Abstract

We characterize the frequency dependence of symmetrically-coupled long-range surface plasmon-polaritons (sc-LRSPPs) excited on double-electrode slab waveguides composed of five layers of insulator(I) and metal(M) stacked in order of IMIMI. When the core insulator has a refractive-index larger than the cladding ones, there is no cut-off core-thickness(D) for sc-LRSPP modes in all frequency range likely for modes in a conventional dielectric slab waveguide. At a specific frequency of ωc which depends on the index difference of insulator layers and the thickness of metal, the sc-LRSPP modes are non-dispersive at all for change in D. Furthermore, regardless of D alteration, the modes at ω=ωc consistently maintain a perfect flat-top profile in the core region and identical decay tails in the cladding. The sc-LRSPP modes with these prominent characteristics may excite an active medium sandwiched in between the metal layers very uniformly, therefore it will be interesting to implement such a non-dispersive flat-top mode for nonlinear applications of SPP waveguides.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  23. R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, "Passive integrated optics elements based on long-range surface plasmon polaritons," J. Lightwave Technol. 24, 477- 494 (2006).
    [CrossRef]
  24. A. Boltasseva, S. I. Bozhevolnyi, T. Søndergaard, T. Nikolajsen, and K. Leosson, "Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons," Opt. Express 13, 4237-4243 (2005).
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    [CrossRef]
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    [CrossRef]
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  29. M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, Art. No. 137404 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]

2006 (4)

2005 (4)

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, 413-422 (2005).
[CrossRef]

A. Boltasseva, S. I. Bozhevolnyi, T. Søndergaard, T. Nikolajsen, and K. Leosson, "Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons," Opt. Express 13, 4237-4243 (2005).
[CrossRef] [PubMed]

T. Nikolajsen, K. Leosson, S. I. Bozhevolnyi, "In-line extinction modulator based on long-range surface plasmon polaritons," Opt. Commun. 244, 455-459 (2005).
[CrossRef]

S. J. Charbonneau, R. Charbonneau, N. Lahoud, G. A. Mattuissi, and P. Berini, "Bragg gratings based on long-range surface plasmon-polariton waveguides: Comparison of theory and experiment," IEEE J. Quantum Electron. 41, 1480-1491 (2005).
[CrossRef]

2004 (1)

J. R. Krenn and J.-C. Weeber, "Surface plasmon polaritons in metal stripes and wires," Phil. Trans. R. Soc. Lond. A 362, 739-756 (2004).
[CrossRef]

2003 (3)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltser, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, "Polymer-based surface-plasmonpolariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, (Insight review articles) "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

2001 (1)

S. Linden, J. Kuhl, and H. Giessen, "Controlling the interaction between light and gold nano particles: Selective suppression of extinction," Phys. Rev. Lett. 86, 4688 (2001).
[CrossRef] [PubMed]

2000 (1)

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bounded modes of symmetric structures," Phys. Rev. B 61, 10484 (2000).
[CrossRef]

1999 (1)

J. Homola, S. S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sensors Actuat. B 54, 3-15 (1999).
[CrossRef]

1983 (1)

G. I. Stegeman and J. J. Burke, "Long-range surface-plasmons in electrode structures," Appl. Phys. Lett. 43, 221-223 (1983).
[CrossRef]

1981 (1)

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

1969 (1)

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

1968 (2)

E. Kretchmann and H. Raether, "Radiative decay of nonradiative surface plasmons excited by light," Z. Naturkorsch. A 23, 2135-2136 (1968).

A. Otto, "Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398 (1968).
[CrossRef]

1941 (1)

1935 (1)

R. W. Wood, "Anomalous diffraction gratings," Phys. Rev. 48, 928-936 (1935).
[CrossRef]

1902 (1)

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Mag. 4, 396 (1902).

Atwater, H. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltser, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, (Insight review articles) "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Berini, P.

G. Gagnon, N. Lahoud, G. A. Mattiussi, and P. Berini, "Thermally activated variable attenuation of longrange surface plasmon-polariton waves," J. Lightwave Technol. 24, 4391-4402 (2006).
[CrossRef]

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, "Passive integrated optics elements based on long-range surface plasmon polaritons," J. Lightwave Technol. 24, 477- 494 (2006).
[CrossRef]

S. J. Charbonneau, R. Charbonneau, N. Lahoud, G. A. Mattuissi, and P. Berini, "Bragg gratings based on long-range surface plasmon-polariton waveguides: Comparison of theory and experiment," IEEE J. Quantum Electron. 41, 1480-1491 (2005).
[CrossRef]

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bounded modes of symmetric structures," Phys. Rev. B 61, 10484 (2000).
[CrossRef]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, "Characterization of long-range surface-plasmonpolariton waveguides," J. Appl. Phys. 98, Art. No. 043109 (2005).
[CrossRef]

Boltasseva, A.

Bozhevolnyi, S. I.

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, 413-422 (2005).
[CrossRef]

T. Nikolajsen, K. Leosson, S. I. Bozhevolnyi, "In-line extinction modulator based on long-range surface plasmon polaritons," Opt. Commun. 244, 455-459 (2005).
[CrossRef]

A. Boltasseva, S. I. Bozhevolnyi, T. Søndergaard, T. Nikolajsen, and K. Leosson, "Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons," Opt. Express 13, 4237-4243 (2005).
[CrossRef] [PubMed]

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, "Polymer-based surface-plasmonpolariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

Breukelaar, I.

Burke, J. J.

G. I. Stegeman and J. J. Burke, "Long-range surface-plasmons in electrode structures," Appl. Phys. Lett. 43, 221-223 (1983).
[CrossRef]

Charbonneau, R.

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, "Passive integrated optics elements based on long-range surface plasmon polaritons," J. Lightwave Technol. 24, 477- 494 (2006).
[CrossRef]

S. J. Charbonneau, R. Charbonneau, N. Lahoud, G. A. Mattuissi, and P. Berini, "Bragg gratings based on long-range surface plasmon-polariton waveguides: Comparison of theory and experiment," IEEE J. Quantum Electron. 41, 1480-1491 (2005).
[CrossRef]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, "Characterization of long-range surface-plasmonpolariton waveguides," J. Appl. Phys. 98, Art. No. 043109 (2005).
[CrossRef]

Charbonneau, S. J.

S. J. Charbonneau, R. Charbonneau, N. Lahoud, G. A. Mattuissi, and P. Berini, "Bragg gratings based on long-range surface plasmon-polariton waveguides: Comparison of theory and experiment," IEEE J. Quantum Electron. 41, 1480-1491 (2005).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, (Insight review articles) "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

U. Schröter and A. Dereux, "Surface plasmon polaritons on metal cylinders with dielectric core," Phys. Rev. B 64, Art. No. 125420 (2001).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, (Insight review articles) "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Economou, E. N.

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Fafard, S.

Fano, U.

Gagnon, G.

Gauglitz, G.

J. Homola, S. S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sensors Actuat. B 54, 3-15 (1999).
[CrossRef]

Giessen, H.

S. Linden, J. Kuhl, and H. Giessen, "Controlling the interaction between light and gold nano particles: Selective suppression of extinction," Phys. Rev. Lett. 86, 4688 (2001).
[CrossRef] [PubMed]

Harel, E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltser, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Homola, J.

J. Homola, S. S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sensors Actuat. B 54, 3-15 (1999).
[CrossRef]

Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltser, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Kim, K. C.

H. S. Won, K. C. Kim, S. H. Song, C.-H. Oh, P. S. Kim, S. Park, and S. I. Kim, "Vertical coupling of longrange surface plasmon polaritons," Appl. Phys. Lett. 88, Art. No. 011110 (2006).
[CrossRef]

Kim, P. S.

H. S. Won, K. C. Kim, S. H. Song, C.-H. Oh, P. S. Kim, S. Park, and S. I. Kim, "Vertical coupling of longrange surface plasmon polaritons," Appl. Phys. Lett. 88, Art. No. 011110 (2006).
[CrossRef]

Kim, S. I.

H. S. Won, K. C. Kim, S. H. Song, C.-H. Oh, P. S. Kim, S. Park, and S. I. Kim, "Vertical coupling of longrange surface plasmon polaritons," Appl. Phys. Lett. 88, Art. No. 011110 (2006).
[CrossRef]

Kjaer, K.

Koel, B. E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltser, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Krenn, J. R.

J. R. Krenn and J.-C. Weeber, "Surface plasmon polaritons in metal stripes and wires," Phil. Trans. R. Soc. Lond. A 362, 739-756 (2004).
[CrossRef]

Kretchmann, E.

E. Kretchmann and H. Raether, "Radiative decay of nonradiative surface plasmons excited by light," Z. Naturkorsch. A 23, 2135-2136 (1968).

Kuhl, J.

S. Linden, J. Kuhl, and H. Giessen, "Controlling the interaction between light and gold nano particles: Selective suppression of extinction," Phys. Rev. Lett. 86, 4688 (2001).
[CrossRef] [PubMed]

Lahoud, N.

G. Gagnon, N. Lahoud, G. A. Mattiussi, and P. Berini, "Thermally activated variable attenuation of longrange surface plasmon-polariton waves," J. Lightwave Technol. 24, 4391-4402 (2006).
[CrossRef]

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, "Passive integrated optics elements based on long-range surface plasmon polaritons," J. Lightwave Technol. 24, 477- 494 (2006).
[CrossRef]

S. J. Charbonneau, R. Charbonneau, N. Lahoud, G. A. Mattuissi, and P. Berini, "Bragg gratings based on long-range surface plasmon-polariton waveguides: Comparison of theory and experiment," IEEE J. Quantum Electron. 41, 1480-1491 (2005).
[CrossRef]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, "Characterization of long-range surface-plasmonpolariton waveguides," J. Appl. Phys. 98, Art. No. 043109 (2005).
[CrossRef]

Larsen, M. S.

Leosson, K.

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, 413-422 (2005).
[CrossRef]

T. Nikolajsen, K. Leosson, S. I. Bozhevolnyi, "In-line extinction modulator based on long-range surface plasmon polaritons," Opt. Commun. 244, 455-459 (2005).
[CrossRef]

A. Boltasseva, S. I. Bozhevolnyi, T. Søndergaard, T. Nikolajsen, and K. Leosson, "Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons," Opt. Express 13, 4237-4243 (2005).
[CrossRef] [PubMed]

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, "Polymer-based surface-plasmonpolariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

Linden, S.

S. Linden, J. Kuhl, and H. Giessen, "Controlling the interaction between light and gold nano particles: Selective suppression of extinction," Phys. Rev. Lett. 86, 4688 (2001).
[CrossRef] [PubMed]

Maier, S. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltser, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Mattiussi, G.

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, "Passive integrated optics elements based on long-range surface plasmon polaritons," J. Lightwave Technol. 24, 477- 494 (2006).
[CrossRef]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, "Characterization of long-range surface-plasmonpolariton waveguides," J. Appl. Phys. 98, Art. No. 043109 (2005).
[CrossRef]

Mattiussi, G. A.

Mattuissi, G. A.

S. J. Charbonneau, R. Charbonneau, N. Lahoud, G. A. Mattuissi, and P. Berini, "Bragg gratings based on long-range surface plasmon-polariton waveguides: Comparison of theory and experiment," IEEE J. Quantum Electron. 41, 1480-1491 (2005).
[CrossRef]

Meltser, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltser, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Nikolajsen, T.

A. Boltasseva, S. I. Bozhevolnyi, T. Søndergaard, T. Nikolajsen, and K. Leosson, "Compact Z-add-drop wavelength filters for long-range surface plasmon polaritons," Opt. Express 13, 4237-4243 (2005).
[CrossRef] [PubMed]

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, 413-422 (2005).
[CrossRef]

T. Nikolajsen, K. Leosson, S. I. Bozhevolnyi, "In-line extinction modulator based on long-range surface plasmon polaritons," Opt. Commun. 244, 455-459 (2005).
[CrossRef]

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, "Polymer-based surface-plasmonpolariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

Oh, C.-H.

H. S. Won, K. C. Kim, S. H. Song, C.-H. Oh, P. S. Kim, S. Park, and S. I. Kim, "Vertical coupling of longrange surface plasmon polaritons," Appl. Phys. Lett. 88, Art. No. 011110 (2006).
[CrossRef]

Otto, A.

A. Otto, "Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398 (1968).
[CrossRef]

Ozbay, E.

E. Ozbay, (Review) "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Park, S.

S. Park and S. H. Song, "Polymeric optical attenuator based on long range surface plasmon polaritons," Electron. Lett. 42, 402-404 (2006).
[CrossRef]

H. S. Won, K. C. Kim, S. H. Song, C.-H. Oh, P. S. Kim, S. Park, and S. I. Kim, "Vertical coupling of longrange surface plasmon polaritons," Appl. Phys. Lett. 88, Art. No. 011110 (2006).
[CrossRef]

Raether, H.

E. Kretchmann and H. Raether, "Radiative decay of nonradiative surface plasmons excited by light," Z. Naturkorsch. A 23, 2135-2136 (1968).

Requicha, A. A. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltser, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Salakhutdinov, I.

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, "Polymer-based surface-plasmonpolariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

Sarid, D.

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

Scales, C.

Schröter, U.

U. Schröter and A. Dereux, "Surface plasmon polaritons on metal cylinders with dielectric core," Phys. Rev. B 64, Art. No. 125420 (2001).
[CrossRef]

Søndergaard, T.

Song, S. H.

S. Park and S. H. Song, "Polymeric optical attenuator based on long range surface plasmon polaritons," Electron. Lett. 42, 402-404 (2006).
[CrossRef]

H. S. Won, K. C. Kim, S. H. Song, C.-H. Oh, P. S. Kim, S. Park, and S. I. Kim, "Vertical coupling of longrange surface plasmon polaritons," Appl. Phys. Lett. 88, Art. No. 011110 (2006).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman and J. J. Burke, "Long-range surface-plasmons in electrode structures," Appl. Phys. Lett. 43, 221-223 (1983).
[CrossRef]

Stockman, M. I.

M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, Art. No. 137404 (2004).
[CrossRef] [PubMed]

M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, Art. No. 137404 (2004).
[CrossRef] [PubMed]

Weeber, J.-C.

J. R. Krenn and J.-C. Weeber, "Surface plasmon polaritons in metal stripes and wires," Phil. Trans. R. Soc. Lond. A 362, 739-756 (2004).
[CrossRef]

Won, H. S.

H. S. Won, K. C. Kim, S. H. Song, C.-H. Oh, P. S. Kim, S. Park, and S. I. Kim, "Vertical coupling of longrange surface plasmon polaritons," Appl. Phys. Lett. 88, Art. No. 011110 (2006).
[CrossRef]

Wood, R. W.

R. W. Wood, "Anomalous diffraction gratings," Phys. Rev. 48, 928-936 (1935).
[CrossRef]

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Mag. 4, 396 (1902).

Yee, S. S.

J. Homola, S. S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sensors Actuat. B 54, 3-15 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. I. Bozhevolnyi, "Polymer-based surface-plasmonpolariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668-670 (2003).
[CrossRef]

G. I. Stegeman and J. J. Burke, "Long-range surface-plasmons in electrode structures," Appl. Phys. Lett. 43, 221-223 (1983).
[CrossRef]

Electron. Lett. (1)

S. Park and S. H. Song, "Polymeric optical attenuator based on long range surface plasmon polaritons," Electron. Lett. 42, 402-404 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. J. Charbonneau, R. Charbonneau, N. Lahoud, G. A. Mattuissi, and P. Berini, "Bragg gratings based on long-range surface plasmon-polariton waveguides: Comparison of theory and experiment," IEEE J. Quantum Electron. 41, 1480-1491 (2005).
[CrossRef]

J. Lightwave technol. (1)

J. Opt. Soc. Am. (1)

Nat. Mater. (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltser, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef] [PubMed]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, (Insight review articles) "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

T. Nikolajsen, K. Leosson, S. I. Bozhevolnyi, "In-line extinction modulator based on long-range surface plasmon polaritons," Opt. Commun. 244, 455-459 (2005).
[CrossRef]

Opt. Express (1)

Phil. Mag. (1)

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Mag. 4, 396 (1902).

Phil. Trans. R. Soc. Lond. A (1)

J. R. Krenn and J.-C. Weeber, "Surface plasmon polaritons in metal stripes and wires," Phil. Trans. R. Soc. Lond. A 362, 739-756 (2004).
[CrossRef]

Phys, Rev. Lett. (1)

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

Phys. Rev. (2)

R. W. Wood, "Anomalous diffraction gratings," Phys. Rev. 48, 928-936 (1935).
[CrossRef]

E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Phys. Rev. B (1)

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bounded modes of symmetric structures," Phys. Rev. B 61, 10484 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

S. Linden, J. Kuhl, and H. Giessen, "Controlling the interaction between light and gold nano particles: Selective suppression of extinction," Phys. Rev. Lett. 86, 4688 (2001).
[CrossRef] [PubMed]

Science (1)

E. Ozbay, (Review) "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Sensors Actuat. B (1)

J. Homola, S. S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sensors Actuat. B 54, 3-15 (1999).
[CrossRef]

Z. Naturkorsch. A (1)

E. Kretchmann and H. Raether, "Radiative decay of nonradiative surface plasmons excited by light," Z. Naturkorsch. A 23, 2135-2136 (1968).

Z. Phys. (1)

A. Otto, "Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398 (1968).
[CrossRef]

Other (7)

M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, Art. No. 137404 (2004).
[CrossRef] [PubMed]

H. S. Won, K. C. Kim, S. H. Song, C.-H. Oh, P. S. Kim, S. Park, and S. I. Kim, "Vertical coupling of longrange surface plasmon polaritons," Appl. Phys. Lett. 88, Art. No. 011110 (2006).
[CrossRef]

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

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, "Characterization of long-range surface-plasmonpolariton waveguides," J. Appl. Phys. 98, Art. No. 043109 (2005).
[CrossRef]

E. D. Palik, Handbook of Optical Constants of Solids II, (Academic Press, San Diego, 1998).

M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, Art. No. 137404 (2004).
[CrossRef] [PubMed]

U. Schröter and A. Dereux, "Surface plasmon polaritons on metal cylinders with dielectric core," Phys. Rev. B 64, Art. No. 125420 (2001).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of a double-electrode slab waveguide structure and the shape of magnetic field profile for a symmetrically coupled LRSPP.

Fig. 2.
Fig. 2.

The dispersion curves of sc-LRSPPs for two different cases of (a) low index core (n1=1.45, n 3=1.47) and (b) high index core (n1=1.47, n3=1.45). Two asymptotic limits of D=0 µm and D=∞ are indicated by two thick curves on the boundaries of grey regions, and the dispersion curves in the grey region are of the core thicknesses ranging from 0.2 µm to 6.0 µm in 0.2 µm step. Please note that the core is thicker as the curve approaches the boundary of the grey region marked by ‘D=∞’. (c) and (d) shows thickness dispersive characteristics of effective index and βi for several frequencies below ωc , respectively. Relative locations in the dispersion diagram for ω 1 and ω 2 are indicated by horizontal lines in (a).

Fig. 3.
Fig. 3.

Dependences of the characteristic frequency on the index difference for several refractive indices of the cladding (a) and some thicknesses of the metal slab (b). The Au thickness is fixed at 20 nm for (a), and the refractive index of the cladding is fixed at 1.45 for (b) respectively.

Fig. 4.
Fig. 4.

(a). Dependences of the propagation lengths of sc-LRSPPs on the core thickness for the case of low index core at several wavelengths. The vacuum wavelengths are selected as representatives for ω<ωc (dashed line), ω=ωc (black solid line) and ω>ωc (dash-dotted line). Each of the upper and the lower grey solid curve represents just below and over the characteristic frequency respectively, and the corresponding differences from ωc are -0.17 and +2.07×106 rad./s. (b) Field profiles (Hz ) of a sc-LRSPP at ω=ωc for the case of low index core. The inset shows the profiles normalized by its value at the core-metal interface in the metal film. In the inset, grey region indicates the metal film.

Fig. 5.
Fig. 5.

(a). Dependences of the propagation lengths of sc-LRSPPs on the core thickness for the case of high index core at several wavelengths. The vacuum wavelengths are selected as representatives for ω<ωc (dotted line), ω=ωc (solid line) and ω>ωc (dash-dotted line). Please note that, differently from Fig. 4(a), the vertical axis is not logarithmic but linear scale. (b), (c), and (d) shows the field profiles (Hz) of sc-LRSPPs for several core thicknesses at ω<ωc , ω=ωc , and ω>ωc respectively. The inset in each figure shows the profiles normalized by its value at the core-metal interface in the metal film (grey region).

Equations (6)

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

H = H 0 f ( y ) exp ( i β x ) e z ,
f ( y ) = { cosh ( α 1 y ) or sinh ( α 1 y ) ( 0 y D 2 ) A exp ( α 2 [ y D 2 ] ) + B exp ( α 2 [ y D 2 ] ) ( D 2 y t + D 2 ) C exp ( α 3 [ y D 2 t ] ) ( t + D 2 y )
α m = ( β 2 ε m k 0 2 ) 1 2 , m = 1 , 2 , or 3 .
α 2 α 3 ε 2 ε 3 + α 1 α 2 ε 1 ε 2 tanh ( α 1 D 2 ) + ( α 2 ε 2 ) 2 tanh ( α 2 t ) + α 3 α 1 ε 3 ε 1 tanh ( α 1 D 2 ) tanh ( α 2 t ) = 0
{ A = 1 2 [ cosh ( α 1 D 2 ) + α 1 ε 1 α 2 ε 2 sinh ( α 1 D 2 ) ] B = 1 2 [ cosh ( α 1 D 2 ) α 1 ε 1 α 2 ε 2 sinh ( α 1 D 2 ) ] C = [ cosh ( α 1 D 2 ) cosh ( α 2 t ) + α 1 ε 1 α 2 ε 2 sinh ( α 1 D 2 ) sinh ( α 2 t ) ]
ω c = c t 1 [ ε 1 ε 2 ( ω c ) ] 1 2 tanh 1 ( ε 2 ( ω c ) ε 3 [ ε 1 ε 3 ε 1 ε 2 ( ω c ) ] 1 2 )

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