Abstract

The effect of nonlocal optical response is studied for a novel silicon hybrid plasmonic waveguide (HPW). Finite element method is used to implement the hydrodynamic model and the propagation mode is analyzed for a hybrid plasmonic waveguide of arbitrary cross section. The waveguide has an inverted metal nano-rib over a silicon-on-insulator (SOI) structure. An extremely small mode area of~10−6 λ2 is achieved together with several microns long propagation distance at the telecom wavelength of 1.55μm. The figure of merit (FoM) is also improved in the same time, compared to the pervious hybrid plasmonic waveguide. We demonstrate the validity of our method by comparing our simulating results with some analytical results for a metal cylindrical waveguide and a metal slab waveguide in a wide wavelength range. For the HPW, we find that the nonlocal effects can give less loss and better confinement. In particular, we explore the influence of the radius of the rib’s tip on the loss and the confinement. We show that the nonlocal effects give some new fundamental limitation on the confinement, leaving the mode area finite even for geometries with infinitely sharp tips.

© 2013 OSA

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2012 (9)

G. Toscano, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express20(4), 4176–4188 (2012).
[CrossRef] [PubMed]

G. Toscano, S. Raza, S. Xiao, M. Wubs, A. P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Surface-enhanced Raman spectroscopy: nonlocal limitations,” Opt. Lett.37(13), 2538–2540 (2012).
[CrossRef] [PubMed]

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett.12(6), 3308–3314 (2012).
[CrossRef] [PubMed]

K. R. Hiremath, L. Zschiedrich, and F. Schmidt, “Numerical solution of nonlocal hydrodynamic Drude model for arbitrary shaped nano-plasmonic structures using Nédélec finite elements,” J. Comput. Phys.231(17), 5890–5896 (2012).
[CrossRef]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108(10), 106802 (2012).
[CrossRef] [PubMed]

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: Nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett.12(3), 1333–1339 (2012).
[CrossRef] [PubMed]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat Commun3, 825 (2012).
[CrossRef] [PubMed]

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]

2011 (4)

2010 (3)

2009 (2)

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett.103(9), 097403 (2009).
[CrossRef] [PubMed]

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]

2008 (6)

T. Ogawa, D. 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), 033102–033106 (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]

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]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

F. J. García de Abajo, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” J. Phys. Chem. C112(46), 17983–17987 (2008).
[CrossRef]

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

2007 (1)

2006 (1)

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 (4)

D. 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), 061106–061103 (2005).
[CrossRef]

L. Liu, Z. H. Han, and S. L. He, “Novel surface plasmon waveguide for high integration,” Opt. Express13(17), 6645–6650 (2005).
[CrossRef] [PubMed]

R. Ruppin, “Effect of non-locality on nanofocusing of surface plasmon field intensity in a conical tip,” Phys. Lett. A340(1-4), 299–302 (2005).
[CrossRef]

R. Ruppin, “Non-local optics of the near field lens,” J. Phys. Condens. Matter17(12), 1803–1810 (2005).
[CrossRef]

2004 (1)

2002 (1)

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A299(2-3), 309–312 (2002).
[CrossRef]

1980 (1)

G. C. Aers, B. V. Paranjape, and A. D. Boardman, “Non-radiative surface plasma-polariton modes of inhomogeneous metal circular cylinders,” J. Phys. F10(1), 53–65 (1980).
[CrossRef]

1977 (1)

F. Forstmann and H. Stenschke, “Electrodynamics at metal boundaries with inclusion of plasma waves,” Phys. Rev. Lett.38(23), 1365–1368 (1977).
[CrossRef]

1970 (1)

A. R. Melnyk and M. J. Harrison, “Theory of optical excitation of plasmons in metals,” Phys. Rev. B2(4), 835–850 (1970).
[CrossRef]

Aers, G. C.

G. C. Aers, B. V. Paranjape, and A. D. Boardman, “Non-radiative surface plasma-polariton modes of inhomogeneous metal circular cylinders,” J. Phys. F10(1), 53–65 (1980).
[CrossRef]

Aizpurua, J.

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: Nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett.12(3), 1333–1339 (2012).
[CrossRef] [PubMed]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat Commun3, 825 (2012).
[CrossRef] [PubMed]

Bartal, G.

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

Berini, P.

Bian, Y. S.

Boardman, A. D.

G. C. Aers, B. V. Paranjape, and A. D. Boardman, “Non-radiative surface plasma-polariton modes of inhomogeneous metal circular cylinders,” J. Phys. F10(1), 53–65 (1980).
[CrossRef]

Boltasseva, A.

Borisov, A. G.

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: Nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett.12(3), 1333–1339 (2012).
[CrossRef] [PubMed]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat Commun3, 825 (2012).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

G. Toscano, S. Raza, S. Xiao, M. Wubs, A. P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Surface-enhanced Raman spectroscopy: nonlocal limitations,” Opt. Lett.37(13), 2538–2540 (2012).
[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]

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]

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.

Chilkoti, A.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

Ciracì, C.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

Dai, D. X.

Devaux, E.

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]

Ebbesen, T. W.

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]

Elezzabi, A. Y.

Esteban, R.

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat Commun3, 825 (2012).
[CrossRef] [PubMed]

Fernández-Domínguez, A. I.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108(10), 106802 (2012).
[CrossRef] [PubMed]

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett.12(6), 3308–3314 (2012).
[CrossRef] [PubMed]

Forstmann, F.

F. Forstmann and H. Stenschke, “Electrodynamics at metal boundaries with inclusion of plasma waves,” Phys. Rev. Lett.38(23), 1365–1368 (1977).
[CrossRef]

Fukui, M.

T. Ogawa, D. 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), 033102–033106 (2008).
[CrossRef]

D. 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), 061106–061103 (2005).
[CrossRef]

García de Abajo, F. J.

F. J. García de Abajo, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” J. Phys. Chem. C112(46), 17983–17987 (2008).
[CrossRef]

García-Vidal, F. J.

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108(10), 106802 (2012).
[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]

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

Gramotnev, D. K.

T. Ogawa, D. 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), 033102–033106 (2008).
[CrossRef]

D. 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), 061106–061103 (2005).
[CrossRef]

D. F. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett.29(10), 1069–1071 (2004).
[CrossRef] [PubMed]

Gray, S. K.

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Calculating nonlocal optical properties of structures with arbitrary shape,” Phys. Rev. B82(3), 035423 (2010).
[CrossRef]

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett.103(9), 097403 (2009).
[CrossRef] [PubMed]

Han, Z.

Han, Z. H.

Hao, R.

Haraguchi, M.

T. Ogawa, D. 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), 033102–033106 (2008).
[CrossRef]

D. 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), 061106–061103 (2005).
[CrossRef]

Harrison, M. J.

A. R. Melnyk and M. J. Harrison, “Theory of optical excitation of plasmons in metals,” Phys. Rev. B2(4), 835–850 (1970).
[CrossRef]

He, S. L.

Hill, R. T.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

Hiremath, K. R.

K. R. Hiremath, L. Zschiedrich, and F. Schmidt, “Numerical solution of nonlocal hydrodynamic Drude model for arbitrary shaped nano-plasmonic structures using Nédélec finite elements,” J. Comput. Phys.231(17), 5890–5896 (2012).
[CrossRef]

Horsfield, A. P.

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett.12(6), 3308–3314 (2012).
[CrossRef] [PubMed]

Jauho, A. P.

Kazansky, A. K.

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: Nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett.12(3), 1333–1339 (2012).
[CrossRef] [PubMed]

Laluet, J. Y.

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]

Li, E.

Liu, J. S.

Liu, L.

Liu, Y.

Maier, S. A.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett.12(6), 3308–3314 (2012).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108(10), 106802 (2012).
[CrossRef] [PubMed]

Marinica, D. C.

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: Nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett.12(3), 1333–1339 (2012).
[CrossRef] [PubMed]

Martín-Moreno, L.

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]

Matsuo, S.

D. 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), 061106–061103 (2005).
[CrossRef]

McMahon, J. M.

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Calculating nonlocal optical properties of structures with arbitrary shape,” Phys. Rev. B82(3), 035423 (2010).
[CrossRef]

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett.103(9), 097403 (2009).
[CrossRef] [PubMed]

Melnyk, A. R.

A. R. Melnyk and M. J. Harrison, “Theory of optical excitation of plasmons in metals,” Phys. Rev. B2(4), 835–850 (1970).
[CrossRef]

Mock, J. J.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

Moreno, E.

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]

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]

Mortensen, N. A.

Nielsen, R. B.

Nordlander, P.

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat Commun3, 825 (2012).
[CrossRef] [PubMed]

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: Nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett.12(3), 1333–1339 (2012).
[CrossRef] [PubMed]

Ogawa, T.

T. Ogawa, D. 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), 033102–033106 (2008).
[CrossRef]

D. 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), 061106–061103 (2005).
[CrossRef]

Okamoto, T.

T. Ogawa, D. 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), 033102–033106 (2008).
[CrossRef]

D. 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), 061106–061103 (2005).
[CrossRef]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

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

Paranjape, B. V.

G. C. Aers, B. V. Paranjape, and A. D. Boardman, “Non-radiative surface plasma-polariton modes of inhomogeneous metal circular cylinders,” J. Phys. F10(1), 53–65 (1980).
[CrossRef]

Pendry, J. B.

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108(10), 106802 (2012).
[CrossRef] [PubMed]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett.12(6), 3308–3314 (2012).
[CrossRef] [PubMed]

Pile, D.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

T. Ogawa, D. 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), 033102–033106 (2008).
[CrossRef]

D. 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), 061106–061103 (2005).
[CrossRef]

Pile, D. F.

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

D. F. Pile and D. K. Gramotnev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett.29(10), 1069–1071 (2004).
[CrossRef] [PubMed]

Raza, S.

Rodrigo, S. G.

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]

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]

Ruppin, R.

R. Ruppin, “Effect of non-locality on nanofocusing of surface plasmon field intensity in a conical tip,” Phys. Lett. A340(1-4), 299–302 (2005).
[CrossRef]

R. Ruppin, “Non-local optics of the near field lens,” J. Phys. Condens. Matter17(12), 1803–1810 (2005).
[CrossRef]

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A299(2-3), 309–312 (2002).
[CrossRef]

Schatz, G. C.

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Calculating nonlocal optical properties of structures with arbitrary shape,” Phys. Rev. B82(3), 035423 (2010).
[CrossRef]

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett.103(9), 097403 (2009).
[CrossRef] [PubMed]

Schmidt, F.

K. R. Hiremath, L. Zschiedrich, and F. Schmidt, “Numerical solution of nonlocal hydrodynamic Drude model for arbitrary shaped nano-plasmonic structures using Nédélec finite elements,” J. Comput. Phys.231(17), 5890–5896 (2012).
[CrossRef]

Shi, Y. C.

Smith, D. R.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

Stenschke, H.

F. Forstmann and H. Stenschke, “Electrodynamics at metal boundaries with inclusion of plasma waves,” Phys. Rev. Lett.38(23), 1365–1368 (1977).
[CrossRef]

Thylen, L.

Toscano, G.

Urzhumov, Y.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

Van, V.

Volkov, V. S.

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]

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]

Wei, X.

Wiener, A.

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108(10), 106802 (2012).
[CrossRef] [PubMed]

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett.12(6), 3308–3314 (2012).
[CrossRef] [PubMed]

Wosinski, L.

Wubs, M.

Xiao, S.

Zhang, X.

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

R. F. Oulton, V. J. Sorger, D. A. Genov, D. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

Zheng, Z.

Zhou, T.

Zhu, J. S.

Zschiedrich, L.

K. R. Hiremath, L. Zschiedrich, and F. Schmidt, “Numerical solution of nonlocal hydrodynamic Drude model for arbitrary shaped nano-plasmonic structures using Nédélec finite elements,” J. Comput. Phys.231(17), 5890–5896 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

D. 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), 061106–061103 (2005).
[CrossRef]

J. Appl. Phys. (1)

T. Ogawa, D. 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), 033102–033106 (2008).
[CrossRef]

J. Comput. Phys. (1)

K. R. Hiremath, L. Zschiedrich, and F. Schmidt, “Numerical solution of nonlocal hydrodynamic Drude model for arbitrary shaped nano-plasmonic structures using Nédélec finite elements,” J. Comput. Phys.231(17), 5890–5896 (2012).
[CrossRef]

J. Phys. Chem. C (1)

F. J. García de Abajo, “Nonlocal effects in the plasmons of strongly interacting nanoparticles, dimers, and waveguides,” J. Phys. Chem. C112(46), 17983–17987 (2008).
[CrossRef]

J. Phys. Condens. Matter (1)

R. Ruppin, “Non-local optics of the near field lens,” J. Phys. Condens. Matter17(12), 1803–1810 (2005).
[CrossRef]

J. Phys. F (1)

G. C. Aers, B. V. Paranjape, and A. D. Boardman, “Non-radiative surface plasma-polariton modes of inhomogeneous metal circular cylinders,” J. Phys. F10(1), 53–65 (1980).
[CrossRef]

Nano Lett. (2)

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: Nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett.12(3), 1333–1339 (2012).
[CrossRef] [PubMed]

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett.12(6), 3308–3314 (2012).
[CrossRef] [PubMed]

Nat Commun (1)

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat Commun3, 825 (2012).
[CrossRef] [PubMed]

Nat. Photonics (1)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

Nature (1)

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]

New J. Phys. (1)

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

Opt. Express (9)

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]

D. X. Dai, Y. C. Shi, S. L. He, L. Wosinski, and L. Thylen, “Silicon hybrid plasmonic submicron-donut resonator with pure dielectric access waveguides,” Opt. Express19(24), 23671–23682 (2011).
[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]

G. Toscano, S. Raza, A. P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response,” Opt. Express20(4), 4176–4188 (2012).
[CrossRef] [PubMed]

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]

D. X. Dai and S. L. He, “Low-loss hybrid plasmonic waveguide with double low-index nano-slots,” Opt. Express18(17), 17958–17966 (2010).
[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]

D. X. Dai, Y. C. Shi, S. L. 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]

L. Liu, Z. H. Han, and S. L. He, “Novel surface plasmon waveguide for high integration,” Opt. Express13(17), 6645–6650 (2005).
[CrossRef] [PubMed]

Opt. Lett. (4)

Phys. Lett. A (2)

R. Ruppin, “Electromagnetic energy density in a dispersive and absorptive material,” Phys. Lett. A299(2-3), 309–312 (2002).
[CrossRef]

R. Ruppin, “Effect of non-locality on nanofocusing of surface plasmon field intensity in a conical tip,” Phys. Lett. A340(1-4), 299–302 (2005).
[CrossRef]

Phys. Rev. B (3)

A. R. Melnyk and M. J. Harrison, “Theory of optical excitation of plasmons in metals,” Phys. Rev. B2(4), 835–850 (1970).
[CrossRef]

S. Raza, G. Toscano, A. P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B84(12), 121412 (2011).
[CrossRef]

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Calculating nonlocal optical properties of structures with arbitrary shape,” Phys. Rev. B82(3), 035423 (2010).
[CrossRef]

Phys. Rev. Lett. (4)

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett.103(9), 097403 (2009).
[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]

F. Forstmann and H. Stenschke, “Electrodynamics at metal boundaries with inclusion of plasma waves,” Phys. Rev. Lett.38(23), 1365–1368 (1977).
[CrossRef]

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108(10), 106802 (2012).
[CrossRef] [PubMed]

Science (1)

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337(6098), 1072–1074 (2012).
[CrossRef] [PubMed]

Other (2)

P. Monk, Finite Element Methods for Maxwell's Equations (Oxford University Press, 2003).

A. D. Boardman, Electromagnetic Surface Modes (Wiley, 1982).

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Figures (5)

Fig. 1
Fig. 1

The real part of the effective index, the propagation distance and electric field distribution for the metal cylindrical waveguide and the metal slab waveguide: (a1) - (a4) the radius of cylinder a = 2nm, (b1) – (b4) the thickness of slab d = 2nm. All panels show comparisons of numerical simulations to analytical results both for local response (β = 0) and for nonlocal response (β = 0.0036c0). All numerical curves overlap the corresponding analytical curves.

Fig. 2
Fig. 2

(a). The cross section of the present hybrid plasmonic waveguide with an inverted metal nano-rib. (b) The distribution of electromagnetic energy density for the present hybrid plasmonic waveguide. (c) The distribution of electromagnetic energy density for the hybrid plasmonic waveguide without the metal nano-rib. (d) The distribution of electromagnetic energy density for the only inverted metal nano-rib. The structure parameters are wco = 22nm, hmetal = 10nm, hrib = 10nm, hSi = 50nm, θ = 10°, g = 0.5nm and R = 0.5nm.

Fig. 3
Fig. 3

The effective index, mode area, propagation distance and the field distributions. (a) The effective index, (b) Propagation distance and the mode area of HWP. Green (Blue) line shows the Drude (nonlocal) results. (c) and (d): electromagnetic energy density distribution for the Drude and nonlocal models, respectively.

Fig. 4
Fig. 4

(a),(b) The mode area Am and the propagation distance Lprop as g varies from 0.5nm to 7nm at λ = 1.55μm.

Fig. 5
Fig. 5

(a) The mode area Am as R varies from 1 nm to 0.005nm at λ = 1.55μm. (b) Normalized energy density along x = 0 for both the Drude model (green) and the nonlocal model (blue) at R = 0.005nm. The shaded grey and brown areas represent the silicon and metal regions, respectively. It shows that the energy density distribution has a sharp peak at the rib’s tip in the Drude model, while such a phenomenon does not exist in the nonlocal model.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

××E= ω 2 c 2 E+iω μ 0 J.
β 2 [ ·J ]+ω( ω+iγ )J=iω ω p 2 ε 0 E,
ω( ω+iγ )= ω p 2 + β 2 k 2 .
δ L = 1 Im(k) = β Im( ω( ω+iγ ) ω p 2 ) .
Ω ( β 2 ( ( ×J )·( × J ˜ )( J )·( J ˜ ) )+ω( ω+iγ )J· J ˜ iω ω p 2 ε 0 E· J ˜ ) dΩ=0,
A m = W m max{ W } = 1 max{ W } WdS ,
W= 1 4 ( Re( d( εω ) dω ) | E | 2 + μ 0 | H | 2 ).
t ( 1 2 ε 0 E 2 + 1 2 μ 0 H 2 + 1 2 ω p 2 ε 0 ( J 2 + β 2 ω 2 ( ·J ) 2 ) )=·( E×H iβ ω p 2 ε 0 ω ( ·J )·J )+ γ ω p 2 ε 0 J 2 .
W= 1 4 ( ε 0 | E | 2 + 1 ω p 2 ε 0 | J | 2 + μ 0 | H | 2 )+ β 2 4 ω p 2 ω 2 ε 0 | ·J | 2 .
p= S metal γ 2 ω p 2 ε 0 ω | J | 2 dS W m ,
FoM= 2 L prop R m =2 L prop π A m ,

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