Abstract

We investigate the focusing of surface plasmon polaritons (SPPs) excited with 1.5 µm light in a tapered Au waveguide on a planar dielectric substrate by experiments and simulations. We find that nanofocusing can be obtained when the asymmetric bound mode at the substrate side of the metal film is excited. The propagation and concentration of this mode to the tip is demonstrated. No sign of a cutoff waveguide width is observed as the SPPs propagate along the tapered waveguide. Simulations show that such concentrating behavior is not possible for excitation of the mode at the low-index side of the film. The mode that enables the focusing exhibits a strong resemblance to the asymmetric mode responsible for focusing in conical waveguides. This work demonstrates a practical implementation of plasmonic nanofocusing on a planar substrate.

© 2008 Optical Society of America

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References

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  1. E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
    [CrossRef] [PubMed]
  2. J.-C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, J. P. Goudonnet, "Near-field observation of surface plasmon polariton propagation on thin metal stripes," Phys. Rev. B 61, 045411 (2001).
    [CrossRef]
  3. A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, F. R. Aussenegg, "Dielectric optical elements for surface plasmons," Opt. Lett. 30, 893-895 (2005).
    [CrossRef] [PubMed]
  4. A. Drezet, A. L. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, J. R. Krenn, "Surface plasmon propagation in an elliptical corral," Appl. Phys. Lett. 86, 074104 (2005).
    [CrossRef]
  5. L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, C. W. Kimball, "Subwavelength focusing and guiding of surface plasmons," Nano Lett. 5, 1399-1402 (2005).
    [CrossRef] [PubMed]
  6. Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, X. Zhang, "Focusing surface plasmons with a plasmonics lens," Nano Lett. 5, 1726-1729 (2005).
    [CrossRef] [PubMed]
  7. H. L. Offerhaus, B. van den Bergen, M. Escalante, F. B. Segerink, J. P. Korterik, N. F. van Hulst, "Creating focused plasmons by noncollinear phasematching on functional gratings," Nano Lett. 5, 2144-2148 (2005).
    [CrossRef] [PubMed]
  8. C. A. Pfeiffer, E. N. Economou, K. L. Ngai, "Surface polaritons in a circularly cylindrical interface: surface plasmons," Phys. Rev. B 10, 3038-3051 (1974).
    [CrossRef]
  9. J. J. Burke and G. I. Stegeman, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
    [CrossRef]
  10. E. N. Economou, "Surface plasmons in thin films," Phys. Rev. 182, 539-554 (1969).
    [CrossRef]
  11. M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, 137404 (2004).
    [CrossRef] [PubMed]
  12. D. K. Gramotnev and K. C. Vernon, "Adiabatic nano-focusing of plasmons by sharp metallic wedges," Appl. Phys. B 86, 7-17 (2007).
    [CrossRef]
  13. D. K. Gramotnev, D. F. P. Pile, M. W. Vogel, X. Zhang, "Local electric field enhancement during nanofocusing of plasmons by a tapered gap," Phys. Rev. B 75, 035431 (2007).
    [CrossRef]
  14. F. Keilmann, "Surface-polariton propagation for scanning near-field optical microscopy application," J. Microsc. 194, 567-570 (1999).
    [CrossRef]
  15. A. Bouhelier, J. Renger, M. R. Beversluis, L. Novotny, "Plasmon-coupled tip-enhanced near-field optical microscopy," J. Microsc. 210, 220-224 (2003).
    [CrossRef] [PubMed]
  16. C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, C. Lienau, "Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source," Nano Lett. 7, 2784-2788 (2007).
    [CrossRef] [PubMed]
  17. J. Koglin, U. C. Fischer, H. Fuchs, "Material contrast in scanning near-field optical microscopy at 1-10 nm resolution," Phys. Rev. B 55, 7977-7984 (1997).
    [CrossRef]
  18. N. A. Janunts, K. S. Baghdasaryan, Kh. V. Nerkararyan, B. Hecht, "Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip," Opt. Commun. 253, 118-124 (2005).
    [CrossRef]
  19. E. Verhagen, L. Kuipers, A. Polman, "Enhanced nonlinear optical effects with a tapered plasmonic waveguide," Nano Lett. 7, 334-337 (2007).
    [CrossRef] [PubMed]
  20. E. Verhagen, A. L. Tchebotareva, A. Polman, "Erbium luminescence imaging of infrared surface plasmon polaritons," Appl. Phys. Lett. 88, 121121 (2006).
    [CrossRef]
  21. R. Zia, J. A. Schuller, M. L. Brongersma, "Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides," Phys. Rev. B 74, 165415 (2006).
    [CrossRef]
  22. D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, C. Lienau, "Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures," Phys. Rev. Lett. 91, 143901 (2003).
    [CrossRef] [PubMed]
  23. E. Devaux, T. W. Ebbesen, J.-C. Weeber, A. Dereux, "Launching and decoupling surface plasmons via micro-gratings," Appl. Phys. Lett. 83, 4936-4938 (2003).
    [CrossRef]
  24. F. Auzel, "Upconversion and anti-Stokes processes with f and d ions in solids," Chem. Rev. 104, 139-173 (2004).
    [CrossRef] [PubMed]
  25. G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, M. K. Smit, "Upconversion in Er-implanted Al2O3 waveguides," J. Appl. Phys. 79, 1258-1266 (1996).
    [CrossRef]
  26. G. N. van den Hoven, E. Snoeks, A. Polman, J. W. M. van Uffelen, Y. S. Oei, M. K. Smit, "Photoluminescence characterization of Er-implanted Al2O3 films," Appl. Phys. Lett. 62, 3065-3067 (1993).
    [CrossRef]
  27. M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Güdel, M. P. Hehlen, "Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems," Phys. Rev. B 61, 3337-3346 (2000).
    [CrossRef]
  28. R. Zia, M. D. Selker, M. L. Brongersma, "Leaky and bound modes of surface plasmon waveguides," Phys. Rev. B 71, 165431 (2005).
    [CrossRef]
  29. Lumerical FDTD Solutions 5.0
  30. P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures," Phys. Rev. B 63, 125417 (2001).
    [CrossRef]
  31. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972)
    [CrossRef]
  32. Z. Zhu and T. G. Brown, "Full-vectorial finite-difference analysis of microstructured optical fibers," Opt. Express 10, 853-864 (2002).
    [PubMed]
  33. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, J. R. Krenn, "Silver nanowires as surface plasmon resonators," Phys. Rev. Lett. 95, 257403 (2005).
    [CrossRef] [PubMed]

2007

D. K. Gramotnev and K. C. Vernon, "Adiabatic nano-focusing of plasmons by sharp metallic wedges," Appl. Phys. B 86, 7-17 (2007).
[CrossRef]

D. K. Gramotnev, D. F. P. Pile, M. W. Vogel, X. Zhang, "Local electric field enhancement during nanofocusing of plasmons by a tapered gap," Phys. Rev. B 75, 035431 (2007).
[CrossRef]

E. Verhagen, L. Kuipers, A. Polman, "Enhanced nonlinear optical effects with a tapered plasmonic waveguide," Nano Lett. 7, 334-337 (2007).
[CrossRef] [PubMed]

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, C. Lienau, "Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source," Nano Lett. 7, 2784-2788 (2007).
[CrossRef] [PubMed]

2006

E. Verhagen, A. L. Tchebotareva, A. Polman, "Erbium luminescence imaging of infrared surface plasmon polaritons," Appl. Phys. Lett. 88, 121121 (2006).
[CrossRef]

R. Zia, J. A. Schuller, M. L. Brongersma, "Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides," Phys. Rev. B 74, 165415 (2006).
[CrossRef]

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

2005

A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, F. R. Aussenegg, "Dielectric optical elements for surface plasmons," Opt. Lett. 30, 893-895 (2005).
[CrossRef] [PubMed]

A. Drezet, A. L. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, J. R. Krenn, "Surface plasmon propagation in an elliptical corral," Appl. Phys. Lett. 86, 074104 (2005).
[CrossRef]

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, C. W. Kimball, "Subwavelength focusing and guiding of surface plasmons," Nano Lett. 5, 1399-1402 (2005).
[CrossRef] [PubMed]

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, X. Zhang, "Focusing surface plasmons with a plasmonics lens," Nano Lett. 5, 1726-1729 (2005).
[CrossRef] [PubMed]

H. L. Offerhaus, B. van den Bergen, M. Escalante, F. B. Segerink, J. P. Korterik, N. F. van Hulst, "Creating focused plasmons by noncollinear phasematching on functional gratings," Nano Lett. 5, 2144-2148 (2005).
[CrossRef] [PubMed]

N. A. Janunts, K. S. Baghdasaryan, Kh. V. Nerkararyan, B. Hecht, "Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip," Opt. Commun. 253, 118-124 (2005).
[CrossRef]

R. Zia, M. D. Selker, M. L. Brongersma, "Leaky and bound modes of surface plasmon waveguides," Phys. Rev. B 71, 165431 (2005).
[CrossRef]

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

2004

F. Auzel, "Upconversion and anti-Stokes processes with f and d ions in solids," Chem. Rev. 104, 139-173 (2004).
[CrossRef] [PubMed]

M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

2003

A. Bouhelier, J. Renger, M. R. Beversluis, L. Novotny, "Plasmon-coupled tip-enhanced near-field optical microscopy," J. Microsc. 210, 220-224 (2003).
[CrossRef] [PubMed]

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, C. Lienau, "Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures," Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

E. Devaux, T. W. Ebbesen, J.-C. Weeber, A. Dereux, "Launching and decoupling surface plasmons via micro-gratings," Appl. Phys. Lett. 83, 4936-4938 (2003).
[CrossRef]

2002

2001

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures," Phys. Rev. B 63, 125417 (2001).
[CrossRef]

J.-C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, J. P. Goudonnet, "Near-field observation of surface plasmon polariton propagation on thin metal stripes," Phys. Rev. B 61, 045411 (2001).
[CrossRef]

2000

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Güdel, M. P. Hehlen, "Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems," Phys. Rev. B 61, 3337-3346 (2000).
[CrossRef]

1999

F. Keilmann, "Surface-polariton propagation for scanning near-field optical microscopy application," J. Microsc. 194, 567-570 (1999).
[CrossRef]

1997

J. Koglin, U. C. Fischer, H. Fuchs, "Material contrast in scanning near-field optical microscopy at 1-10 nm resolution," Phys. Rev. B 55, 7977-7984 (1997).
[CrossRef]

1996

G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, M. K. Smit, "Upconversion in Er-implanted Al2O3 waveguides," J. Appl. Phys. 79, 1258-1266 (1996).
[CrossRef]

1993

G. N. van den Hoven, E. Snoeks, A. Polman, J. W. M. van Uffelen, Y. S. Oei, M. K. Smit, "Photoluminescence characterization of Er-implanted Al2O3 films," Appl. Phys. Lett. 62, 3065-3067 (1993).
[CrossRef]

1986

J. J. Burke and G. I. Stegeman, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

1974

C. A. Pfeiffer, E. N. Economou, K. L. Ngai, "Surface polaritons in a circularly cylindrical interface: surface plasmons," Phys. Rev. B 10, 3038-3051 (1974).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972)
[CrossRef]

1969

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

Appl. Phys. B

D. K. Gramotnev and K. C. Vernon, "Adiabatic nano-focusing of plasmons by sharp metallic wedges," Appl. Phys. B 86, 7-17 (2007).
[CrossRef]

Appl. Phys. Lett.

A. Drezet, A. L. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, J. R. Krenn, "Surface plasmon propagation in an elliptical corral," Appl. Phys. Lett. 86, 074104 (2005).
[CrossRef]

E. Verhagen, A. L. Tchebotareva, A. Polman, "Erbium luminescence imaging of infrared surface plasmon polaritons," Appl. Phys. Lett. 88, 121121 (2006).
[CrossRef]

E. Devaux, T. W. Ebbesen, J.-C. Weeber, A. Dereux, "Launching and decoupling surface plasmons via micro-gratings," Appl. Phys. Lett. 83, 4936-4938 (2003).
[CrossRef]

G. N. van den Hoven, E. Snoeks, A. Polman, J. W. M. van Uffelen, Y. S. Oei, M. K. Smit, "Photoluminescence characterization of Er-implanted Al2O3 films," Appl. Phys. Lett. 62, 3065-3067 (1993).
[CrossRef]

Chem. Rev.

F. Auzel, "Upconversion and anti-Stokes processes with f and d ions in solids," Chem. Rev. 104, 139-173 (2004).
[CrossRef] [PubMed]

J. Appl. Phys.

G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, M. K. Smit, "Upconversion in Er-implanted Al2O3 waveguides," J. Appl. Phys. 79, 1258-1266 (1996).
[CrossRef]

J. Microsc.

F. Keilmann, "Surface-polariton propagation for scanning near-field optical microscopy application," J. Microsc. 194, 567-570 (1999).
[CrossRef]

A. Bouhelier, J. Renger, M. R. Beversluis, L. Novotny, "Plasmon-coupled tip-enhanced near-field optical microscopy," J. Microsc. 210, 220-224 (2003).
[CrossRef] [PubMed]

Nano Lett.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, C. Lienau, "Grating-coupling of surface plasmons onto metallic tips: A nanoconfined light source," Nano Lett. 7, 2784-2788 (2007).
[CrossRef] [PubMed]

L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, C. W. Kimball, "Subwavelength focusing and guiding of surface plasmons," Nano Lett. 5, 1399-1402 (2005).
[CrossRef] [PubMed]

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, X. Zhang, "Focusing surface plasmons with a plasmonics lens," Nano Lett. 5, 1726-1729 (2005).
[CrossRef] [PubMed]

H. L. Offerhaus, B. van den Bergen, M. Escalante, F. B. Segerink, J. P. Korterik, N. F. van Hulst, "Creating focused plasmons by noncollinear phasematching on functional gratings," Nano Lett. 5, 2144-2148 (2005).
[CrossRef] [PubMed]

E. Verhagen, L. Kuipers, A. Polman, "Enhanced nonlinear optical effects with a tapered plasmonic waveguide," Nano Lett. 7, 334-337 (2007).
[CrossRef] [PubMed]

Opt. Commun.

N. A. Janunts, K. S. Baghdasaryan, Kh. V. Nerkararyan, B. Hecht, "Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip," Opt. Commun. 253, 118-124 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

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

Phys. Rev. B

J.-C. Weeber, J. R. Krenn, A. Dereux, B. Lamprecht, Y. Lacroute, J. P. Goudonnet, "Near-field observation of surface plasmon polariton propagation on thin metal stripes," Phys. Rev. B 61, 045411 (2001).
[CrossRef]

C. A. Pfeiffer, E. N. Economou, K. L. Ngai, "Surface polaritons in a circularly cylindrical interface: surface plasmons," Phys. Rev. B 10, 3038-3051 (1974).
[CrossRef]

J. J. Burke and G. I. Stegeman, "Surface-polariton-like waves guided by thin, lossy metal films," Phys. Rev. B 33, 5186-5201 (1986).
[CrossRef]

D. K. Gramotnev, D. F. P. Pile, M. W. Vogel, X. Zhang, "Local electric field enhancement during nanofocusing of plasmons by a tapered gap," Phys. Rev. B 75, 035431 (2007).
[CrossRef]

J. Koglin, U. C. Fischer, H. Fuchs, "Material contrast in scanning near-field optical microscopy at 1-10 nm resolution," Phys. Rev. B 55, 7977-7984 (1997).
[CrossRef]

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures," Phys. Rev. B 63, 125417 (2001).
[CrossRef]

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972)
[CrossRef]

R. Zia, J. A. Schuller, M. L. Brongersma, "Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides," Phys. Rev. B 74, 165415 (2006).
[CrossRef]

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Güdel, M. P. Hehlen, "Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems," Phys. Rev. B 61, 3337-3346 (2000).
[CrossRef]

R. Zia, M. D. Selker, M. L. Brongersma, "Leaky and bound modes of surface plasmon waveguides," Phys. Rev. B 71, 165431 (2005).
[CrossRef]

Phys. Rev. Lett.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, C. Lienau, "Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures," Phys. Rev. Lett. 91, 143901 (2003).
[CrossRef] [PubMed]

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

M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

Science

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

Other

Lumerical FDTD Solutions 5.0

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Figures (10)

Fig. 1.
Fig. 1.

(a) Energy level diagram of Er3+ ions. The black arrows depict the cooperative upconversion mechanism which causes the excitation of higher energy levels by energy transfer between two excited ions. (b) SEM image of the end of a fabricated, tapered Au waveguide on an Er-implanted sapphire substrate. The scale bar is 1 µm.

Fig. 2.
Fig. 2.

Schematic of the experimental geometry in the case of upconversion luminescence detection through the substrate (a), or from the air side of the sample (b). In both cases the SPPs are excited with infrared light at the Au/Al2O3 interface in the direction of the arrow. The red line schematically indicates the Er depth profile.

Fig. 3.
Fig. 3.

(a) Upconversion luminescence image from the hole array (left side) and 60 µm long tapered waveguide (right side) sections, taken at 550 nm. The excitation spot is marked by the arrow on the left side of the image. (b) and (c): Detailed maps of the upconversion intensity near the tip of the waveguide, taken at 550 nm and 660 nm, respectively. A 1.48 µm pump at a power of 20 mW was used. The arrows indicate the positions at which power dependency curves were obtained. (d) Optical microscopy image of the same region as (b) and (c), obtained by detecting reflected light from a halogen lamp at a wavelength of 550 nm.

Fig. 4.
Fig. 4.

Excitation laser power dependence (λ=1.48 µm) of the upconversion luminescence at 550 and 660 nm collected at positions A and B (indicated with arrows in Fig. 3(b)). The lines are linear fits to the data for luminescence intensities between 100 and 1000 counts/s, and the slopes of these fits are indicated. The error in the fit is of order 0.01.

Fig. 5.
Fig. 5.

Upconversion luminescence images taken from the air side of the film at (a) 550 nm and (b) 660 nm. The edge of the taper is indicated by the dotted line. Upconversion luminescence excited by SPPs on the substrate side of the film is observed from the edges of the taper, and the maximum intensity is detected at the taper tip.

Fig. 6.
Fig. 6.

(a) Sketch of the electric field of the two SPP modes in an infinitely extended metal film, showing the symmetry of the transverse electric field and the surface charge. The direction of propagation is normal to the image plane. (b) Schematic of the geometry used in the FDTD calculations. The Au taper has a length of 7.8 µm and an apex diameter of 60 nm. The refractive index of the substrate is n 2, and that of the surrounding medium is n 1.

Fig. 7.
Fig. 7.

Mode profile of the asymmetric bound mode used as excitation source at x=0 in the FDTD simulation. Shown are the electric field intensity (a) and the real part of the electric field component in the z direction (b).

Fig. 8.
Fig. 8.

Electric field intensity in the planes z=-35 nm (a), and y=0 (b). The scale is normalized to the average intensity at the start of the tapered waveguide. Both color scales are saturated to improve the visibility away from the tip. The intensity enhancement at z=-10 nm below the tip apex is 100. The inset of (a) shows a detail of the electric field intensity in the plane z=-35 nm at the tip. The intensity distribution at the tip has a full width at half maximum of 92 nm. Normalized vertical cross sections of (b) at the start (x=0.5 µm, black) and the end (x=7.77 µm, red) of the taper are depicted in (c), showing the increase of vertical confinement towards the taper tip.

Fig. 9.
Fig. 9.

Cross section of the electric field intensity near the tip of the tapered waveguide, at x=7.77 µm. The field is predominantly localized at the metal corners. No field nodes are present along the metal surface.

Fig. 10.
Fig. 10.

Electric field intensity in the y=0 plane for the asymmetric bound mode at the high index side of the film (a), and the symmetric leaky mode at the low index side of the film (b). The color scale is saturated in (a), and the same for both figures.

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