Abstract

Fractal shaped periodic nanostructures formed with a 100nm period square lattice of gold nanoparticles placed on a gold film are characterized using far-field nonlinear scanning optical microscopy, in which two-photon photoluminescence (TPL) excited with a strongly focused femtosecond laser beam (in the wavelength range of 730790nm) is detected. TPL images obtained for all wavelengths in the laser range feature diffraction-limited (0.6μm) bright spots corresponding to intensity enhancements of up to 170, whose positions are dictated by the incident light wavelength and polarization. We relate the observed TPL enhancements to constructive interference of surface plasmon polaritons partially reflected inside the structure boundaries and support the analysis with numerical simulations using the Green dyadic field propagator.

© 2008 Optical Society of America

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  1. V. M. Markel and T. F. George, Optics of Nanostructured Materials (Wiley, 2001).
  2. G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30, 519-526 (1984), and references therein.
    [CrossRef]
  3. E. J. Sánchez, L. Novotny, and X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82, 4014-4017 (1999).
    [CrossRef]
  4. K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys.: Condens. Matter , 14, R597-R624 (2002).
    [CrossRef]
  5. P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
    [CrossRef] [PubMed]
  6. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
    [CrossRef] [PubMed]
  7. A. Hohenau, J. R. Krenn, S. G. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, J. Beermann, and S. I. Bozhevolnyi, “Spectroscopy and nonlinear microscopy of gold nanoparticle arrays on gold films,” Phys. Rev. B 75, 085104 (2007).
    [CrossRef]
  8. A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335, 275-371 (2000).
    [CrossRef]
  9. M. I. Stockman, “Local fields' localization and chaos and nonlinear-optical enhancement in clusters and composites,” in Optics of Nanostructured Materials (Wiley, 2001), p. 313, and references therein.
  10. S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90, 197403 (2003).
    [CrossRef] [PubMed]
  11. C. Even, S. Russ, V. Repain, P. Pieranski, and B. Sapoval, “Localizations in fractal drums: an experimental study,” Phys. Rev. Lett. 83, 726-729 (1999).
    [CrossRef]
  12. A. Mooradian, “Photoluminescence of metals,” Phys. Rev. Lett. 22, 185-187 (1969).
    [CrossRef]
  13. G. T. Boyd, Z. H. Yu, and Y. R. Shen, “Photoinduced luminescence from the noble metals and its enhancement on roughened surfaces,” Phys. Rev. B 33, 7923-7936 (1986).
    [CrossRef]
  14. M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003).
    [CrossRef]
  15. A. Bouhelier, M. R. Beversluis, and L. Novotny, “Characterization of nanoplasmonic structures by locally excited photoluminescence,” Appl. Phys. Lett. 83, 5041-5043 (2003).
    [CrossRef]
  16. J. Beermann, I. P. Radko, A. Boltasseva, and S. I. Bozhevolnyi, “Localized field enhancements in fractal shaped periodic metal nanostructures,” Opt. Express 15, 15234-15241 (2007).
    [CrossRef] [PubMed]
  17. K. Falconer, Fractal Geometry: Mathematical Foundations and Application, 2nd ed., (Wiley, 2003).
    [CrossRef]
  18. J. Beermann and S. I. Bozhevolnyi, “Microscopy of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. B 69, 155429 (2004).
    [CrossRef]
  19. J. Beermann, V. Coello, and S. I. Bozhevolnyi, “Modeling of nonlinear microscopy of localized field enhancements in random metal nanostructures,” Phys. Rev. B 73, 115408 (2006).
    [CrossRef]
  20. O. Keller, M. Xiao, and S. I. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217-230 (1993).
    [CrossRef]
  21. A. B. Evlyukhin and S. I. Bozhevolnyi, “Point-dipole approximation for surface plasmon polariton scattering: Implications and limitations,” Phys. Rev. B 71, 134304 (2005).
    [CrossRef]
  22. T. Søndergaard and S. I. Bozhevolnyi, “Vectorial model for multiple scattering by surface nanoparticles via surface polariton-to-polariton interactions,” Phys. Rev. B 67, 165405 (2003).
    [CrossRef]
  23. L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1708-1714 (1997).
    [CrossRef]
  24. J. E. Sansonetti and J. K. Furdyna, “Depolarization effects in array of spheres,” Phys. Rev. B 22, 2866-2874 (1980).
    [CrossRef]
  25. V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B 53, 2425-2436 (1996).
    [CrossRef]
  26. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848-872 (1988).
    [CrossRef]
  27. E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
    [CrossRef]
  28. E. Palik, Handbook of Optical Constant of Solids (Academic, 1985).
  29. I. P. Radko, S. I. Bozhevolnyi, A. B. Evlyukhin, and A. Boltasseva, “Surface plasmon polariton beam focusing with parabolic nanoparticle chains,” Opt. Express 15, 6576-6582 (2007).
    [CrossRef] [PubMed]
  30. S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiber-accessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
    [CrossRef]
  31. T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, “Theoretical analysis of ridge gratings for long-range surface plasmon polaritons,” Phys. Rev. B 73, 045320 (2006).
    [CrossRef]
  32. A. Hohenau, J. R. Krenn, J. Beermann, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martin-Moreno, and F. Garcia-Vidal, “Spectroscopy and nonlinear microscopy of Au nanoparticle arrays: experiment and theory,” Phys. Rev. B 73, 155404 (2006).
    [CrossRef]

2007

2006

T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, “Theoretical analysis of ridge gratings for long-range surface plasmon polaritons,” Phys. Rev. B 73, 045320 (2006).
[CrossRef]

A. Hohenau, J. R. Krenn, J. Beermann, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martin-Moreno, and F. Garcia-Vidal, “Spectroscopy and nonlinear microscopy of Au nanoparticle arrays: experiment and theory,” Phys. Rev. B 73, 155404 (2006).
[CrossRef]

J. Beermann, V. Coello, and S. I. Bozhevolnyi, “Modeling of nonlinear microscopy of localized field enhancements in random metal nanostructures,” Phys. Rev. B 73, 115408 (2006).
[CrossRef]

2005

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiber-accessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
[CrossRef]

A. B. Evlyukhin and S. I. Bozhevolnyi, “Point-dipole approximation for surface plasmon polariton scattering: Implications and limitations,” Phys. Rev. B 71, 134304 (2005).
[CrossRef]

2004

J. Beermann and S. I. Bozhevolnyi, “Microscopy of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. B 69, 155429 (2004).
[CrossRef]

2003

T. Søndergaard and S. I. Bozhevolnyi, “Vectorial model for multiple scattering by surface nanoparticles via surface polariton-to-polariton interactions,” Phys. Rev. B 67, 165405 (2003).
[CrossRef]

M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003).
[CrossRef]

A. Bouhelier, M. R. Beversluis, and L. Novotny, “Characterization of nanoplasmonic structures by locally excited photoluminescence,” Appl. Phys. Lett. 83, 5041-5043 (2003).
[CrossRef]

K. Falconer, Fractal Geometry: Mathematical Foundations and Application, 2nd ed., (Wiley, 2003).
[CrossRef]

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90, 197403 (2003).
[CrossRef] [PubMed]

2002

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys.: Condens. Matter , 14, R597-R624 (2002).
[CrossRef]

2001

V. M. Markel and T. F. George, Optics of Nanostructured Materials (Wiley, 2001).

M. I. Stockman, “Local fields' localization and chaos and nonlinear-optical enhancement in clusters and composites,” in Optics of Nanostructured Materials (Wiley, 2001), p. 313, and references therein.

2000

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335, 275-371 (2000).
[CrossRef]

1999

E. J. Sánchez, L. Novotny, and X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82, 4014-4017 (1999).
[CrossRef]

C. Even, S. Russ, V. Repain, P. Pieranski, and B. Sapoval, “Localizations in fractal drums: an experimental study,” Phys. Rev. Lett. 83, 726-729 (1999).
[CrossRef]

1997

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1708-1714 (1997).
[CrossRef]

1996

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B 53, 2425-2436 (1996).
[CrossRef]

1993

O. Keller, M. Xiao, and S. I. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217-230 (1993).
[CrossRef]

1988

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848-872 (1988).
[CrossRef]

1986

G. T. Boyd, Z. H. Yu, and Y. R. Shen, “Photoinduced luminescence from the noble metals and its enhancement on roughened surfaces,” Phys. Rev. B 33, 7923-7936 (1986).
[CrossRef]

1985

E. Palik, Handbook of Optical Constant of Solids (Academic, 1985).

1984

G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30, 519-526 (1984), and references therein.
[CrossRef]

1980

J. E. Sansonetti and J. K. Furdyna, “Depolarization effects in array of spheres,” Phys. Rev. B 22, 2866-2874 (1980).
[CrossRef]

1973

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

1969

A. Mooradian, “Photoluminescence of metals,” Phys. Rev. Lett. 22, 185-187 (1969).
[CrossRef]

Armstrong, R. L.

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B 53, 2425-2436 (1996).
[CrossRef]

Barclay, P. E.

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiber-accessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
[CrossRef]

Beermann, J.

J. Beermann, I. P. Radko, A. Boltasseva, and S. I. Bozhevolnyi, “Localized field enhancements in fractal shaped periodic metal nanostructures,” Opt. Express 15, 15234-15241 (2007).
[CrossRef] [PubMed]

A. Hohenau, J. R. Krenn, S. G. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, J. Beermann, and S. I. Bozhevolnyi, “Spectroscopy and nonlinear microscopy of gold nanoparticle arrays on gold films,” Phys. Rev. B 75, 085104 (2007).
[CrossRef]

A. Hohenau, J. R. Krenn, J. Beermann, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martin-Moreno, and F. Garcia-Vidal, “Spectroscopy and nonlinear microscopy of Au nanoparticle arrays: experiment and theory,” Phys. Rev. B 73, 155404 (2006).
[CrossRef]

J. Beermann, V. Coello, and S. I. Bozhevolnyi, “Modeling of nonlinear microscopy of localized field enhancements in random metal nanostructures,” Phys. Rev. B 73, 115408 (2006).
[CrossRef]

J. Beermann and S. I. Bozhevolnyi, “Microscopy of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. B 69, 155429 (2004).
[CrossRef]

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90, 197403 (2003).
[CrossRef] [PubMed]

Beversluis, M. R.

M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003).
[CrossRef]

A. Bouhelier, M. R. Beversluis, and L. Novotny, “Characterization of nanoplasmonic structures by locally excited photoluminescence,” Appl. Phys. Lett. 83, 5041-5043 (2003).
[CrossRef]

Boltasseva, A.

Bouhelier, A.

M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003).
[CrossRef]

A. Bouhelier, M. R. Beversluis, and L. Novotny, “Characterization of nanoplasmonic structures by locally excited photoluminescence,” Appl. Phys. Lett. 83, 5041-5043 (2003).
[CrossRef]

Boyd, G. T.

G. T. Boyd, Z. H. Yu, and Y. R. Shen, “Photoinduced luminescence from the noble metals and its enhancement on roughened surfaces,” Phys. Rev. B 33, 7923-7936 (1986).
[CrossRef]

G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30, 519-526 (1984), and references therein.
[CrossRef]

Bozhevolnyi, S. I.

I. P. Radko, S. I. Bozhevolnyi, A. B. Evlyukhin, and A. Boltasseva, “Surface plasmon polariton beam focusing with parabolic nanoparticle chains,” Opt. Express 15, 6576-6582 (2007).
[CrossRef] [PubMed]

J. Beermann, I. P. Radko, A. Boltasseva, and S. I. Bozhevolnyi, “Localized field enhancements in fractal shaped periodic metal nanostructures,” Opt. Express 15, 15234-15241 (2007).
[CrossRef] [PubMed]

A. Hohenau, J. R. Krenn, S. G. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, J. Beermann, and S. I. Bozhevolnyi, “Spectroscopy and nonlinear microscopy of gold nanoparticle arrays on gold films,” Phys. Rev. B 75, 085104 (2007).
[CrossRef]

A. Hohenau, J. R. Krenn, J. Beermann, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martin-Moreno, and F. Garcia-Vidal, “Spectroscopy and nonlinear microscopy of Au nanoparticle arrays: experiment and theory,” Phys. Rev. B 73, 155404 (2006).
[CrossRef]

T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, “Theoretical analysis of ridge gratings for long-range surface plasmon polaritons,” Phys. Rev. B 73, 045320 (2006).
[CrossRef]

J. Beermann, V. Coello, and S. I. Bozhevolnyi, “Modeling of nonlinear microscopy of localized field enhancements in random metal nanostructures,” Phys. Rev. B 73, 115408 (2006).
[CrossRef]

A. B. Evlyukhin and S. I. Bozhevolnyi, “Point-dipole approximation for surface plasmon polariton scattering: Implications and limitations,” Phys. Rev. B 71, 134304 (2005).
[CrossRef]

J. Beermann and S. I. Bozhevolnyi, “Microscopy of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. B 69, 155429 (2004).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, “Vectorial model for multiple scattering by surface nanoparticles via surface polariton-to-polariton interactions,” Phys. Rev. B 67, 165405 (2003).
[CrossRef]

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90, 197403 (2003).
[CrossRef] [PubMed]

O. Keller, M. Xiao, and S. I. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217-230 (1993).
[CrossRef]

Coello, V.

J. Beermann, V. Coello, and S. I. Bozhevolnyi, “Modeling of nonlinear microscopy of localized field enhancements in random metal nanostructures,” Phys. Rev. B 73, 115408 (2006).
[CrossRef]

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90, 197403 (2003).
[CrossRef] [PubMed]

Dasari, R. R.

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys.: Condens. Matter , 14, R597-R624 (2002).
[CrossRef]

Draine, B. T.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848-872 (1988).
[CrossRef]

Eisler, H.-J.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Even, C.

C. Even, S. Russ, V. Repain, P. Pieranski, and B. Sapoval, “Localizations in fractal drums: an experimental study,” Phys. Rev. Lett. 83, 726-729 (1999).
[CrossRef]

Evlyukhin, A. B.

I. P. Radko, S. I. Bozhevolnyi, A. B. Evlyukhin, and A. Boltasseva, “Surface plasmon polariton beam focusing with parabolic nanoparticle chains,” Opt. Express 15, 6576-6582 (2007).
[CrossRef] [PubMed]

A. B. Evlyukhin and S. I. Bozhevolnyi, “Point-dipole approximation for surface plasmon polariton scattering: Implications and limitations,” Phys. Rev. B 71, 134304 (2005).
[CrossRef]

Falconer, K.

K. Falconer, Fractal Geometry: Mathematical Foundations and Application, 2nd ed., (Wiley, 2003).
[CrossRef]

Feld, M. S.

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys.: Condens. Matter , 14, R597-R624 (2002).
[CrossRef]

Friedman, M. D.

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiber-accessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
[CrossRef]

Fromm, D. P.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Furdyna, J. K.

J. E. Sansonetti and J. K. Furdyna, “Depolarization effects in array of spheres,” Phys. Rev. B 22, 2866-2874 (1980).
[CrossRef]

Garcia-Vidal, F.

A. Hohenau, J. R. Krenn, S. G. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, J. Beermann, and S. I. Bozhevolnyi, “Spectroscopy and nonlinear microscopy of gold nanoparticle arrays on gold films,” Phys. Rev. B 75, 085104 (2007).
[CrossRef]

A. Hohenau, J. R. Krenn, J. Beermann, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martin-Moreno, and F. Garcia-Vidal, “Spectroscopy and nonlinear microscopy of Au nanoparticle arrays: experiment and theory,” Phys. Rev. B 73, 155404 (2006).
[CrossRef]

George, T. F.

V. M. Markel and T. F. George, Optics of Nanostructured Materials (Wiley, 2001).

Hecht, B.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1708-1714 (1997).
[CrossRef]

Hohenau, A.

A. Hohenau, J. R. Krenn, S. G. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, J. Beermann, and S. I. Bozhevolnyi, “Spectroscopy and nonlinear microscopy of gold nanoparticle arrays on gold films,” Phys. Rev. B 75, 085104 (2007).
[CrossRef]

A. Hohenau, J. R. Krenn, J. Beermann, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martin-Moreno, and F. Garcia-Vidal, “Spectroscopy and nonlinear microscopy of Au nanoparticle arrays: experiment and theory,” Phys. Rev. B 73, 155404 (2006).
[CrossRef]

Itzkan, I.

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys.: Condens. Matter , 14, R597-R624 (2002).
[CrossRef]

Keller, O.

O. Keller, M. Xiao, and S. I. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217-230 (1993).
[CrossRef]

Kim, W.

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B 53, 2425-2436 (1996).
[CrossRef]

Kino, G. S.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Kneipp, H.

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys.: Condens. Matter , 14, R597-R624 (2002).
[CrossRef]

Kneipp, K.

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys.: Condens. Matter , 14, R597-R624 (2002).
[CrossRef]

Krenn, J. R.

A. Hohenau, J. R. Krenn, S. G. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, J. Beermann, and S. I. Bozhevolnyi, “Spectroscopy and nonlinear microscopy of gold nanoparticle arrays on gold films,” Phys. Rev. B 75, 085104 (2007).
[CrossRef]

A. Hohenau, J. R. Krenn, J. Beermann, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martin-Moreno, and F. Garcia-Vidal, “Spectroscopy and nonlinear microscopy of Au nanoparticle arrays: experiment and theory,” Phys. Rev. B 73, 155404 (2006).
[CrossRef]

Leite, J. R. R.

G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30, 519-526 (1984), and references therein.
[CrossRef]

Maier, S. A.

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiber-accessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
[CrossRef]

Markel, V. A.

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B 53, 2425-2436 (1996).
[CrossRef]

Markel, V. M.

V. M. Markel and T. F. George, Optics of Nanostructured Materials (Wiley, 2001).

Martin, O. J. F.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Martin-Moreno, L.

A. Hohenau, J. R. Krenn, S. G. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, J. Beermann, and S. I. Bozhevolnyi, “Spectroscopy and nonlinear microscopy of gold nanoparticle arrays on gold films,” Phys. Rev. B 75, 085104 (2007).
[CrossRef]

A. Hohenau, J. R. Krenn, J. Beermann, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martin-Moreno, and F. Garcia-Vidal, “Spectroscopy and nonlinear microscopy of Au nanoparticle arrays: experiment and theory,” Phys. Rev. B 73, 155404 (2006).
[CrossRef]

Moerner, W. E.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Mooradian, A.

A. Mooradian, “Photoluminescence of metals,” Phys. Rev. Lett. 22, 185-187 (1969).
[CrossRef]

Mühlschlegel, P.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Novotny, L.

A. Bouhelier, M. R. Beversluis, and L. Novotny, “Characterization of nanoplasmonic structures by locally excited photoluminescence,” Appl. Phys. Lett. 83, 5041-5043 (2003).
[CrossRef]

M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003).
[CrossRef]

E. J. Sánchez, L. Novotny, and X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82, 4014-4017 (1999).
[CrossRef]

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1708-1714 (1997).
[CrossRef]

Painter, O.

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiber-accessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
[CrossRef]

Palik, E.

E. Palik, Handbook of Optical Constant of Solids (Academic, 1985).

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Pieranski, P.

C. Even, S. Russ, V. Repain, P. Pieranski, and B. Sapoval, “Localizations in fractal drums: an experimental study,” Phys. Rev. Lett. 83, 726-729 (1999).
[CrossRef]

Pohl, D. W.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1708-1714 (1997).
[CrossRef]

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Radko, I. P.

Rasing, Th.

G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30, 519-526 (1984), and references therein.
[CrossRef]

Repain, V.

C. Even, S. Russ, V. Repain, P. Pieranski, and B. Sapoval, “Localizations in fractal drums: an experimental study,” Phys. Rev. Lett. 83, 726-729 (1999).
[CrossRef]

Rodrigo, S. G.

A. Hohenau, J. R. Krenn, S. G. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, J. Beermann, and S. I. Bozhevolnyi, “Spectroscopy and nonlinear microscopy of gold nanoparticle arrays on gold films,” Phys. Rev. B 75, 085104 (2007).
[CrossRef]

A. Hohenau, J. R. Krenn, J. Beermann, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martin-Moreno, and F. Garcia-Vidal, “Spectroscopy and nonlinear microscopy of Au nanoparticle arrays: experiment and theory,” Phys. Rev. B 73, 155404 (2006).
[CrossRef]

Russ, S.

C. Even, S. Russ, V. Repain, P. Pieranski, and B. Sapoval, “Localizations in fractal drums: an experimental study,” Phys. Rev. Lett. 83, 726-729 (1999).
[CrossRef]

Sánchez, E. J.

E. J. Sánchez, L. Novotny, and X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82, 4014-4017 (1999).
[CrossRef]

Sansonetti, J. E.

J. E. Sansonetti and J. K. Furdyna, “Depolarization effects in array of spheres,” Phys. Rev. B 22, 2866-2874 (1980).
[CrossRef]

Sapoval, B.

C. Even, S. Russ, V. Repain, P. Pieranski, and B. Sapoval, “Localizations in fractal drums: an experimental study,” Phys. Rev. Lett. 83, 726-729 (1999).
[CrossRef]

Sarychev, A. K.

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335, 275-371 (2000).
[CrossRef]

Schuck, P. J.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Shalaev, V. M.

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335, 275-371 (2000).
[CrossRef]

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B 53, 2425-2436 (1996).
[CrossRef]

Shen, Y. R.

G. T. Boyd, Z. H. Yu, and Y. R. Shen, “Photoinduced luminescence from the noble metals and its enhancement on roughened surfaces,” Phys. Rev. B 33, 7923-7936 (1986).
[CrossRef]

G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30, 519-526 (1984), and references therein.
[CrossRef]

Søndergaard, T.

T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, “Theoretical analysis of ridge gratings for long-range surface plasmon polaritons,” Phys. Rev. B 73, 045320 (2006).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, “Vectorial model for multiple scattering by surface nanoparticles via surface polariton-to-polariton interactions,” Phys. Rev. B 67, 165405 (2003).
[CrossRef]

Stechel, E. B.

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B 53, 2425-2436 (1996).
[CrossRef]

Stockman, M. I.

M. I. Stockman, “Local fields' localization and chaos and nonlinear-optical enhancement in clusters and composites,” in Optics of Nanostructured Materials (Wiley, 2001), p. 313, and references therein.

Sundaramurthy, A.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Xiao, M.

O. Keller, M. Xiao, and S. I. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217-230 (1993).
[CrossRef]

Xie, X. S.

E. J. Sánchez, L. Novotny, and X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82, 4014-4017 (1999).
[CrossRef]

Yu, Z. H.

G. T. Boyd, Z. H. Yu, and Y. R. Shen, “Photoinduced luminescence from the noble metals and its enhancement on roughened surfaces,” Phys. Rev. B 33, 7923-7936 (1986).
[CrossRef]

Appl. Phys. Lett.

A. Bouhelier, M. R. Beversluis, and L. Novotny, “Characterization of nanoplasmonic structures by locally excited photoluminescence,” Appl. Phys. Lett. 83, 5041-5043 (2003).
[CrossRef]

S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiber-accessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005).
[CrossRef]

Astrophys. J.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848-872 (1988).
[CrossRef]

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

J. Appl. Phys.

L. Novotny, B. Hecht, and D. W. Pohl, “Interference of locally excited surface plasmons,” J. Appl. Phys. 81, 1708-1714 (1997).
[CrossRef]

J. Phys.: Condens. Matter

K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys.: Condens. Matter , 14, R597-R624 (2002).
[CrossRef]

Opt. Express

Phys. Rep.

A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites,” Phys. Rep. 335, 275-371 (2000).
[CrossRef]

Phys. Rev. B

A. Hohenau, J. R. Krenn, S. G. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, J. Beermann, and S. I. Bozhevolnyi, “Spectroscopy and nonlinear microscopy of gold nanoparticle arrays on gold films,” Phys. Rev. B 75, 085104 (2007).
[CrossRef]

G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30, 519-526 (1984), and references therein.
[CrossRef]

J. Beermann and S. I. Bozhevolnyi, “Microscopy of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. B 69, 155429 (2004).
[CrossRef]

J. Beermann, V. Coello, and S. I. Bozhevolnyi, “Modeling of nonlinear microscopy of localized field enhancements in random metal nanostructures,” Phys. Rev. B 73, 115408 (2006).
[CrossRef]

G. T. Boyd, Z. H. Yu, and Y. R. Shen, “Photoinduced luminescence from the noble metals and its enhancement on roughened surfaces,” Phys. Rev. B 33, 7923-7936 (1986).
[CrossRef]

M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003).
[CrossRef]

J. E. Sansonetti and J. K. Furdyna, “Depolarization effects in array of spheres,” Phys. Rev. B 22, 2866-2874 (1980).
[CrossRef]

V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, “Small-particle composites. I. Linear optical properties,” Phys. Rev. B 53, 2425-2436 (1996).
[CrossRef]

A. B. Evlyukhin and S. I. Bozhevolnyi, “Point-dipole approximation for surface plasmon polariton scattering: Implications and limitations,” Phys. Rev. B 71, 134304 (2005).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, “Vectorial model for multiple scattering by surface nanoparticles via surface polariton-to-polariton interactions,” Phys. Rev. B 67, 165405 (2003).
[CrossRef]

T. Søndergaard, S. I. Bozhevolnyi, and A. Boltasseva, “Theoretical analysis of ridge gratings for long-range surface plasmon polaritons,” Phys. Rev. B 73, 045320 (2006).
[CrossRef]

A. Hohenau, J. R. Krenn, J. Beermann, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martin-Moreno, and F. Garcia-Vidal, “Spectroscopy and nonlinear microscopy of Au nanoparticle arrays: experiment and theory,” Phys. Rev. B 73, 155404 (2006).
[CrossRef]

Phys. Rev. Lett.

S. I. Bozhevolnyi, J. Beermann, and V. Coello, “Direct observation of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. Lett. 90, 197403 (2003).
[CrossRef] [PubMed]

C. Even, S. Russ, V. Repain, P. Pieranski, and B. Sapoval, “Localizations in fractal drums: an experimental study,” Phys. Rev. Lett. 83, 726-729 (1999).
[CrossRef]

A. Mooradian, “Photoluminescence of metals,” Phys. Rev. Lett. 22, 185-187 (1969).
[CrossRef]

E. J. Sánchez, L. Novotny, and X. S. Xie, “Near-field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82, 4014-4017 (1999).
[CrossRef]

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Science

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607-1609 (2005).
[CrossRef] [PubMed]

Surf. Sci.

O. Keller, M. Xiao, and S. I. Bozhevolnyi, “Configurational resonances in optical near-field microscopy: a rigorous point-dipole approach,” Surf. Sci. 280, 217-230 (1993).
[CrossRef]

Other

K. Falconer, Fractal Geometry: Mathematical Foundations and Application, 2nd ed., (Wiley, 2003).
[CrossRef]

V. M. Markel and T. F. George, Optics of Nanostructured Materials (Wiley, 2001).

M. I. Stockman, “Local fields' localization and chaos and nonlinear-optical enhancement in clusters and composites,” in Optics of Nanostructured Materials (Wiley, 2001), p. 313, and references therein.

E. Palik, Handbook of Optical Constant of Solids (Academic, 1985).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the experimental setup for nonlinear scanning optical microscopy working in reflection with a Ti-sapphire laser, optical isolator (OI), half-wave-plate ( λ 2 ) , polarizer (P), beam splitter (BS), filters F 1 and F 2 , wavelength selective beam splitter (WSBS), objective (L), sample (S) placed on X Y table, analyzers A 1 and A 2 , and photomultiplier tubes (PMTs).

Fig. 2
Fig. 2

(a) Entire geometry ( 100 μ m × 100 μ m ) of the fractal structure defined for EBL, along with corresponding (b) SEM, and pseudo-color optical (c) FH and (d) TPL images of the fabricated structure of 60 nm diameter gold particles. The used excitation wavelength (FH) was 730 nm and the polarization configurations are indicated by a pair (incident FH, detection) of colored arrows on the optical images. The maximum TPL signal in (d) was 12 kcps obtained at 1.2 mW incident power. The tiny red-dashed square in (a) indicates the zoom area shown in Fig. 3, while the blue-dashed rectangle corresponds to zoom images shown in Fig. 4.

Fig. 3
Fig. 3

Comparison of a small ( 5.5 μ m × 5.5 μ m ) part of (a) the designed geometry with (b), (c) SEM images of the EBL fabricated structures. The diameters of the gold particles are (b) 50 and (c) 60 nm .

Fig. 4
Fig. 4

Merged TPL and SEM images of a ( 21 μ m × 15 μ m ) area in the center of the fractal structure exhibiting wavelength dependence [(a)–(c)] from 730 790 nm and polarization dependence [(c)–(f)] shown at 790 nm . The maximum TPL signal is (a) 3.6 , (b) 1.3 , (c) 9.1 , (d) 0.88 , (e) 0.78 , and (f) 0.96 kcps , corresponding to intensity enhancements in the range 45 170 . White-dashed arcs in (c)–(f) indicate the main boundaries leading to SPP defocusing for the specific excitation polarizations.

Fig. 5
Fig. 5

Simulated [(a),(c),(e),(g)] and experimental [(b),(d),(f),(h)] TPL images ( 7.5 μ m × 4.2 μ m ) obtained at the outer part of the fractal structure seen in Fig. 3 and merged with either the designed geometry or the corresponding SEM images, respectively. The TPL images were obtained for the wavelengths and polarization combinations indicated on the images and show simulated TPL intensity enhancements of [(a),(e),(g)] 220 and (c) 45 , compared to experimental values of (b) 145 , (d) 30 , (f) 117 , and (h) 41 .

Fig. 6
Fig. 6

Merged TPL and SEM image ( 5.75 μ m × 7.2 μ m ) of an individual defect formed next to the fractal structure with 50 nm diameter gold particles. The inset shows a detailed SEM zoom on the defect. The TPL image was obtained using 1.2 mW incident radiation at 730 nm leading to a maximum TPL signal of 19 kcps and intensity enhancement of 105 .

Equations (10)

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E ( r i ) = E 0 ( r i ) + k 0 2 ε 0 G s ( r i , r i ) α E ( r i ) + k 0 2 ε 0 j i N G ( r i , r j ) α E ( r j ) ,
α = α x x ̂ x ̂ + α y y ̂ y ̂ + α z z ̂ z ̂ ,
α τ = ε 0 V ( ε p 1 ) ( 1 + ( ε p 1 ) m τ ) , τ = x , y , z ,
m z = 1 + ζ 2 ζ 3 ( ζ arctan ζ ) , m x = m y = 1 2 ( 1 m z ) ,
G ( r i , r j ) = { G 0 ( r i , r j ) + G s ( r i , r j ) r i r j 3 λ G SPP ( r i , r j ) r i r j > 3 λ } ,
G SPP ( r i , r j ) = i a k SPP H 0 ( 1 ) ( k SPP ρ ) e a k SPP ( z i + z j ) 2 ( 1 a 4 ) ( 1 a 2 ) [ z ̂ z ̂ + a 2 ρ ̂ ρ ̂ + i a ( z ̂ ρ ̂ ρ ̂ z ̂ ) ] ,
E 0 ( r i ) = e p exp ( ( x i x scan ) 2 + ( y i y scan ) 2 W 2 ) [ e i k 0 z i + 1 ε m 1 + ε m e i k 0 z i ] ,
I TPL ( x scan , y scan ) = i = 1 N E ( r i ) ( x scan , y scan ) 4 ,
χ 2 = I fractal TPL I particle TPL .
χ 2 = TPL frac P film 2 A film TPL film P frac 2 A frac ,

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