Abstract

This study reports a symmetric hybrid plasmonic waveguide consisting of a cylindrical metal nanowire surrounded by low-index SiO2 and high-index Si covered with SiO2. The symmetric circumambience relative to the metal nanowire significantly facilitates the present design to minimize the energy attenuation resulting from Ohmic losses while retaining highly confined modes guided in the low-index nanoscale gaps between the metal nanowire and the high-index Si. The geometric dependence of the mode characteristics on the proposed structure is analyzed in detail, showing long propagation lengths beyond 10 mm with normalized mode areas on the order of 10−2. In addition to enabling the building of long-range plasmonic circuit interconnects, the compactness and high-density integration of the proposed structure are examined by analyzing crosstalk in a directional coupler composed of two such waveguides and bending losses for a 90° bend. A relatively short coupling length of 1.16 μm is obtained at a center-to-center separation of 0.26 μm between adjacent waveguides. Increasing the separation to 1.65 μm could completely prevent coupling between waveguides. Power transmission exceeds 80% in the case of a 90° bend with small radius of curvature of 0.5 μm. Moreover, the dependence of spectral response on coupling length and the transmission of a 90° bend, ranging from telecom wavelengths of 1.40 to 1.65 μm, are investigated. Over a wide wavelength range, a strong coupling length dependence on wavelength and a high transmission for a 90° bend also make the proposed plasmonic waveguide promising for the realization of wavelength-selective components.

© 2013 Optical Society of America

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2013 (7)

2012 (5)

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

Y. S. Bian, Z. Zheng, X. Zhao, Y. L. Su, L. Liu, J. S. Liu, J. S. Zhu, and T. Zhou, “Guiding of long-range hybrid plasmon polariton in a coupled nanowire array at deep-subwavelength scale,” IEEE Photon. Technol. Lett.24(15), 1279–1281 (2012).
[CrossRef]

L. Chen, T. Zhang, X. Li, and W. P. Huang, “Novel hybrid plasmonic waveguide consisting of two identical dielectric nanowires symmetrically placed on each side of a thin metal film,” Opt. Express20(18), 20535–20544 (2012).
[CrossRef] [PubMed]

C. C. Huang, “Hybrid plasmonic waveguide comprising a semiconductor nanowire and metal ridge for low-loss propagation and nanoscale confinement,” IEEE J. Sel. Top. Quantum Electron.18(6), 1661–1668 (2012).
[CrossRef]

Y. J. Lu, J. S. Kim, H. Y. Chen, C. H. Wu, N. Dabidian, C. E. Sanders, C. Y. Wang, M. Y. Lu, B. H. Li, X. G. Qiu, W. H. Chang, L. J. Chen, G. Shvets, C. K. Shih, and S. G. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science337(6093), 450–453 (2012).
[CrossRef] [PubMed]

2011 (7)

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

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. B. Yin, and X. Zhang, “Experimental demonstration of low-loss optical waveguiding at deep sub-wavelength scales,” Nat. Commun.2(331), 1–5 (2011).

X. L. Zuo and Z. J. Sun, “Low-loss plasmonic hybrid optical ridge waveguide on silicon-on-insulator substrate,” Opt. Lett.36(15), 2946–2948 (2011).
[CrossRef] [PubMed]

Y. S. Bian, Z. Zheng, Y. Liu, J. S. Liu, J. S. 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. S. Volkov, Z. H. Han, M. G. Nielsen, K. Leosson, H. Keshmiri, J. Gosciniak, O. Albrektsen, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon polariton waveguides operating at telecommunication wavelengths,” Opt. Lett.36(21), 4278–4280 (2011).
[CrossRef] [PubMed]

Y. Kou, F. W. Ye, and X. F. Chen, “Low-loss hybrid plasmonic waveguide for compact and high-efficient photonic integration,” Opt. Express19(12), 11746–11752 (2011).
[CrossRef] [PubMed]

S. M. García-Blanco, M. Pollnau, and S. I. Bozhevolnyi, “Loss compensation in long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express19(25), 25298–25311 (2011).
[CrossRef] [PubMed]

2010 (5)

2009 (6)

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]

R. Adato and J. P. Guo, “Modification of dispersion, localization, and attenuation of thin metal stripe symmetric surface plasmon-polariton modes by thin dielectric layers,” J. Appl. Phys.105(3), 034306 (2009).
[CrossRef]

B. F. Yun, G. H. Hu, Y. Ji, and Y. P. 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]

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]

X. Guo, M. Qiu, J. Bao, B. J. Wiley, Q. Yang, X. Zhang, Y. Ma, H. Yu, and L. Tong, “Direct coupling of plasmonic and photonic nanowires for hybrid nanophotonic components and circuits,” Nano Lett.9(12), 4515–4519 (2009).
[CrossRef] [PubMed]

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]

2008 (4)

A. V. Krasavin and A. V. Zayats, “Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides,” Phys. Rev. B78(4), 045425 (2008).
[CrossRef]

G. Veronis and S. H. Fan, “Crosstalk between three-dimensional plasmonic slot waveguides,” Opt. Express16(3), 2129–2140 (2008).
[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]

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]

2007 (3)

2006 (2)

P. Berini and J. J. Lu, “Curved long-range surface plasmon-polariton waveguides,” Opt. Express14(6), 2365–2371 (2006).
[CrossRef] [PubMed]

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]

2005 (2)

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]

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]

2004 (1)

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

2001 (1)

2000 (2)

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B61(15), 10484–10503 (2000).
[CrossRef]

P. Berini, “Plasmon-polariton modes guided by a metal film of finite width bounded by different dielectrics,” Opt. Express7(10), 329–335 (2000).
[CrossRef] [PubMed]

1997 (1)

1995 (1)

V. R. Chinni, T. C. Huang, P. K. A. Wai, C. R. Menyuk, and G. J. Simonis, “Crosstalk in a lossy directional coupler switch,” J. Lightwave Technol.13(7), 1530–1535 (1995).
[CrossRef]

1994 (1)

W. P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A.11(3), 963–983 (1994)

1992 (1)

W. P. Huang, C. Xu, S. T. Chu, and S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol.10(3), 295–305 (1992).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Adato, R.

R. Adato and J. P. Guo, “Modification of dispersion, localization, and attenuation of thin metal stripe symmetric surface plasmon-polariton modes by thin dielectric layers,” J. Appl. Phys.105(3), 034306 (2009).
[CrossRef]

Aitchison, J. S.

Alam, M. Z.

Albrektsen, O.

Almeida, V. R.

Amirhosseini, A.

A. Amirhosseini and R. Safian, “A hybrid plasmonic waveguide for the propagation of surface plasmon polariton at 1.55 μm on SOI substrate,” IEEE Trans. NanoTechnol.12(6), 1031–1036 (2013).
[CrossRef]

Bao, J.

X. Guo, M. Qiu, J. Bao, B. J. Wiley, Q. Yang, X. Zhang, Y. Ma, H. Yu, and L. Tong, “Direct coupling of plasmonic and photonic nanowires for hybrid nanophotonic components and circuits,” Nano Lett.9(12), 4515–4519 (2009).
[CrossRef] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Barrios, C. A.

Bartal, G.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. B. Yin, and X. Zhang, “Experimental demonstration of low-loss optical waveguiding at deep sub-wavelength scales,” Nat. Commun.2(331), 1–5 (2011).

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]

Berini, P.

Bian, Y. S.

Bozhevolnyi, S. I.

V. A. Zenin, Z. H. Han, V. S. Volkov, K. Leosson, I. P. Radko, and S. I. Bozhevolnyi, “Directional coupling in long-range dielectric-loaded plasmonic waveguides,” Opt. Express21(7), 8799–8807 (2013).
[CrossRef] [PubMed]

V. S. Volkov, Z. H. Han, M. G. Nielsen, K. Leosson, H. Keshmiri, J. Gosciniak, O. Albrektsen, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon polariton waveguides operating at telecommunication wavelengths,” Opt. Lett.36(21), 4278–4280 (2011).
[CrossRef] [PubMed]

S. M. García-Blanco, M. Pollnau, and S. I. Bozhevolnyi, “Loss compensation in long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express19(25), 25298–25311 (2011).
[CrossRef] [PubMed]

T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express18(22), 23009–23015 (2010).
[CrossRef] [PubMed]

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]

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon polariton waveguides,” Phys. Rev. B75(24), 245405 (2007).
[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]

Buckley, R.

Cerrina, F.

Chang, W. H.

Y. J. Lu, J. S. Kim, H. Y. Chen, C. H. Wu, N. Dabidian, C. E. Sanders, C. Y. Wang, M. Y. Lu, B. H. Li, X. G. Qiu, W. H. Chang, L. J. Chen, G. Shvets, C. K. Shih, and S. G. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science337(6093), 450–453 (2012).
[CrossRef] [PubMed]

Chaudhuri, S. K.

W. P. Huang, C. Xu, S. T. Chu, and S. K. Chaudhuri, “The finite-difference vector beam propagation method: analysis and assessment,” J. Lightwave Technol.10(3), 295–305 (1992).
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Figures (12)

Fig. 1
Fig. 1

(a). Schematic of the proposed symmetric hybrid plasmonic waveguide (SHPW) consisting of a cylinder silver (Ag) nanowire surrounded, from the inner to outer media, by low-index SiO2 and high-index Si covered with SiO2. (b). The Ey and (c). |Ez | field profiles for dimensions of w = 200 nm, h = 400 nm, wa = 100 nm, d = 10 nm, and g = 2 nm.

Fig. 2
Fig. 2

The Ey field distributions of the proposed SHPW of (a) g = 2 nm, (b) g = 5 nm, and (c) g = 10 nm for dimensions of w = 200 nm, h = 400 nm, wa = 100 nm, and d = 10 nm. The energy density W(r) along (d) the y = d/2 and (e) the x = 0 directions for different gaps.

Fig. 3
Fig. 3

Mode properties of the proposed SHPW versus the width wa of the inner SiO2: (a) real part of the effective refractive index Re(ne), (b) normalized mode area Ae/A0, (c) propagation length Lm, (d) figure of merit (FOM), for a gap of g = 2 nm, and Si width of w = 200 nm and height of h = 400 nm, for the three diameters of nanowire shown in Fig. 2(a).

Fig. 4
Fig. 4

The Ey distributions of (a) d = 10 nm, (b) d = 30 nm, and (c) d = 50 nm, and the longitudinal electric field |Ez | profiles of (d) d = 10 nm, (e) d = 30 nm, and (f) d = 50 nm, all with dimensions w = 200 nm, h = 400 nm, and wa = 50 nm.

Fig. 5
Fig. 5

Mode properties of the proposed SHPW versus the Si width w: (a) real part of the effective refractive index Re(ne), (b) normalized mode area Ae/A0, (c) propagation length Lm, (d) figure of merit (FOM), with a gap of g = 2 nm, width of d = 10 nm, and height of wa = 100 nm, for the three heights of Si shown in Fig. 5(a).

Fig. 6
Fig. 6

The Ey distributions of (a) wa = 10 nm, (b) wa = 50 nm, and (c) wa = 100 nm for the dimensions w = 100 nm and h = 300 nm; the Ey distributions of (d) wa = 10 nm, (e) wa = 50 nm, and (f) wa = 100 nm for the dimensions w = 200 nm and h = 400 nm.

Fig. 7
Fig. 7

(a) Schematic of a directional coupler made of two proposed SHPWs, and s is the center-to-center separation distance. Field distributions of Ey for the (a) even and (b) odd modes of the directional coupler with dimensions g = 2 nm, d = 10 nm, wa = 50 nm, w = 200 nm, h = 400 nm, and s = 0.3 μm.

Fig. 8
Fig. 8

(a). Real parts of the effective refractive index for even and odd modes of the directional coupler composed of two SHPWs, along with a single SHPW for comparison, and (b) the normalized coupling length Lc/Lave (solid lines) and maximum transfer power ρmax (dashed lines) as functions of separation for three different sizes (see the text for details) of Si. The black circles are the results obtained from 3D simulations.

Fig. 9
Fig. 9

Poynting vectors Pz for cases (a) I, (b) II, and (c) III for the proposed SHPW for s = 0.6 μm along the propagation direction, and the 3D power evolutions of cases (d) I, (e) II, and (f) III.

Fig. 10
Fig. 10

The coupling length Lc versus excitation wavelength for the three cases (see the text for details) of the proposed SHPW for s = 0.7 μm.

Fig. 11
Fig. 11

(a) The power transmission (%) versus the bending radius of the three cases. The power evolution of cases (b) I, (c) II, and (d) III at radius of curvature r = 1 μm.

Fig. 12
Fig. 12

The power transmission (%) versus excitation wavelength for case II, for radius of curvature r = 1 μm.

Tables (2)

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Table 1 Comparison of Mode Properties for Different Hybrid Plasmonic Waveguides

Tables Icon

Table 2 Mode Properties for Three Different Silicon Geometries

Equations (2)

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W(r)= 1 2 { Re[ dε(r)ω dω ] | E(r) | 2 + μ 0 | H(r) | 2 },
A e = W m max{W(r)} = 1 max{W(r)} W(r) d 2 r.

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