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Surface-Plasmon-Enhanced Nonlinearities in Percolating 2-D Metal—Dielectric Films: Calculation of the Localized Giant Field and Their Observation in SNOM

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Optical Properties of Nanostructured Random Media

Part of the book series: Topics in Applied Physics ((TAP,volume 82))

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Abstract

The surfaces of percolating random 2-D metal—dielectric films consist of several spectral resonances, which have been calculated and afterward observed by near-field optical microscopy. These films show anomalous optical properties which are investigated in the first section. Nonlinear electrical and optical properties of metal—dielectric film percolation composites, though recognized very early, were not well understood. It is only recently that calculation of local fields in semicontinuous films allows us to define the enhancement factors of optical nonlinearities. These calculations are outlined from basic principles in the second section and compared with experimental results. An insightful approach to the same problem is to use a network description to represent the random system and discretize the equations satisfied by the scalar potential of the electrical field. We recall in the third section how such discretization leads to a Hamiltonian which is paradigmatic in the theory of Anderson localization. The imaging and spectroscopy of localized optical excitation in gold-on-glass percolation films was performed using near-field optical microscopy (SNOM), and the fourth section recalls the basic features of the experimental technique and describes the first experimental observation of “hot spots” in a nanometer-scale area.

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References

  1. S. Ducourtieux, S. Gresillon, A. C. Boccara, J. C. Rivoal, X. Quelin, P. Gadenne, V. P. Dratchev, W. D. Bragg, V. P. Safonov, V. A. Podolskiy, Z. C. Ying, R. L. Armstrong and V. M. Shalaev: Percolation and fractal composites: Optical studies, J. Nonlin. Opt. Phys. Mater. 9, 105–116 (2000)

    ADS  Google Scholar 

  2. A. K. Sarychev, V. A. Shubin, V. M. Shalaev, Anderson localization of surface plasmons and nonlinear optics of metal-dielectric composites, Phys. Rev. B 60, 16389–16408 (1999)

    Article  ADS  Google Scholar 

  3. S. Gresillon, H. Cory, J. C. Rivoal, A. C. Boccara:Transmission-mode apertureless near-field microscope: Optical and magneto-optical studies, J. Opt. Soc. A 1, 178–184 (1999)

    ADS  Google Scholar 

  4. P. Gadenne, Modifications of the optical and electrical properties of thin Au films as a function of structure during deposition, Thin Solid Films 57, 77 (1979)

    Article  ADS  Google Scholar 

  5. Y. Yagil, M. Yosephin, D. J. Bergman, G. Deutscher, P. Gadenne, Scaling theory for the optical properties of semi-continuous metal films; Phys. Rev. B 43, 11342 (1991).

    Article  ADS  Google Scholar 

  6. J. C. Maxwell-Garnett, Philos. Trans. R. Soc. 203, 395 (1904); 205, 237 (1905)

    ADS  Google Scholar 

  7. D. Bruggeman, Ann. Phys. 24, 636 (1935); R. W. Cohen, G. D. Cody, M. D. Coutts, B. Abeles, Optical properties of granular silver and gold films, Phys. Rev. B 8, 3689 (1973); C. G. Granqvist, O. Hunderi, Optical properties of ultrafine gold particles, Phys. Rev. B 16, 3513 (1977); and Optical properties of Ag —SiO 2 cermet films: A comparison of effective-medium theories, Phys. Rev. B 18, 2897 (1978; F. Brouers, J. P. Clerc, G. Giraud, Z. A. Randriamanantany, Dielectric and optical properties close to percolation threshold II, Phys. Rev. B 47, 666 (1993); O. Hunderi, Effective Medium Theory and Nonlocal effects for Superlattices, J. Wave-Mater. Interactions 2, 29-39 (1987); P. Sheng, Phys. Rev. Lett. 45, 60 (1979)

    Article  Google Scholar 

  8. J. C. Garland, D. B. Tanner (Eds.), Electrical Transport and Optical Properties of Inhomogeneous Media, Conf. Proc. ETOPIM1 (American Institute of Physics, New York 1978); J. Lafait, D. B. Tanner (Eds.), ETOPIM2 Physica A (North Holland Amsterdam 1987); L. Mochan, R. Barreira (Eds.), ETOPIM3 Physica A (North Holland Amsterdam 1994); A. N. Lagarkov and A. K. Sarychev (Eds.), ETOPIM4 Physica A 241, (North Holland Amsterdam 1997); ETOPIM5 Ping Sheng and L. H. Tan (Eds.) Physica B 279 (North Holland Amsterdam 2000)

    Google Scholar 

  9. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York 1982)

    MATH  Google Scholar 

  10. R. F. Voss, R. B. Laibovitz, E. L. Alessandrini, Fractal (Scaling) clusters in thin gold films near the percolation threshold, Phys. Rev. Lett. 49, 1441 (1982)

    Article  ADS  Google Scholar 

  11. A. Kapitulnik, G. Deutscher, Percolation characteristics in discontinuous thin films of Pb, Phys. Rev. Lett. 49, 1444 (1982)

    Article  ADS  Google Scholar 

  12. S. Blacher, F. Brouers, A. K. Sarychev, A. Ramsamugh, P. Gadenne, Relation between morphology and alternating current electrical properties of granular metallic films close to percolation threshold, Langmuir 12, 183 (1996); A. K. Sarychev, V. A. Shubin, V. M. Shalaev, Percolation-enhanced nonlinear scattering from metal-dielectric composites, Phys. Rev. E 59, 7239 (1999); A. K. Sarychev, V. M. Shalaev, Electromagnetic field fluctuations and optical non-linearities in metal-dielectric composites, Phys. Rep. 335 (2000)

    Article  Google Scholar 

  13. M. I. Stockman, V. M. Shalaev, M. Moskvits, R. Botet, T. F. George, Enhanced Raman Scattering by fractal clusters: scale-invariant theory, Phys. Rev. B 46, 2821–2840 (1992); V. A. Markel, L. S. Muratov, M. I. Stockman, T. F. George, Theory and numerical simulations of optical properties of fractals, Phys. Rev. B 43, 8133-8198 (1991)

    Article  ADS  Google Scholar 

  14. F. Didier, J. Jupille, Surf. Sci. 314, 378 (1994) and 307-309, 587 (1994); D. Martin-Gagnot, F. Creuset, J. Jupille, Y. Borensztein, P. Gadenne, 2D and 3D silver adlayers on TiO2 (110) surfaces, Surf. Sci. 377, 958 (1997)

    Article  ADS  Google Scholar 

  15. T. Lopez-Rios, Y. Borensztein, G. Vuye, Roughening of Al surfaces by Ag deposits studied by differential reflectivity, Phys. Rev. B 30, 659 (1984)

    Article  ADS  Google Scholar 

  16. Y. Borensztein, M. Roy, R. Alameh, Threshold and linear dispersion of the plasma resonance in thin films, Europhys. Lett. 31, 311 (1995); C. Beita, Y. Borensztein, R. Lazzari, J. Nieto, R. G. Barrera, Substrate-induced multipolar resonances in supported free electron metal spheres, Phys. Rev. B 60, 6018 (1999)

    Article  ADS  Google Scholar 

  17. J. P. Clerc, G. Giraud, S. Alexander, E. Guyon, Conductivity of a mixture of conducting and insulating grains: Dimensionality effects, Phys. Rev. B 22, 2489 (1980); M. Gadenne, P. Gadenne, Electrical and optical properties of AuAl2O3 films: dimensionality effects, Physica A 157, 344 (1989)

    Article  ADS  Google Scholar 

  18. H. Kiessig, Ann. Phys. 10, 769 (1931); W. Umrath; Z Angew. Phys. 22, 406 (1967)

    Article  Google Scholar 

  19. J. P. Straley, Critical phenomena in resistor networks, J. Phys. C 9, 783 (1976)

    Article  ADS  Google Scholar 

  20. S. Kirkpatrick, Models of disordered materials, in Condensed Matter Les Houches Summer School, R. Balian, R. Maynard, G. Toulouse (Eds.), (North Holland Amsterdam 1979); A. L. Efros, B. I. Schlovskii, Critical behaviour of conductivity and dielectric constant near the metal-non metal transition threshold, Phys. Status Solidi B 76, 475 (1976)

    Google Scholar 

  21. D. Stauffer, A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor, London 1991)

    Google Scholar 

  22. A. Beghdadi, A. Constans, P. Gadenne, J. Lafait, Optimum image processing for morphological study of granular films; Rev. Phys. Appl. 21, 73 (1986); A. Beghdadi, J. Lafait, P. Gadenne, A. Constans, O. Bouet, Thin film morphology; Acta Stereologica 6, 809 (1987)

    Google Scholar 

  23. D. J. Bergman, D. Stroud, Physical properties of macroscopically inhomogeneous media, Solid State Phys. 46, 147 (1992)

    Article  Google Scholar 

  24. S. Blacher, F. Brouers, P. Gadenne, J. Lafait, Morphological analysis of discontinuous thin films on various substrates, J. App. Phys. 74, 207 (1993)

    Article  ADS  Google Scholar 

  25. P. Gadenne, Croissance de couches minces d’or: Proprietes optiques, conductivite electrique et etude morphologique, Dissertation, Chap. 5, Univ. Paris 6 Univ. (1986); P. Gadenne, A. Beghdadi, J. Lafait, Optical cross-over analysis of granular gold films at percolation, Opt. Commun. 65, 17 (1988)

    Google Scholar 

  26. F. Abeles, J. Opt. Soc. Am. 47, 473–482 (1957)

    Article  ADS  Google Scholar 

  27. Y. Yagil, P. Gadenne, C. Julien, G. Deutscher, Scaling theory for the optical properties of semi-continuous metal films, Phys. Rev. B 43, 11342, (1991)

    Article  ADS  Google Scholar 

  28. P. Gadenne, Y. Yagil, G. Deutscher, In situ measurements of the optical properties of gold films near the percolation threshold, Physica A 157, 279 (1989); P. Gadenne, Y. Yagil, G. Deutscher, Transmittance and Reflectance in situ measurements of semicontinuous gold films, J. Appl. Phys. 66, 3019 (1989)

    Article  ADS  Google Scholar 

  29. R. Lazzari, J. Jupille, Y. Borensztein; Appl. Surf. Sci. 142, 451 (1999)

    Article  ADS  Google Scholar 

  30. M. L. Theye, Investigation of optical properties of Au by means of thin semi-transparent films, Phys. Rev. B 2, 3060 (1970)

    Article  ADS  Google Scholar 

  31. P. B. Johnson, R. W. Christy, Optical properties of the noble metals, Phys. Rev. B 6, 4370 (1972)

    Article  ADS  Google Scholar 

  32. P. J. Reynolds, W. Klein, H. E. Stanley, A real space renormalization group for site and bond percolation, J. Phys. C 10, L167 (1977)

    Article  ADS  Google Scholar 

  33. A. K. Sarychev, Zh. Eksp. Teor. Fiz. 72, 1001 (1977) [Sov. Phys. JETP 45, 524 (1977)]

    Google Scholar 

  34. A. K. Sarychev, V. A. Shubin, V. M. Shalaev, Anderson localization of surface plasmons and nonlinear optics of metal-dielectric composites, Phys. Rev. B 60, 16389–16408 (1999)

    Article  ADS  Google Scholar 

  35. P. Gadenne, D. Gagnot, M. Masson, Surface enhanced resonant Raman scattering induced by silver thin films close to the percolation threshold, Physica A 241, 161 (1997); P. Gadenne, F. Brouers, V. M. Shalaev, A. K. Sarychev, Giant Stokes fields on semicontinuous metal films, J. Opt. Soc. Am. B 15, 68 (1998)

    Article  ADS  Google Scholar 

  36. F. Brouers, S. Blacher, A. N. Lagarkov, A. K. Sarychev, P. Gadenne, V. M. Shalaev, Theory of giant Raman scattering from semicontinuous metal films, Phys. Rev. B 55, 13234 (1997)

    Article  ADS  Google Scholar 

  37. V. M. Shalaev, Electromagnetic properties of small-particles composites, Phys. Rep. 272, 61–137 (1996)

    Article  ADS  Google Scholar 

  38. V. M. Shalaev, A. K. Sarychev, Nonlinear optics of random metal-dielectric films, Phys. Rev. B 57, 13265–13288 (1998)

    Article  ADS  Google Scholar 

  39. R. P. Feynman, R. B. Leighton, M. Sands, in The Feynman Lectures on Physics, Vol. 2 (Addison-Wesley, 1965)

    Google Scholar 

  40. V. M. Shalaev, Nonlinear Optics of Random Media, Springer Tracts Mod. Phys. 158 (Springer, Berlin, Heidelberg 2000)

    Google Scholar 

  41. D. J. Bergman, D. Stroud, Physical properties of macroscopically inhomogeneous media, Solid State Phys. 46, 147 (1992)

    Article  Google Scholar 

  42. J. P. Clerc, G. Girard, J. M. Laugier, J. M. Luck, Adv. Phys. 39, 191 (1990)

    Article  ADS  Google Scholar 

  43. Y. V. Fyodorov, Fluctuations in random RL-C network: Non-linear ó-model description; JETP Lett. 70, 743 (1999)

    Article  ADS  Google Scholar 

  44. P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109, (1958)

    Google Scholar 

  45. D. W. Pohl, D. Courjon (Eds.), Near-Field Optics (Kluwer Academic, Dordrecht 1993)

    Google Scholar 

  46. M. A. Pasler, J. P. Moyer, Near-Field Optics (Wiley-Interscience, New York 1996)

    Google Scholar 

  47. E. Betzig, J. K. Trautman, Near-Field Optics: Microscopy, spectroscopy and surface modification beyond the diffraction limit, Science 257, 189–195 (1992)

    Article  ADS  Google Scholar 

  48. F. Zenhausern, Y. Martin, H. K. Wickramasinghe, Scanning interferometric aperturless microscopy: Optical imaging at 10 Å resolution, Science 269, 1083–1085 (1995)

    Article  ADS  Google Scholar 

  49. Y. Inouye, S. Kawata, Near-Field scanning optical microscope with a metallic tip, Opt. Lett. 19, 159–161 (1994)

    Article  ADS  Google Scholar 

  50. R. Bachelot, P. Gleyses, A. C. Boccara, Near field optical microscope using local perturbation of a diffraction spot, Opt. Lett. 20, 1924–1926 (1995)

    Article  ADS  Google Scholar 

  51. C. Girard, A. Dereux, Near-field optics theories, Rep. Prog. Phys. 59, 657–699 (1996)

    Article  ADS  Google Scholar 

  52. J. J. Greffet, R. Carminati, Image formation in near-field optics, Prog. Surf. Sci. 56, 133–237 (1997)

    Article  ADS  Google Scholar 

  53. E. H. Synge, A suggested method for extending microscopic resolution into the ultramicroscopic region, Philos. Mag. 6, 356–362 (1928)

    Google Scholar 

  54. A. Lewis, M. Isaacson, A. Harootunian, A. Muray, Development of a 500 Å spatial resolution light microscope, Ultramicroscopy 13, 227–232 (1984)

    Article  Google Scholar 

  55. D. W. Pohl, W. Denk, M. Lanz, Image recording with resolution λ/20, Appl. Phys. Lett. 44, 651–653 (1984)

    Article  ADS  Google Scholar 

  56. A. Piednoir, C. Licoppe, F. Creuset, Imaging and local spectroscopy with a near field optical microscope, Opt. Commun. 129, 414–422 (1996)

    ADS  Google Scholar 

  57. H Cory, A. C. Boccara, J. C. Rivoal, A. Lahrech, Electric field intensity variation in the vicinity of a perfectly conducting conical probe: Application to near-field microscopy, Microwave Opt. Technol. Lett. 18, 120 (1998)

    Article  Google Scholar 

  58. E. J. Sanchez, L. Novotny, X. S. Xie, Near-Field Fluorescence Microscopy based on two-photon excitation with metal tip, Phys. Rev. Lett. 82, 4014–4017 (1999)

    Article  ADS  Google Scholar 

  59. L. Aigouy, F. X. Andreani, C. Boccara, J. C. Rivoal, J. A. Porto, R. Carminati, J. J. Greffet, R. J. C. Megy, Near-field spectroscopy using an incoherent ligth source, Appl. Phys. Lett. 76, 397–399 (2000)

    Article  ADS  Google Scholar 

  60. J. A. Porto, R. Carminati, J. J. Greffet, Theory of electromagnetic fiels imaging and spectroscopy in scanning near-field optical microscopy, J. Appl. Phys. 88, 4845–4850 (2000)

    Article  ADS  Google Scholar 

  61. R. Hillenbrand, F. Keilmann, Complex optical constants on a subwavelength scale, Phys. Rev. Lett. 85, 3029 (2000)

    Article  ADS  Google Scholar 

  62. L. Novotny, Allowed and forbidden light in near-field optics. II-Interacting dipolar particles; J. Opt. Soc. Am. A 14, 105–113 (1997)

    Article  ADS  Google Scholar 

  63. L. Aigouy, A. Lahrech, S. Gresillon, H. Cory, A. C. Boccara, J. C. Rivoal, Polarization effects in aperturless scanning near-field optical microscopy: An experimental study, Opt. Lett. 24, 187–189 (1999)

    Article  ADS  Google Scholar 

  64. S. Gresillon, S. Ducourtieux, A. Lahrech, L. Aigouy, J. C. Rivoal, A. C. Boccara, Nanometer scale aperturless near field microscopy, Appl. Surf. Sci. 164, 118–123 (2000)

    Article  ADS  Google Scholar 

  65. S. Gresillon, L. Aigouy, A. C. Boccara, J. C. Rivoal, X. Quelin, C. Desmaret, P. Gadenne, V. A. Shubin, A. K. Sarychev, V. M. Shalaev, Experimental observation of localized excitations in random metal-dielectric films, Phys. Rev. Lett. 82, 4520–4523 (1999)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Magnétisme et d’Optique, Université de Versailles Saint Quentin, CNRS UMR 8624, F-78035, Versailles, France

    Patrice Gadenne

  2. Laboratoire d’Optique Physique ESPCI, Université Pierre et Marie Curie, CNRS UPR 5, F-75231, Paris, France

    Jean C. Rivoal

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  1. Patrice Gadenne
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  1. School of Electronical and omputer Engineering, Purdue University, West Lafayette, IN, 47907-1285, USA

    Vladimir M. Shalaev

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Gadenne, P., Rivoal, J.C. (2002). Surface-Plasmon-Enhanced Nonlinearities in Percolating 2-D Metal—Dielectric Films: Calculation of the Localized Giant Field and Their Observation in SNOM. In: Shalaev, V.M. (eds) Optical Properties of Nanostructured Random Media. Topics in Applied Physics, vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44948-5_9

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