Abstract

We study guided modes in a conductor-gap-dielectric (CGD) system that includes a low-index dielectric gap layer of deep sub-wavelength thickness sandwiched between a conductor and a high-index dielectric cladding. Analysis of the dispersion equation for CGD modes provides an analytical estimation for the cut-off thickness of the gap layer. This guided mode is unusual because it exists when the gap thickness is less than the cutoff thickness. In the direction normal to the interfaces, the modal electric field is tightly confined within the gap. Sub-wavelength lateral mode confinement is readily provided by a spatial variation of the gap-layer thickness: the modal field localizes at the narrowest gap. Various lateral confinement schemes are proposed and verified by numerical simulations. Possible applications of CGD modes include surface-plasmon nano-lasers (SPASERs) and sensors. If these plasmonic waveguides are scaled for operation at far infrared rather than telecomm wavelengths, then the propagation losses are dramatically reduced, thereby enabling the construction of practical chip-scale plasmonic integrated circuits or PLICs.

© 2009 OSA

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2009 (5)

R. Gordon, A. I. K. Choudhury, and T. Lu, “Gap plasmon mode of eccentric coaxial metal waveguide,” Opt. Express 17(7), 5311–5320 (2009).
[CrossRef] [PubMed]

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]

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

J. W. Cleary, R. E. Peale, D. Shelton, G. Boreman, R. Soref, and W. R. Buchwald, “Drude parameters of silicides and doped silicon for infrared plasmonics,” submitted to J. Opt. Soc. Am. B (3 Oct 2009).

S.-Y. Cho and R. A. Soref, “Low-loss silicide/silicon plasmonic ribbon waveguides for mid- and far-infrared applications,” Opt. Lett. 34(12), 1759–1761 (2009).
[CrossRef] [PubMed]

2008 (5)

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

R. A. Soref, R. E. Peale, and W. Buchwald, “Longwave plasmonics on doped silicon and silicides,” Opt. Express 16(9), 6507–6514 (2008).
[CrossRef] [PubMed]

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]

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]

E. J. R. Vesseur, R. de Waele, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Surface plasmon polariton modes in a single-crystal Au nanoresonator fabricated using focused-ion-beam milling,” Appl. Phys. Lett. 92(8), 083110 (2008).
[CrossRef]

2007 (3)

P. Sanchis, J. Blasco, A. Martínez, and J. Marti, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” J. Lightwave Technol. 25(5), 1298–1305 (2007).
[CrossRef]

N.-N. Feng, M. L. Brongersma, and L. Dal Negro, “Metal-dielectric slot-waveguide structures for the propagation of surface plasmon polaritons at 1.55 μm,” IEEE J. Quantum Electron. 43(6), 479–485 (2007).
[CrossRef]

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[CrossRef]

2006 (5)

P. Müllner and R. Hainberger, “Structural optimization of silicon-on-insulator slot waveguides,” IEEE Photon. Technol. Lett. 18(24), 2557–2559 (2006).
[CrossRef]

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Pev. B 74, 205419 (2006).

E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express 14(9), 3853–3863 (2006).
[CrossRef] [PubMed]

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

K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, “Long-range surface plasmon polariton nanowire waveguides for device applications,” Opt. Express 14(1), 314–319 (2006).
[CrossRef] [PubMed]

2005 (5)

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-range surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005).
[CrossRef]

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005).
[CrossRef] [PubMed]

C. A. Barrios and M. Lipson, “Electrically driven silicon resonant light emitting device based on slot-waveguide,” Opt. Express 13(25), 10092–10101 (2005).
[CrossRef] [PubMed]

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86(8), 081101 (2005).
[CrossRef]

2004 (3)

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photon. Technol. Lett. 16(7), 1661–1663 (2004).
[CrossRef]

I. Avrutsky, “Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain,” Phys. Rev. B 70(15), 155416 (2004).
[CrossRef]

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004).
[CrossRef]

2003 (2)

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82(8), 1158–1160 (2003).
[CrossRef]

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[CrossRef] [PubMed]

1981 (1)

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981).
[CrossRef]

Atwater, H. A.

E. J. R. Vesseur, R. de Waele, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Surface plasmon polariton modes in a single-crystal Au nanoresonator fabricated using focused-ion-beam milling,” Appl. Phys. Lett. 92(8), 083110 (2008).
[CrossRef]

Aussenegg, F. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Avrutsky, I.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[CrossRef]

I. Avrutsky, “Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain,” Phys. Rev. B 70(15), 155416 (2004).
[CrossRef]

Baehr-Jones, T.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86(8), 081101 (2005).
[CrossRef]

Baida, F. I.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Pev. B 74, 205419 (2006).

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Barrios, C. A.

Bartal, G.

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]

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]

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Belkhir, A.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Pev. B 74, 205419 (2006).

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[CrossRef] [PubMed]

Blasco, J.

Boltasseva, A.

Boreman, G.

J. W. Cleary, R. E. Peale, D. Shelton, G. Boreman, R. Soref, and W. R. Buchwald, “Drude parameters of silicides and doped silicon for infrared plasmonics,” submitted to J. Opt. Soc. Am. B (3 Oct 2009).

Bozhevolnyi, S. I.

Brongersma, M. L.

N.-N. Feng, M. L. Brongersma, and L. Dal Negro, “Metal-dielectric slot-waveguide structures for the propagation of surface plasmon polaritons at 1.55 μm,” IEEE J. Quantum Electron. 43(6), 479–485 (2007).
[CrossRef]

Buchwald, W.

Buchwald, W. R.

J. W. Cleary, R. E. Peale, D. Shelton, G. Boreman, R. Soref, and W. R. Buchwald, “Drude parameters of silicides and doped silicon for infrared plasmonics,” submitted to J. Opt. Soc. Am. B (3 Oct 2009).

Cassan, E.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photon. Technol. Lett. 16(7), 1661–1663 (2004).
[CrossRef]

Cho, S.-Y.

Choudhury, A. I. K.

Cleary, J. W.

J. W. Cleary, R. E. Peale, D. Shelton, G. Boreman, R. Soref, and W. R. Buchwald, “Drude parameters of silicides and doped silicon for infrared plasmonics,” submitted to J. Opt. Soc. Am. B (3 Oct 2009).

Dai, L.

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]

Dal Negro, L.

N.-N. Feng, M. L. Brongersma, and L. Dal Negro, “Metal-dielectric slot-waveguide structures for the propagation of surface plasmon polaritons at 1.55 μm,” IEEE J. Quantum Electron. 43(6), 479–485 (2007).
[CrossRef]

Davis, C. C.

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005).
[CrossRef] [PubMed]

de Waele, R.

E. J. R. Vesseur, R. de Waele, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Surface plasmon polariton modes in a single-crystal Au nanoresonator fabricated using focused-ion-beam milling,” Appl. Phys. Lett. 92(8), 083110 (2008).
[CrossRef]

Ditlbacher, H.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Dulkeith, E.

Elliott, J.

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005).
[CrossRef] [PubMed]

Elser, J.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[CrossRef]

Fedotov, V. A.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

Feng, N.-N.

N.-N. Feng, M. L. Brongersma, and L. Dal Negro, “Metal-dielectric slot-waveguide structures for the propagation of surface plasmon polaritons at 1.55 μm,” IEEE J. Quantum Electron. 43(6), 479–485 (2007).
[CrossRef]

García de Abajo, F. J.

E. J. R. Vesseur, R. de Waele, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Surface plasmon polariton modes in a single-crystal Au nanoresonator fabricated using focused-ion-beam milling,” Appl. Phys. Lett. 92(8), 083110 (2008).
[CrossRef]

Genov, D. A.

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]

Girard, C.

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

Gladden, C.

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]

Gordon, R.

Gramotnev, D. K.

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004).
[CrossRef]

Green, W. M. J.

Grillot, F.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photon. Technol. Lett. 16(7), 1661–1663 (2004).
[CrossRef]

Hainberger, R.

P. Müllner and R. Hainberger, “Structural optimization of silicon-on-insulator slot waveguides,” IEEE Photon. Technol. Lett. 18(24), 2557–2559 (2006).
[CrossRef]

Herz, E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Hochberg, M.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86(8), 081101 (2005).
[CrossRef]

Hofer, F.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Hohenau, A.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Kjaer, K.

Kreibig, U.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Krenn, J. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Lamrous, O.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Pev. B 74, 205419 (2006).

Laroche, T.

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

Larsen, M. S.

Laval, S.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photon. Technol. Lett. 16(7), 1661–1663 (2004).
[CrossRef]

Leosson, K.

Lezec, H. J.

E. J. R. Vesseur, R. de Waele, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Surface plasmon polariton modes in a single-crystal Au nanoresonator fabricated using focused-ion-beam milling,” Appl. Phys. Lett. 92(8), 083110 (2008).
[CrossRef]

Lipson, M.

Lu, T.

Ma, R.-M.

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]

Marti, J.

Martínez, A.

Müllner, P.

P. Müllner and R. Hainberger, “Structural optimization of silicon-on-insulator slot waveguides,” IEEE Photon. Technol. Lett. 18(24), 2557–2559 (2006).
[CrossRef]

Narimanov, E. E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Nikolajsen, T.

Noginov, M. A.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Oulton, R. F.

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]

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]

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]

Papasimakis, N.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

Pascal, D.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photon. Technol. Lett. 16(7), 1661–1663 (2004).
[CrossRef]

Peale, R. E.

J. W. Cleary, R. E. Peale, D. Shelton, G. Boreman, R. Soref, and W. R. Buchwald, “Drude parameters of silicides and doped silicon for infrared plasmonics,” submitted to J. Opt. Soc. Am. B (3 Oct 2009).

R. A. Soref, R. E. Peale, and W. Buchwald, “Longwave plasmonics on doped silicon and silicides,” Opt. Express 16(9), 6507–6514 (2008).
[CrossRef] [PubMed]

Pile, D. F. P.

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]

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]

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004).
[CrossRef]

Podolskiy, V.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[CrossRef]

Polman, A.

E. J. R. Vesseur, R. de Waele, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Surface plasmon polariton modes in a single-crystal Au nanoresonator fabricated using focused-ion-beam milling,” Appl. Phys. Lett. 92(8), 083110 (2008).
[CrossRef]

Prosvirnin, S. L.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

Rogers, M.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Salakhutdinov, I.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[CrossRef]

Sanchis, P.

Sarid, D.

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981).
[CrossRef]

Schares, L.

Scherer, A.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86(8), 081101 (2005).
[CrossRef]

Shalaev, V. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Shelton, D.

J. W. Cleary, R. E. Peale, D. Shelton, G. Boreman, R. Soref, and W. R. Buchwald, “Drude parameters of silicides and doped silicon for infrared plasmonics,” submitted to J. Opt. Soc. Am. B (3 Oct 2009).

Smolyaninov, I. I.

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005).
[CrossRef] [PubMed]

Soref, R.

J. W. Cleary, R. E. Peale, D. Shelton, G. Boreman, R. Soref, and W. R. Buchwald, “Drude parameters of silicides and doped silicon for infrared plasmonics,” submitted to J. Opt. Soc. Am. B (3 Oct 2009).

Soref, R. A.

Sorger, V. J.

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]

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]

Stockman, M. I.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[CrossRef] [PubMed]

Stout, S.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Suteewong, T.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Tanaka, K.

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82(8), 1158–1160 (2003).
[CrossRef]

Tanaka, M.

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82(8), 1158–1160 (2003).
[CrossRef]

Van Labeke, D.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Pev. B 74, 205419 (2006).

Vesseur, E. J. R.

E. J. R. Vesseur, R. de Waele, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Surface plasmon polariton modes in a single-crystal Au nanoresonator fabricated using focused-ion-beam milling,” Appl. Phys. Lett. 92(8), 083110 (2008).
[CrossRef]

Vivien, L.

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photon. Technol. Lett. 16(7), 1661–1663 (2004).
[CrossRef]

Vlasov, Y. A.

Wagner, D.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Walker, C.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86(8), 081101 (2005).
[CrossRef]

Wiesner, U.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Xia, F.

Zayats, A. V.

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005).
[CrossRef] [PubMed]

Zentgraf, T.

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]

Zhang, X.

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]

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]

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]

Zheludev, N. I.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

Zhu, G.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

Appl. Phys. Lett. (5)

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86(8), 081101 (2005).
[CrossRef]

D. K. Gramotnev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel plasmon-polaritons in triangular grooves on a metal surface,” Appl. Phys. Lett. 85(26), 6323–6325 (2004).
[CrossRef]

E. J. R. Vesseur, R. de Waele, H. J. Lezec, H. A. Atwater, F. J. García de Abajo, and A. Polman, “Surface plasmon polariton modes in a single-crystal Au nanoresonator fabricated using focused-ion-beam milling,” Appl. Phys. Lett. 92(8), 083110 (2008).
[CrossRef]

K. Tanaka and M. Tanaka, “Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide,” Appl. Phys. Lett. 82(8), 1158–1160 (2003).
[CrossRef]

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

IEEE J. Quantum Electron. (1)

N.-N. Feng, M. L. Brongersma, and L. Dal Negro, “Metal-dielectric slot-waveguide structures for the propagation of surface plasmon polaritons at 1.55 μm,” IEEE J. Quantum Electron. 43(6), 479–485 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

F. Grillot, L. Vivien, S. Laval, D. Pascal, and E. Cassan, “Size influence on the propagation loss induced by sidewall roughness in ultrasmall SOI waveguides,” IEEE Photon. Technol. Lett. 16(7), 1661–1663 (2004).
[CrossRef]

P. Müllner and R. Hainberger, “Structural optimization of silicon-on-insulator slot waveguides,” IEEE Photon. Technol. Lett. 18(24), 2557–2559 (2006).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

J. W. Cleary, R. E. Peale, D. Shelton, G. Boreman, R. Soref, and W. R. Buchwald, “Drude parameters of silicides and doped silicon for infrared plasmonics,” submitted to J. Opt. Soc. Am. B (3 Oct 2009).

N. J. Phys. (1)

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]

Nat. Photonics (2)

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]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008).
[CrossRef]

Nature (2)

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009).
[CrossRef] [PubMed]

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]

Opt. Express (5)

Opt. Lett. (1)

Phys. Pev. B (1)

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Pev. B 74, 205419 (2006).

Phys. Rev. B (2)

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75(24), 241402 (2007).
[CrossRef]

I. Avrutsky, “Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain,” Phys. Rev. B 70(15), 155416 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90(2), 027402 (2003).
[CrossRef] [PubMed]

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47(26), 1927–1930 (1981).
[CrossRef]

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, “Far-field optical microscopy with a nanometer-scale resolution based on the in-plane image magnification by surface plasmon polaritons,” Phys. Rev. Lett. 94(5), 057401 (2005).
[CrossRef] [PubMed]

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005).
[CrossRef] [PubMed]

Other (7)

R. A. Soref, S. Y. Cho, W. R. Buchwald, R. E. Peale, and J. W. Cleary, “Silicon plasmonic waveguides”, chapter in An Introduction to Silicon Photonics, S. Fathpour and B. Jalali, Editors, Taylor and Francis UK (2010).

R. A. Soref, S. Y. Cho, W. R. Buchwald and R. E. Peale, “Silicon plasmonic waveguides for infrared and Terahertz applications”, (invited) SPIE Photonics North, session on waveguide design and simulation, Quebec City, Canada 25 May 2009.

V. M. Agranovich, and D. L. Mills, Surface Polaritons: ElectromagneticWaves at Surfaces and Interfaces (Elsevier, New York, 1982).

Electromagnetic Surface Modes, edited by A. D. Boardman (Wiley, New York, 1982).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, Berlin, 1988).

Material parameters are extrapolated using data from http://refractiverndex.info.

J. Liu, X. Sun, L. C. Kimerling, and J. Michel, “A Ge-on-Si Laser,” paper FD2, IEEE 6th International Conference on Group IV Photonics, San Francisco, CA, September 11, 2009.

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Figures (6)

Fig. 1
Fig. 1

Schematic view of the conductor-gap-dielectric (CGD) structure comprising a low-index dielectric gap layer between high-index dielectric and conductor claddings.

Fig. 2
Fig. 2

Graphs at the top show schematically fields of surface plasmon polariton, SPP (left), modified SPP in a CGD structure (center), and critical CGD mode close to cutoff (right). Thickness of the low-index gap layer is shown not to scale compared to the field penetration depth into the high-index dielectric and conductor claddings. Graphs at the bottom are a concrete numerical illustration for the case of nd = 4.26 (Ge), ng = 1.44 (SiO2), nc = 0.583 + 10.1i (Au), λ = 1590nm. Thickness of the gap layer is 0 (left), 2nm (center), and 3.5nm (right). Blue curves show strength of tangent component of magnetic field, and red curves show normal component of electric field.

Fig. 3
Fig. 3

Modal index (top left) and losses (bottom left) for CGD mode in a structure with nd = 4.26(Ge), ng = 1.44(SiO2), nc = 0.583 + 10.1i(Au) at λ = 1590nm. Solid lines represent numerical solution of the dispersion equation, and dashed lines calculated using the approximate formulas. Graphs at the right show modal indices (top) and losses (bottom) for CGD mode (red), large gap CGD (blue), dielectric core mode (green), and SPP mode at conductor/gap interface (brown).

Fig. 4
Fig. 4

Mode profiles for Ge/SiO2(1nm)/Au CGD structure (solid red) and SiO2/ Ge(250nm)/SiO2(1nm)/Au (short-dash green) and SiO2/Ge(250nm)/SiO2(10nm)/Au (long-dash green) dielectric core structures. Graph at the right shows a detail of the profiles in the vicinity of the gap.

Fig. 5
Fig. 5

Modal index (top) and losses (bottom) versus gap layer thickness for CGD (red) and LG-CGD (blue) mode in a structure with nd = 4.26(Ge), ng = 3.48(Si), nc = 0.583 + 10.1i(Au) at λ = 1590nm. The insets show modal index and losses for CGD mode in linear scale. Solid curves are calculated by solving numerically the dispersion equation. The dashed lines in the insets are calculated using the approximate formulas.

Fig. 6
Fig. 6

Sample structures that show lateral confinement. Minimal gap size is 50 nm for the top left, 20 nm top right and bottom left figures, and 10 nm for the bottom right figure. Radius of curved surfaces in the top right and bottom left graphs is 1000 nm. The conductor tip in the bottom right figure has 30 nm wide flat top continued with arcs of 30 nm radius. Colors indicate light wave intensity in the cross section of the structure with dark blue corresponding to minimal intensity and red corresponding to maximal intensity. Arrows show direction of electric field vector.

Equations (15)

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

n S P P = ε d ε c ε d + ε c .
Δ n S P P = R e ( n S P P ) n d n d 3 2 | ε c ' | .
α S P P 2 π λ n d 3 ε c ' ' ε c ' 2 .
l d = λ 2 π 1 R e ( n S P P 2 n d 2 ) λ 2 π | ε c ' | n d 2 .
l c = λ 2 π 1 R e ( n S P P 2 ε c ) λ 2 π 1 | ε c ' | ,
e 2 q t ( q ε g p ε d ) ( q ε g r ε c ) = ( q ε g + p ε d ) ( q ε g + r ε c ) ,
p = 2 π λ n C G D 2 ε d ,    q = 2 π λ n C G D 2 ε g ,    r = 2 π λ n C G D 2 ε c .
t m i n R e [ λ 4 π ε d ε g l n ( ε c ε d ε g ε g ε d ε c ε c ε d ε g + ε g ε d ε c ) ]
          λ 4 π ε d ε g l n ( ε c ' ε d ε g ε g ε d ε c ' ε c ' ε d ε g + ε g ε d ε c ' ) .
t m i n λ 2 π ε g | ε c ' | 1 ε d ε g .
R e ( n C G D ) n d [ 1 + ε d 2 ( ε d ε g ε g 2 π λ ( t m i n t ) ) 2 ] .
R e ( n C G D ) n d + Δ n S P P ( 1 t t m i n ) 2 ,
R e ( n C G D ) n d + [ R e ( ε d ε c ε d + ε c ) n d ] ( 1 t t m i n ) 2 .
α C G D α S P P ( 1 t t m i n ) ,
α C G D 4 π λ I m ( ε d ε c ε d + ε c ) ( 1 t t m i n ) .

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