feature to note here is that while the loss decreases remarkably as the metal wire radius decreases, the mode area does not show significant change. As shown in Fig. 4(b)
Fig. 4 Modal characteristics of the 2nd mode with different r values in the circular HPW and the fundamental mode in the dielectric wire waveguide. (a) Normalized mode area and (b) propagation distance as a function of thigh. Electric field profiles for (c) r = 0 nm, tlow = 0 nm, and thigh = 165 nm, (d) r = 2 nm, tlow = 1 nm, and thigh = 180 nm, and (e) r = 20 nm, tlow = 1 nm, and thigh = 170 nm. One-dimensional graphs show the field distributions along the central lines and the insets show the blow-up of the electric field distributions near the metal wire region. (f) Propagation distance to mode size ratio and (g) the effective index of the mode as a function of thigh.
, when the metal wire radius decreases from 20 nm to 2 nm, the propagation distance is increased by 1000 times, whereas the mode area is increased just by a factor of 4.

Figure 4(f) shows Lp/Am, which increases remarkably fast due to the reduced loss as r decreases. As shown in Fig. 4(g), the effective index of the 2nd mode is not affected much by the metal wire thickness, which implies that little portion of the field experiences the metal wire in the 2nd mode. The effective index of the dielectric wire waveguide mode is also plotted in Fig. 4(g), which shows the smallest value.

5. Comparison among various waveguide structures

Figure 5
Fig. 5 Normalized mode area versus propagation distance. Top three trajectories indicate the circular HPWs, and bottom two indicate the dielectric wire HPW and metal wire, respectively. Data has been obtained by varying tlow in the circular HPWs, h in the dielectric wire HPW, and r in the metal wire. The rest parameters at the given geometries are thigh = 180 nm for the green and red lines, thigh = 180 nm for the purple line, and d = 200 nm for the blue line.
shows the overall comparison among various plasmonic waveguide structures. We plot the mode area versus propagation distance for a fair comparison. A structure with ideal performance should exhibit small mode area and long propagation distance at the same time. We compare the circular HPW with the metal wire waveguide [25

25. T. Laroche and C. Girard, “Near-field optical properties of single plasmonic nanowires,” Appl. Phys. Lett. 89(23), 233119 (2006). [CrossRef]

] and dielectric wire HPW [26

26. 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]

] since their waveguide performances are known to be superior to other plasmonic waveguides reported in the literature.

For the circular HPWs, three geometrical parameter sets are considered; (r, thigh) = (2, 180), (5, 180), (10, 180) nm. The value of thigh is chosen as the value near the minima in Fig. 4(a). The mode area and the propagation distance are calculated with tlow varied. For the dielectric wire HPW, the dielectric wire diameter of 200 nm is also chosen as the value close to the mode area minimum. In this case, the mode area and the propagation distance are also calculated with tlow varied. In the case of the metal wire waveguide, the radius is varied since it is the only geometrical parameter. As shown in Fig. 5, the circular HPW shows superior performance to other types of waveguides. For the circular HPW, the smaller metal wire radius, the better performance is achieved.

6. Applications of the circular hybrid plasmonic waveguide

Due to the low-loss and small mode area characteristics, the circular HPW can be used to form a plasmonic nanolaser cavity with a relatively high quality factor to volume ratio (Q/V) as well as a lightwave circuit element. As for the lightwave circuit element, the circular HPW structure is not easy to fabricate since the outermost InGaAs layer is hard to be grown. So, a planarized version of the circular HPW needs to be devised for the lightwave circuit element application as depicted in Fig. 6(a)
Fig. 6 Schematics of (a) the lightwave circuit element and (b) the plasmonic nanolaser cavity as the applications of the circular HPW. As for the lightwave circuit element, the planarized structure is devised from the fact that the dipole-like mode of the circular HPW is confined via index-guiding in one-direction.
. The structure is devised from the fact that the dipole-like mode of the circular HPW is confined via index-guiding in one-direction. The analysis of the waveguide shown in Fig. 6(a) will be reported in another paper. As for the plasmonic nanolaser cavity application, the structure depicted in Fig. 6(b) can be considered, where the circular HPW structure provides the horizontal confinement. This structure can be fabricated by etching a hole in the center of an InGaAs mesa and filling the hole with the low-index dielectric shell and the metal. The volume of the structure can be much smaller than (λ/2)3 due to the small mode area of the circular HPW. The high propagation distance to mode size ratio of the circular HPW will also bring about a relatively high Q/V value. The detailed analysis and the fabrication of the plasmonic nanolaser structure are in progress and will be reported soon.

7. Conclusion

Acknowledgment

This work was supported by National Research Foundation of Korea Grant (NRF-2011-0014265).

References and links

1.

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384), 204–207 (2012). [CrossRef] [PubMed]

2.

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot–nanocavity system,” Nat. Phys. 6(4), 279–283 (2010). [CrossRef]

3.

K. F. MacDonald, Z. L. Sámson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics 3(1), 55–58 (2009). [CrossRef]

4.

A. Y. Elezzabi, Z. Han, S. Sederberg, and V. Van, “Ultrafast all-optical modulation in silicon-based nanoplasmonic devices,” Opt. Express 17(13), 11045–11056 (2009). [CrossRef] [PubMed]

5.

M. I. Stockman, “The spaser as a nanoscale quantum generator and ultrafast amplifier,” J. Opt. 12(2), 024004 (2010). [CrossRef]

6.

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]

7.

L. Y. M. Tobing, L. Tjahjana, and D. H. Zhang, “Demonstration of low-loss on-chip integrated plasmonic waveguide based on simple fabrication steps on silicon-on-insulator platform,” Appl. Phys. Lett. 101(4), 041117 (2012). [CrossRef]

8.

J. H. Kang, Y. S. No, S. H. Kwon, and H. G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett. 36(11), 2011–2013 (2011). [CrossRef] [PubMed]

9.

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett. 9(2), 897–902 (2009). [CrossRef] [PubMed]

10.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).

11.

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

12.

V. J. Sorger and X. Zhang, “Physics. Spotlight on plasmon lasers,” Science 333(6043), 709–710 (2011). [CrossRef] [PubMed]

13.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007). [CrossRef]

14.

K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18(9), 8790–8799 (2010). [CrossRef] [PubMed]

15.

S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10(9), 3679–3683 (2010). [CrossRef] [PubMed]

16.

V. J. Sorger, N. D. L. Kimura, R. M. Ma, and X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” Nanophotonics 1(1), 17–22 (2012). [CrossRef]

17.

L. A. Sweatlock and K. Diest, “Vanadium dioxide based plasmonic modulators,” Opt. Express 20(8), 8700–8709 (2012). [CrossRef] [PubMed]

18.

W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9(12), 4403–4411 (2009). [CrossRef] [PubMed]

19.

J. Wang, X. Guan, Y. He, Y. Shi, Z. Wang, S. He, P. Holmström, L. Wosinski, L. Thylen, and D. Dai, “Sub-μm2 power splitters by using silicon hybrid plasmonic waveguides,” Opt. Express 19(2), 838–847 (2011). [CrossRef] [PubMed]

20.

F. Lou, D. Dai, and L. Wosinski, “Ultracompact polarization beam splitter based on a dielectric-hybrid plasmonic-dielectric coupler,” Opt. Lett. 37(16), 3372–3374 (2012). [CrossRef] [PubMed]

21.

J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6(9), 1928–1932 (2006). [CrossRef] [PubMed]

22.

L. Gao, L. Tang, F. Hu, R. Guo, X. Wang, and Z. Zhou, “Active metal strip hybrid plasmonic waveguide with low critical material gain,” Opt. Express 20(10), 11487–11495 (2012). [CrossRef] [PubMed]

23.

D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Gain enhancement in a hybrid plasmonic nano-waveguide with a low-index or high-index gain medium,” Opt. Express 19(14), 12925–12936 (2011). [CrossRef] [PubMed]

24.

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]

25.

T. Laroche and C. Girard, “Near-field optical properties of single plasmonic nanowires,” Appl. Phys. Lett. 89(23), 233119 (2006). [CrossRef]

26.

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]

27.

R. Hao, E. Li, and X. Wei, “Two-dimensional light confinement in cross-index-modulation plasmonic waveguides,” Opt. Lett. 37(14), 2934–2936 (2012). [CrossRef] [PubMed]

28.

S. Lee and S. Kim, “Plasmonic mode-gap waveguides using hetero-metal films,” Opt. Express 18(3), 2197–2208 (2010). [CrossRef] [PubMed]

OCIS Codes
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons
(050.6624) Diffraction and gratings : Subwavelength structures
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Optics at Surfaces

History
Original Manuscript: May 28, 2013
Revised Manuscript: July 8, 2013
Manuscript Accepted: July 8, 2013
Published: July 12, 2013

Citation
Chang Yeong Jeong, Myunghwan Kim, and Sangin Kim, "Circular hybrid plasmonic waveguide with ultra-long propagation distance," Opt. Express 21, 17404-17412 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-14-17404


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature482(7384), 204–207 (2012). [CrossRef] [PubMed]
  2. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot–nanocavity system,” Nat. Phys.6(4), 279–283 (2010). [CrossRef]
  3. K. F. MacDonald, Z. L. Sámson, M. I. Stockman, and N. I. Zheludev, “Ultrafast active plasmonics,” Nat. Photonics3(1), 55–58 (2009). [CrossRef]
  4. A. Y. Elezzabi, Z. Han, S. Sederberg, and V. Van, “Ultrafast all-optical modulation in silicon-based nanoplasmonic devices,” Opt. Express17(13), 11045–11056 (2009). [CrossRef] [PubMed]
  5. M. I. Stockman, “The spaser as a nanoscale quantum generator and ultrafast amplifier,” J. Opt.12(2), 024004 (2010). [CrossRef]
  6. 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]
  7. L. Y. M. Tobing, L. Tjahjana, and D. H. Zhang, “Demonstration of low-loss on-chip integrated plasmonic waveguide based on simple fabrication steps on silicon-on-insulator platform,” Appl. Phys. Lett.101(4), 041117 (2012). [CrossRef]
  8. J. H. Kang, Y. S. No, S. H. Kwon, and H. G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett.36(11), 2011–2013 (2011). [CrossRef] [PubMed]
  9. J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: a metal-oxide-Si field effect plasmonic modulator,” Nano Lett.9(2), 897–902 (2009). [CrossRef] [PubMed]
  10. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).
  11. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]
  12. V. J. Sorger and X. Zhang, “Physics. Spotlight on plasmon lasers,” Science333(6043), 709–710 (2011). [CrossRef] [PubMed]
  13. M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics1(10), 589–594 (2007). [CrossRef]
  14. K. Yu, A. Lakhani, and M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express18(9), 8790–8799 (2010). [CrossRef] [PubMed]
  15. S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett.10(9), 3679–3683 (2010). [CrossRef] [PubMed]
  16. V. J. Sorger, N. D. L. Kimura, R. M. Ma, and X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” Nanophotonics1(1), 17–22 (2012). [CrossRef]
  17. L. A. Sweatlock and K. Diest, “Vanadium dioxide based plasmonic modulators,” Opt. Express20(8), 8700–8709 (2012). [CrossRef] [PubMed]
  18. W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett.9(12), 4403–4411 (2009). [CrossRef] [PubMed]
  19. J. Wang, X. Guan, Y. He, Y. Shi, Z. Wang, S. He, P. Holmström, L. Wosinski, L. Thylen, and D. Dai, “Sub-μm2 power splitters by using silicon hybrid plasmonic waveguides,” Opt. Express19(2), 838–847 (2011). [CrossRef] [PubMed]
  20. F. Lou, D. Dai, and L. Wosinski, “Ultracompact polarization beam splitter based on a dielectric-hybrid plasmonic-dielectric coupler,” Opt. Lett.37(16), 3372–3374 (2012). [CrossRef] [PubMed]
  21. J. A. Dionne, H. J. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett.6(9), 1928–1932 (2006). [CrossRef] [PubMed]
  22. L. Gao, L. Tang, F. Hu, R. Guo, X. Wang, and Z. Zhou, “Active metal strip hybrid plasmonic waveguide with low critical material gain,” Opt. Express20(10), 11487–11495 (2012). [CrossRef] [PubMed]
  23. D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Gain enhancement in a hybrid plasmonic nano-waveguide with a low-index or high-index gain medium,” Opt. Express19(14), 12925–12936 (2011). [CrossRef] [PubMed]
  24. 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]
  25. T. Laroche and C. Girard, “Near-field optical properties of single plasmonic nanowires,” Appl. Phys. Lett.89(23), 233119 (2006). [CrossRef]
  26. 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]
  27. R. Hao, E. Li, and X. Wei, “Two-dimensional light confinement in cross-index-modulation plasmonic waveguides,” Opt. Lett.37(14), 2934–2936 (2012). [CrossRef] [PubMed]
  28. S. Lee and S. Kim, “Plasmonic mode-gap waveguides using hetero-metal films,” Opt. Express18(3), 2197–2208 (2010). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited