Chinese Science Bulletin

, Volume 55, Issue 24, pp 2608–2617 | Cite as

Solving surface plasmon resonances and near field in metallic nanostructures: Green’s matrix method and its applications

  • Ying Gu
  • Jia Li
  • Olivier J. F. Martin
  • QiHuang Gong
Review Special Topic Plasmonics


With the development of nanotechnology, many new optical phenomena in nanoscale have been demonstrated. Through the coupling of optical waves and collective oscillations of free electrons in metallic nanostructures, surface plasmon polaritons can be excited accompanying a strong near field enhancement that decays in a subwavelength scale, which have potential applications in the surface-enhanced Raman scattering, biosensor, optical communication, solar cells, and nonlinear optical frequency mixing. In the present article, we review the Green’s matrix method for solving the surface plasmon resonances and near field in arbitrarily shaped nanostructures and in binary metallic nanostructures. Using this method, we design the plasmonic nanostructures whose resonances are tunable from the visible to near-infrared, study the interplay of plasmon resonances, and propose a new way to control plasmonic resonances in binary metallic nanostructures.


nanooptics surface plasmon resonance near field metallic nanostructure 


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  1. 1.
    Girard C, Dereux A. Near-field optics theories. Rep Prog Phys, 1996, 59: 657–699CrossRefGoogle Scholar
  2. 2.
    Girard C, Joachim C, Gauthier S. The physics of the near-field. Rep Prog Phys, 2000, 63: 893–938CrossRefGoogle Scholar
  3. 3.
    Boardman A D. Electromagnetic Surface Modes. New York: John Wiley and Sons, 1982Google Scholar
  4. 4.
    Raether H. Surface Plasmons. Berlin: Springer, 1988Google Scholar
  5. 5.
    Zayats A V, Smolyaninov I I, Maradudin A A. Nano-optics of surface plasmon polaritons. Phys Rep, 2005, 408: 131–314CrossRefGoogle Scholar
  6. 6.
    Rather H. Surface Plasmons on Smooth and Rough Surfaces and on Gratings. Berlin: Springer, 2004Google Scholar
  7. 7.
    Kottmann J P, Martin O J F, Smith D R, et al. Plasmon resonances of silver nanowires with a nonregular cross section. Phys Rev B, 2001, 64: 235402CrossRefGoogle Scholar
  8. 8.
    Wokaun A, Gordon J P, Liao P F. Radiation damping in surface-enhanced Raman scattering. Phys Rev Lett, 1982, 48: 957–960CrossRefGoogle Scholar
  9. 9.
    Lal S, Link S, Halas N J. Nano-optics from sensing to waveguiding. Nat Photonics, 2007, 1: 641–648CrossRefGoogle Scholar
  10. 10.
    Maier S A, Kik P G, Atwater H A. Observation of coupled plasmonpolariton modes in Au nanoparticle chain waveguides of different lengths: Estimation of waveguide loss. Appl Phys Lett, 2002, 81: 1714–1716CrossRefGoogle Scholar
  11. 11.
    Mitsui K, Handa Y, Kajikawa K. Optical fiber affinity biosensor based on localized surface plasmon resonance. Appl Phys Lett, 2004, 85: 4231–4233CrossRefGoogle Scholar
  12. 12.
    Wang T J, Lin W S. Electro-optically modulated localized surface plasmon resonance biosensors with gold nanoparticles. Appl Phys Lett, 2006, 89: 173903CrossRefGoogle Scholar
  13. 13.
    Mhlschlegel P, Eisler H J, Martin O J F, et al. Resonant optical antennas. Science, 2005, 308: 1607–1609CrossRefGoogle Scholar
  14. 14.
    Cole J R, Halas N J. Optimized plasmonic nanoparticle distributions for solar spectrum harvesting. Appl Phys Lett, 2006, 89: 153120CrossRefGoogle Scholar
  15. 15.
    Catchpole K R, Polman A. Plasmonic solar cells. Opt Express, 2008, 16: 21793–21800CrossRefGoogle Scholar
  16. 16.
    Wokaun A, Bergman J G, Heritage J P, et al. Surface second-harmonic generation from metal island films and microlithographic structures. Phys Rev B, 1981, 24: 849–856CrossRefGoogle Scholar
  17. 17.
    Kim E M, Elovikov S S, Murzina T V, et al. Surface-enhanced optical third-Harmonic generation in Ag island films. Phys Rev Lett, 2005, 95: 227402CrossRefGoogle Scholar
  18. 18.
    Danckwerts M, Novotny L. Optical frequency mixing at coupled gold nanoparticles. Phys Rev Lett, 2007, 98: 026104CrossRefGoogle Scholar
  19. 19.
    Murphy C J, Sau T K, Gole A M, et al. Anisotropic metal nanoparticles: Synthesis, assembly, and optical applications. J Phys Chem B, 2005, 109: 13857–13870CrossRefGoogle Scholar
  20. 20.
    Kim F, Song J H, Yang P D. Photochemical synthesis of gold nanorods. J Am Chem Soc, 2002, 124: 14316–14317CrossRefGoogle Scholar
  21. 21.
    Li J, Gu Y, Zhou F, et al. A designer approach to plasmonic nanostructures: tuning their resonance from visible to near-infrared. J Mod Opt, 2009, 56: 1396–1402CrossRefGoogle Scholar
  22. 22.
    Wiley B J, Chen Y C, McLellan J M, et al. Synthesis and optical properties of silver nanobars and nanorice. Nano Lett, 2007, 7: 1032–1036CrossRefGoogle Scholar
  23. 23.
    Lu Y, Liu G L, Kim J, et al. Nanophotonic crescent Moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect. Nano Lett, 2005, 5: 119–124CrossRefGoogle Scholar
  24. 24.
    Tamaru H, Kuwata H, Miyazaki H T, et al. Resonant light scattering from individual Ag nanoparticles and particle pairs. Appl Phys Lett, 2002, 80: 1826–1828CrossRefGoogle Scholar
  25. 25.
    Gunnarsson L, Rindzevicius T, Prikulis J, et al. Confined plasmons in nanofabricated single silver particle pairs: Experimental observations of strong interparticle interactions. J Phys Chem. B, 2005, 109: 1079–1087CrossRefGoogle Scholar
  26. 26.
    Jain P K, Eustis S, El-Sayed M A. Plasmon coupling in nanorod assemblies: Optical absorption, discrete dipole approximation simulation, and exciton-coupling model. J Phys Chem B, 2006, 110: 18243–18253CrossRefGoogle Scholar
  27. 27.
    Reinhard B M, Siu M, Agarwal H, et al. Calibration of dynamic molecular rulers based on plasmon coupling between gold nanoparticles. Nano Lett, 2005, 5: 2246–2252CrossRefGoogle Scholar
  28. 28.
    Jain P K, Huang W Y, El-Sayed M A. On the universal scaling behavior of the distance decay of plasmon coupling in metal nanoparticle pairs: A plasmon ruler equation. Nano Lett, 2007, 7: 2080–2088CrossRefGoogle Scholar
  29. 29.
    Jain P K, El-Sayed M A. Universal scaling of plasmon coupling in metal nanostructures: Extension from particle pairs to nanoshells. Nano Lett, 2007, 7: 2854–2858CrossRefGoogle Scholar
  30. 30.
    Gu Y, Wang Y, Li J, et al. Interplay of plasmon resonances in binary nanostructures. Appl Phys B, 2010, 98: 353–363CrossRefGoogle Scholar
  31. 31.
    Gu Y, Li J, Martin O J F, et al. Controlling plasmonic resonances in binary metallic nanostructures. J Appl Phys, 2010, 107: 114313CrossRefGoogle Scholar
  32. 32.
    Taflove A, Hagness S C. Computational Electrodynamics: The Finite-Difference Time-Domain Method. Boston: Artech House, 2005Google Scholar
  33. 33.
    Draine B T, Flatau P J. Discrete-dipole approximation for scattering calculations. J Opt Soc Am A, 1994, 11: 1491–1499CrossRefGoogle Scholar
  34. 34.
    Kreibig U, Vollmer M. Optical Properties of Metal Clusters. Berlin: Springer-Verlag, 1995Google Scholar
  35. 35.
    Martin O J F, Girard C, Dereux A. Generalized field propagator for electromagnetic scattering and light confinement. Phys Rev Lett, 1995, 74: 526529Google Scholar
  36. 36.
    Prodan E, Radloff C, Halas N J, et al. A hybridization model for the plasmon response of complex nanostructures. Science, 2003, 302: 419–422CrossRefGoogle Scholar
  37. 37.
    Noguez C. Surface plasmons on metal nanoparticles: The influence of shape and physical environment. J Phys Chem C, 2007, 111: 3806–3819CrossRefGoogle Scholar
  38. 38.
    Gu Y, Yu K W, Sun H. Local-field distribution in resonant composites: Greens-function formalism. Phys Rev B, 1999, 59: 12847–12852CrossRefGoogle Scholar
  39. 39.
    Gu Y, Chen L L, Zhang H X, et al. Resonance capacity of surface plasmon on subwavelength metallic structures. Europhys Lett, 2008, 83: 27004CrossRefGoogle Scholar
  40. 40.
    Morse P M, Feshbach H. Methods of Theoretical Physics. New York: McGraw-Hill, 1953Google Scholar
  41. 41.
    Economou E N. Green’s Functions in Quantum Physics. 2nd ed. Berlin: Springer, 1990Google Scholar
  42. 42.
    Danckwerts M, Novotny L. Optical frequency mixing at coupled gold nanoparticles. Phys Rev Lett, 2007, 98: 026104CrossRefGoogle Scholar
  43. 43.
    Fuchs R. Theory of the optical properties of ionic crystal cubes. Phys Rev B, 1975, 11: 1732–1740CrossRefGoogle Scholar
  44. 44.
    Oldenburg S J, Averitt R D, Westcott S L, et al. Nanoengineering of optical resonances. Chem Phys Lett, 1998, 288: 243–247CrossRefGoogle Scholar
  45. 45.
    Hartschuh A, Sanchez E J, Xie X S, et al. High-resolution near-field Raman microscopy of single-walled carbon nanotubes. Phys Rev Lett, 2003, 90: 095503CrossRefGoogle Scholar
  46. 46.
    Jackson J B, Westcott S L, Hirsch L R, et al. Controlling the surface enhanced Raman effect via the nanoshell geometry. Appl Phys Lett, 2003, 82: 257–259CrossRefGoogle Scholar
  47. 47.
    Wang F, Shen Y R. General properties of local plasmons in metal nanostructures. Phys Rev Lett 2006, 97: 206806CrossRefGoogle Scholar
  48. 48.
    Johnson P B, Christy R W. Optical constants of the noble metals. Phys Rev B, 1972, 6: 4370–4379CrossRefGoogle Scholar
  49. 49.
    Sheridan A K, Clark A W, Glidle A, et al. Multiple plasmon resonances from gold nanostructures. Appl Phys Lett, 2007, 90: 143105CrossRefGoogle Scholar
  50. 50.
    Clark A W, Sheridan A K, Glidle A, et al. Tuneable visible resonances in crescent shaped nano-split-ring resonators. Appl Phys Lett, 2007, 91: 093109CrossRefGoogle Scholar
  51. 51.
    Gu Y, Gong Q H. Avoiding crossing of dielectric resonances in three-component composites. Phys Rev B, 2003, 67: 014209CrossRefGoogle Scholar
  52. 52.
    Gu Y, Gong Q H. Localized mode transfer and optical response in three-component composites. Phys Rev B, 2004, 69: 035105CrossRefGoogle Scholar
  53. 53.
    Li Z, Gong Q H. The plasmonic coupling of metal nanoparticles and its implication for scanning near-field optical microscope characterization. Chinese Sci Bull, 2009, 54: 3843–3843CrossRefGoogle Scholar
  54. 54.
    Cao Z X, Wu L N. Display technique based on surface plasmon resonant effect. Chinese Sci Bull, 2008, 53: 2257–2264CrossRefGoogle Scholar
  55. 55.
    Yao H M, Li Z, Gong Q H. Coupling-induced excitation of a forbidden surface plasmon mode of a gold nanorod. Sci China Ser G-Phys Mech Astron, 2009, 52: 1129–1138CrossRefGoogle Scholar
  56. 56.
    Zhao H W, Huang X G, Huang J T. Surface plasmon polaritons based optical directional coupler. Sci China Ser G-Phys Mech Astron, 2008, 51: 1877–1882CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ying Gu
    • 1
  • Jia Li
    • 1
  • Olivier J. F. Martin
    • 2
  • QiHuang Gong
    • 1
  1. 1.State Key Laboratory for Mesoscopic Physics, Department of PhysicsPeking UniversityBeijingChina
  2. 2.Nanophotonics and Metrology LaboratorySwiss Federal Institute of Technology Lausanne (EPFL)LausanneSwitzerland

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