Abstract

Using exact solutions of Maxwell’s equations, we investigate the evolution of the transversal profile of a surface plasmon polariton (SPP) packet propagating along a planar interface between a dielectric and a lossy metal. We introduce a parameter to measure the propagation length of the SPP packet and analyze its behavior with respect to the shape of the packet and the dielectric characteristics of the interface. Furthermore, we study the polarization properties of the SPP packet and define two parameters to quantify the fraction of the irradiance contained in the s- and p-polarization components of the associated field. Our results help to advance in the understanding of the SPP optics beyond the single-mode description.

© 2015 Optical Society of America

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References

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  1. R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
    [Crossref]
  2. J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
    [Crossref]
  3. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  4. E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
    [Crossref] [PubMed]
  5. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72, 075405 (2005).
    [Crossref]
  6. G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30, 3359–3361 (2005).
    [Crossref]
  7. 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,” Nature 440, 508–511 (2006).
    [Crossref] [PubMed]
  8. E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. Garćıa-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
    [Crossref]
  9. A. Manjavacas and F. J. Garćıa de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett. 9, 1285–1289 (2009).
    [Crossref]
  10. C. E. H. Berger, T. A. M. Beumer, and R. P. H. K. J. Greve, “Surface Plasmon Resonance Multisensing,” Anal. Chem. 70, 703–706 (1998).
    [Crossref]
  11. J. Homola, S. Yee, and G. Gauglitz, “Surface-plasmon resonance sensors: review,” Sensors and Actuators B: Chemical 54, 3–15 (1999).
    [Crossref]
  12. M. A. Cooper, “Optical biosensors in drug discovery,” Nat. Rev. Drug. Discov. 1, 515–528 (2002).
    [Crossref] [PubMed]
  13. A. J. Haes and R. P. V. Duyne, “A unified view of propagating and localized surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 379, 920–930 (2004).
    [Crossref] [PubMed]
  14. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [Crossref] [PubMed]
  15. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
    [Crossref] [PubMed]
  16. D. Melville and R. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 13, 2127–2134 (2005).
    [Crossref] [PubMed]
  17. F. Wei, D. Lu, H. Shen, W. Wan, J. L. Ponsetto, E. Huang, and Z. Liu, “Wide field super-resolution surface imaging through plasmonic structured illumination microscopy,” Nano Lett. 14, 4634–4639 (2014).
    [Crossref] [PubMed]
  18. T. V. Teperik, A. Archambault, F. Marquier, and J. J. Greffet, “Huygens-Fresnel principle for surface plasmons,” Opt. Express 17(20), 17483–17490 (2009).
    [Crossref]
  19. A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79, 195414 (2009).
    [Crossref]
  20. A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Surface plasmon polaritons on metallic surfaces,” Opt. Express 15, 183–197 (2006).
    [Crossref]
  21. A. Norrman, T. Setäalä, and A. T. Friberg, “Exact surface-plasmon polariton solutions at a lossy interface,” Opt. Lett. 38, 1119–1121 (2013).
    [Crossref] [PubMed]
  22. A. Norrman, T. Setälä, and A. T. Friberg, “Surface-plasmon polariton solutions at a lossy slab in a symmetric surrounding,” Opt. Express 22, 4628–4648 (2014).
    [Crossref] [PubMed]
  23. O. El Gawhary, A. J. L. Adam, and H. P. Urbach, “Nonexistence of pure S- and P-polarized surface waves at the interface between a perfect dielectric and a real metal,” Phys. Rev. A 89, 023834 (2014).
    [Crossref]
  24. R. Martínez-Herrero, P. M. Mejías, and A. Carnicer, “Evanescent field of vectorial highly non-paraxial beams,” Opt. Express 16(5), 2845–2858 (2008).
    [Crossref] [PubMed]
  25. R. Martínez-Herrero, P. M. Mejías, and G. Piquero, Characterization of Partially Polarized Light Fields (Springer-Verlag, 2008).
  26. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [Crossref]
  27. R. Martínez-Herrero, P. M. Mejías, and A. Manjavacas, “Beam width of highly-focused radially-polarized fields,” Opt. Express 18, 20817–20826 (2010).
    [Crossref]

2014 (3)

F. Wei, D. Lu, H. Shen, W. Wan, J. L. Ponsetto, E. Huang, and Z. Liu, “Wide field super-resolution surface imaging through plasmonic structured illumination microscopy,” Nano Lett. 14, 4634–4639 (2014).
[Crossref] [PubMed]

O. El Gawhary, A. J. L. Adam, and H. P. Urbach, “Nonexistence of pure S- and P-polarized surface waves at the interface between a perfect dielectric and a real metal,” Phys. Rev. A 89, 023834 (2014).
[Crossref]

A. Norrman, T. Setälä, and A. T. Friberg, “Surface-plasmon polariton solutions at a lossy slab in a symmetric surrounding,” Opt. Express 22, 4628–4648 (2014).
[Crossref] [PubMed]

2013 (1)

2010 (1)

2009 (3)

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

T. V. Teperik, A. Archambault, F. Marquier, and J. J. Greffet, “Huygens-Fresnel principle for surface plasmons,” Opt. Express 17(20), 17483–17490 (2009).
[Crossref]

A. Manjavacas and F. J. Garćıa de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett. 9, 1285–1289 (2009).
[Crossref]

2008 (2)

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. Garćıa-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[Crossref]

R. Martínez-Herrero, P. M. Mejías, and A. Carnicer, “Evanescent field of vectorial highly non-paraxial beams,” Opt. Express 16(5), 2845–2858 (2008).
[Crossref] [PubMed]

2007 (1)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[Crossref]

2006 (3)

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[Crossref] [PubMed]

A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Surface plasmon polaritons on metallic surfaces,” Opt. Express 15, 183–197 (2006).
[Crossref]

2005 (4)

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72, 075405 (2005).
[Crossref]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[Crossref] [PubMed]

D. Melville and R. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 13, 2127–2134 (2005).
[Crossref] [PubMed]

G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30, 3359–3361 (2005).
[Crossref]

2004 (1)

A. J. Haes and R. P. V. Duyne, “A unified view of propagating and localized surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 379, 920–930 (2004).
[Crossref] [PubMed]

2002 (1)

M. A. Cooper, “Optical biosensors in drug discovery,” Nat. Rev. Drug. Discov. 1, 515–528 (2002).
[Crossref] [PubMed]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

1999 (1)

J. Homola, S. Yee, and G. Gauglitz, “Surface-plasmon resonance sensors: review,” Sensors and Actuators B: Chemical 54, 3–15 (1999).
[Crossref]

1998 (1)

C. E. H. Berger, T. A. M. Beumer, and R. P. H. K. J. Greve, “Surface Plasmon Resonance Multisensing,” Anal. Chem. 70, 703–706 (1998).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

1957 (1)

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
[Crossref]

Adam, A. J. L.

O. El Gawhary, A. J. L. Adam, and H. P. Urbach, “Nonexistence of pure S- and P-polarized surface waves at the interface between a perfect dielectric and a real metal,” Phys. Rev. A 89, 023834 (2014).
[Crossref]

Archambault, A.

T. V. Teperik, A. Archambault, F. Marquier, and J. J. Greffet, “Huygens-Fresnel principle for surface plasmons,” Opt. Express 17(20), 17483–17490 (2009).
[Crossref]

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72, 075405 (2005).
[Crossref]

Berger, C. E. H.

C. E. H. Berger, T. A. M. Beumer, and R. P. H. K. J. Greve, “Surface Plasmon Resonance Multisensing,” Anal. Chem. 70, 703–706 (1998).
[Crossref]

Beumer, T. A. M.

C. E. H. Berger, T. A. M. Beumer, and R. P. H. K. J. Greve, “Surface Plasmon Resonance Multisensing,” Anal. Chem. 70, 703–706 (1998).
[Crossref]

Blaikie, R.

Bozhevolnyi, S. I.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. Garćıa-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[Crossref]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[Crossref] [PubMed]

Carnicer, A.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Chulkov, E. V.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[Crossref]

Cooper, M. A.

M. A. Cooper, “Optical biosensors in drug discovery,” Nat. Rev. Drug. Discov. 1, 515–528 (2002).
[Crossref] [PubMed]

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,” Nature 440, 508–511 (2006).
[Crossref] [PubMed]

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72, 075405 (2005).
[Crossref]

Duyne, R. P. V.

A. J. Haes and R. P. V. Duyne, “A unified view of propagating and localized surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 379, 920–930 (2004).
[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,” Nature 440, 508–511 (2006).
[Crossref] [PubMed]

Echenique, P. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[Crossref]

El Gawhary, O.

O. El Gawhary, A. J. L. Adam, and H. P. Urbach, “Nonexistence of pure S- and P-polarized surface waves at the interface between a perfect dielectric and a real metal,” Phys. Rev. A 89, 023834 (2014).
[Crossref]

Fan, S.

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[Crossref] [PubMed]

Friberg, A. T.

Garcia de Abajo, F. J.

A. Manjavacas and F. J. Garćıa de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett. 9, 1285–1289 (2009).
[Crossref]

Garcia-Vidal, F. J.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. Garćıa-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[Crossref]

Gauglitz, G.

J. Homola, S. Yee, and G. Gauglitz, “Surface-plasmon resonance sensors: review,” Sensors and Actuators B: Chemical 54, 3–15 (1999).
[Crossref]

Greffet, J. J.

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

T. V. Teperik, A. Archambault, F. Marquier, and J. J. Greffet, “Huygens-Fresnel principle for surface plasmons,” Opt. Express 17(20), 17483–17490 (2009).
[Crossref]

Greve, R. P. H. K. J.

C. E. H. Berger, T. A. M. Beumer, and R. P. H. K. J. Greve, “Surface Plasmon Resonance Multisensing,” Anal. Chem. 70, 703–706 (1998).
[Crossref]

Haes, A. J.

A. J. Haes and R. P. V. Duyne, “A unified view of propagating and localized surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 379, 920–930 (2004).
[Crossref] [PubMed]

Homola, J.

J. Homola, S. Yee, and G. Gauglitz, “Surface-plasmon resonance sensors: review,” Sensors and Actuators B: Chemical 54, 3–15 (1999).
[Crossref]

Huang, E.

F. Wei, D. Lu, H. Shen, W. Wan, J. L. Ponsetto, E. Huang, and Z. Liu, “Wide field super-resolution surface imaging through plasmonic structured illumination microscopy,” Nano Lett. 14, 4634–4639 (2014).
[Crossref] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

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,” Nature 440, 508–511 (2006).
[Crossref] [PubMed]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[Crossref] [PubMed]

Liu, Z.

F. Wei, D. Lu, H. Shen, W. Wan, J. L. Ponsetto, E. Huang, and Z. Liu, “Wide field super-resolution surface imaging through plasmonic structured illumination microscopy,” Nano Lett. 14, 4634–4639 (2014).
[Crossref] [PubMed]

Lu, D.

F. Wei, D. Lu, H. Shen, W. Wan, J. L. Ponsetto, E. Huang, and Z. Liu, “Wide field super-resolution surface imaging through plasmonic structured illumination microscopy,” Nano Lett. 14, 4634–4639 (2014).
[Crossref] [PubMed]

Maier, S. A.

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

Manjavacas, A.

R. Martínez-Herrero, P. M. Mejías, and A. Manjavacas, “Beam width of highly-focused radially-polarized fields,” Opt. Express 18, 20817–20826 (2010).
[Crossref]

A. Manjavacas and F. J. Garćıa de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett. 9, 1285–1289 (2009).
[Crossref]

Mansuripur, M.

Marquier, F.

T. V. Teperik, A. Archambault, F. Marquier, and J. J. Greffet, “Huygens-Fresnel principle for surface plasmons,” Opt. Express 17(20), 17483–17490 (2009).
[Crossref]

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

Martínez-Herrero, R.

Martín-Moreno, L.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. Garćıa-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[Crossref]

Mejías, P. M.

Melville, D.

Moloney, J. V.

Moreno, E.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. Garćıa-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[Crossref]

Norrman, A.

Ozbay, E.

E. Ozbay, “Plasmonics: Merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

Piquero, G.

R. Martínez-Herrero, P. M. Mejías, and G. Piquero, Characterization of Partially Polarized Light Fields (Springer-Verlag, 2008).

Pitarke, J. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[Crossref]

Polman, A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72, 075405 (2005).
[Crossref]

Ponsetto, J. L.

F. Wei, D. Lu, H. Shen, W. Wan, J. L. Ponsetto, E. Huang, and Z. Liu, “Wide field super-resolution surface imaging through plasmonic structured illumination microscopy,” Nano Lett. 14, 4634–4639 (2014).
[Crossref] [PubMed]

Ritchie, R. H.

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
[Crossref]

Rodrigo, S. G.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. Garćıa-Vidal, “Guiding and focusing of electromagnetic fields with wedge plasmon polaritons,” Phys. Rev. Lett. 100, 023901 (2008).
[Crossref]

Setäalä, T.

Setälä, T.

Shen, H.

F. Wei, D. Lu, H. Shen, W. Wan, J. L. Ponsetto, E. Huang, and Z. Liu, “Wide field super-resolution surface imaging through plasmonic structured illumination microscopy,” Nano Lett. 14, 4634–4639 (2014).
[Crossref] [PubMed]

Silkin, V. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70, 1–87 (2007).
[Crossref]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[Crossref] [PubMed]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Planar metal plasmon waveguides: frequency-dependent dispersion, propagation, localization, and loss beyond the free electron model,” Phys. Rev. B 72, 075405 (2005).
[Crossref]

Teperik, T. V.

T. V. Teperik, A. Archambault, F. Marquier, and J. J. Greffet, “Huygens-Fresnel principle for surface plasmons,” Opt. Express 17(20), 17483–17490 (2009).
[Crossref]

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

Urbach, H. P.

O. El Gawhary, A. J. L. Adam, and H. P. Urbach, “Nonexistence of pure S- and P-polarized surface waves at the interface between a perfect dielectric and a real metal,” Phys. Rev. A 89, 023834 (2014).
[Crossref]

Veronis, G.

Volkov, V. S.

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,” Nature 440, 508–511 (2006).
[Crossref] [PubMed]

Wan, W.

F. Wei, D. Lu, H. Shen, W. Wan, J. L. Ponsetto, E. Huang, and Z. Liu, “Wide field super-resolution surface imaging through plasmonic structured illumination microscopy,” Nano Lett. 14, 4634–4639 (2014).
[Crossref] [PubMed]

Wei, F.

F. Wei, D. Lu, H. Shen, W. Wan, J. L. Ponsetto, E. Huang, and Z. Liu, “Wide field super-resolution surface imaging through plasmonic structured illumination microscopy,” Nano Lett. 14, 4634–4639 (2014).
[Crossref] [PubMed]

Yee, S.

J. Homola, S. Yee, and G. Gauglitz, “Surface-plasmon resonance sensors: review,” Sensors and Actuators B: Chemical 54, 3–15 (1999).
[Crossref]

Zakharian, A. R.

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[Crossref] [PubMed]

Anal. Bioanal. Chem. (1)

A. J. Haes and R. P. V. Duyne, “A unified view of propagating and localized surface plasmon resonance biosensors,” Anal. Bioanal. Chem. 379, 920–930 (2004).
[Crossref] [PubMed]

Anal. Chem. (1)

C. E. H. Berger, T. A. M. Beumer, and R. P. H. K. J. Greve, “Surface Plasmon Resonance Multisensing,” Anal. Chem. 70, 703–706 (1998).
[Crossref]

Nano Lett. (2)

A. Manjavacas and F. J. Garćıa de Abajo, “Robust plasmon waveguides in strongly interacting nanowire arrays,” Nano Lett. 9, 1285–1289 (2009).
[Crossref]

F. Wei, D. Lu, H. Shen, W. Wan, J. L. Ponsetto, E. Huang, and Z. Liu, “Wide field super-resolution surface imaging through plasmonic structured illumination microscopy,” Nano Lett. 14, 4634–4639 (2014).
[Crossref] [PubMed]

Nat. Rev. Drug. Discov. (1)

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Figures (5)

Fig. 1
Fig. 1

Schematics of the system under study. We consider a planar interface between a dielectric and a lossy metal placed perpendicularly to the z-axis.

Fig. 2
Fig. 2

Square modulus of the SPP packet field, Esp(x,y) for a silver-vacuum interface. We assume a Gaussian packet, i.e. F(u) given by Eq. (2), with three different values of a: 0.05 (upper panel), 0.1 (middle panel), and 0.2 (lower panel). In all cases we choose a vacuum wavelength λ = 633nm.

Fig. 3
Fig. 3

Propagation length, x ¯ 0, for a Gaussian SPP packet (see Eq. (2)) propagating along an interface between silver and a dielectric medium with dielectric function εd. Panel (a) shows x ¯ 0 plotted as a function of a (solid curves) for three different values of εd : 1 (upper panel), 2 (middle panel), and 4 (lower panel). The dashed lines in these plots represent the propagation length for a single-mode SPP, x0 = 1/(2Im {ksp}). Panel (b) shows x ¯ 0 plotted as a function of εd for three different values of a: 0.1 (green curve), 1 (blue curve), and 2 (red curve). In all cases the vacuum wavelength λ is 633 nm.

Fig. 4
Fig. 4

Fraction of the irradiance contained in the p-component of the field of a Gaussian SPP packet, ρp(x,y), with a = 1 propagating on a silver-vacuum interface. (b) Square modulus of the field for the packet of panel (a). In both cases the vacuum wavelength is λ = 633nm.

Fig. 5
Fig. 5

Global fraction of the irradiance contained in the p-component of the field, ρ ˜ p ( x ), for a Gaussian SPP packet propagating along a metal-dielectric interface. Panel (a) shows ρ ˜ p ( x ) plotted as a function of the position x normalized to the propagation length x ¯ 0. We consider two values of a: 0.1 (dashed curves), and 2 (solid curves), and two different εd: 1 (green curves), and 4 (red curves). Panel (b) shows ρ ˜ p ( x ) as a function of the ratio between the dielectric functions of silver and the dielectric medium, εd/|Re {εc}|. We consider two different positions: x = 0 (green curves) and x = 0.3 x ¯ 0 (red 0 curves) and two different values of a: 0.1 (dashed curves, right scale) and 2 (solid curves, left scale). In all cases the vacuum wavelength is λ = 633nm.

Equations (18)

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E ( r , u ) = E 0 , j ( u ) e i r k j ( u ) ,
k j ( u ) = ( k x ( u ) , Re { k sp 2 } u , k j z ) ,
E 0 j ( u ) = ( k x ( u ) k sp , Re { k sp 2 } u k sp , k sp k j z ) ,
E sp ( x , y ) = d u F ( u ) E 0 j ( u ) e i x k x ( u ) e i y Re { k sp 2 } u ,
F ( u ) = e ( u / a ) 2 a π ,
x ¯ 0 = 0 d x I sp ( x ) x 0 d x I sp ( x ) ,
x ¯ 0 = d u | E 0 d ( u ) F ( u ) | 2 / Im 2 { k x ( u ) } 2 d u | E 0 d ( u ) F ( u ) | 2 / Im { k x ( u ) } .
x ¯ 0 = 1 2 Im { k sp } 1 u 2 0 Re { k sp 2 } ( 1 + γ ) | k sp 2 | ( γ + Re { k sp 2 } | k sp 2 | ) 1 u 2 0 Re { k sp 2 } ( 1 + γ ) | k sp 2 | ( γ 1 2 + Re { k sp 2 } | k sp 2 | ) ,
u 2 0 = d u | F ( u ) | 2 u 2 d u | F ( u ) | 2 ,
ρ σ ( x , y ) = | E sp , σ ( x , y ) | 2 | E sp ( x , y ) | 2 ,
ρ ˜ σ ( x ) = d y ρ σ ( x , y ) | E sp ( x , y ) | 2 d y | E sp ( x , y ) | 2 ,
ρ ˜ p ( x ) = 1 Re { k sp 2 } u 2 ( x ) | k sp 2 | ( 1 + γ ) + 2 Re { k sp 2 } u 2 ( x ) Im 2 { k sp } | k sp 2 | ,
u 2 ( x ) = d u | F ( u ) | 2 u 2 exp [ x u 2 Re { k sp 2 } Im { k sp } | k sp 2 | ] d u | F ( u ) | 2 exp [ x u 2 Re { k sp 2 } Im { k sp } | k sp 2 | ] .
E j ( r ) = E 0 j e i r k j ,
k j = ( k x , k y , k j z ) ,
k x 2 + k y 2 = k sp 2 .
E 0 j = ( k x k sp , k y k sp , k sp k j z ) .
k x 2 = k sp 2 u 2 Re { k sp 2 } i v 2 Im { k sp 2 } , k y 2 = u 2 Re { k sp 2 } + i v 2 Im { k sp 2 } ,

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