Advertisement

The Mie Theory pp 135-155 | Cite as

Dipole Re-Radiation Effects in Surface Enhanced Raman Scattering

  • Logan K. Ausman
  • George C. SchatzEmail author
Chapter
Part of the Springer Series in Optical Sciences book series (SSOS, volume 169)

Abstract

In this chapter we use extensions of Mie theory to study electromagnetic enhancement factors associated with surface enhanced Raman scattering (SERS) from molecules adsorbed onto metal sphere array structures, comparing results from the more rigorous dipole re-radiation (DR) expression for Raman enhancement with the commonly used plane-wave (PW) enhancement formula. The DR and PW calculations are based on the T-matrix method for determining optical scattering from multiple spheres. In the PW expression, the enhancement is considered to be equal to the product of the squares of the local electric fields, \(|\mathbf{E}_\mathrm{ loc}(\omega )|^2|\mathbf{E}_\mathrm{ loc}(\omega ^{\prime })|^2\) or \(|\mathbf{E}_\mathrm{ loc}(\omega )|^4\) for zero Stokes shift, obtained from plane wave Mie scattering. In the DR calculation, the induced dipole in a molecule that is located at the surface of one of the particles serves as a dipole source at the Stokes-shifted frequency that scatters from the particles to define an overall enhancement factor. The SERS enhancement factors are determined for chains of 100 nm diameter Ag spheres and for chains of 100 nm Ag sphere dimers for various sphere and dimer separations and for various chain lengths, with the dimer gap fixed at 6.25 nm. We compare the PW and DR results for two different detector locations, a backscattering configuration normal to the axis of the chain, and a \(135^\circ \) scattering direction that includes the plane of the chain axis, in order to highlight far-field phase interference effects that are incorporated in the DR result but not PW. We find that the DR and PW results have negligible differences for the backscattering geometry, but far-field effects play a significant role in the overall enhancement factor for the non-backscattered location. This demonstrates the importance of including DR effects in the interpretation of SERS experiments.

Keywords

Surface Enhance Raman Scattering Enhancement Factor Extinction Spectrum Detector Location Plane Wave Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This research was supported by grant DE-SC0004752 funded by the US Department of Energy, Office of Science and Office of Basic Energy Sciences.

References

  1. 1.
    M.G. Albrecht, J.A. Creighton, J. Am. Chem. Soc. 99, 5215 (1977)CrossRefGoogle Scholar
  2. 2.
    D.L. Jeanmaire, R.P. van Duyne, Electroanal. Chem. 84, 1 (1977)CrossRefGoogle Scholar
  3. 3.
    M. Fleischmann, P.J. Hendra, A.J. McQuillian, Chem. Phys. Lett. 26, 163 (1974)ADSCrossRefGoogle Scholar
  4. 4.
    M. Moskovits, J. Chem. Phys. 69, 4159 (1978)ADSCrossRefGoogle Scholar
  5. 5.
    M.R. Philpott, J. Phys. Colloques 44, 295 (1983)CrossRefGoogle Scholar
  6. 6.
    H. Metiu, P. Das, Ann. Rev. Phys. Chem. 35, 507 (1984)ADSCrossRefGoogle Scholar
  7. 7.
    G.C. Schatz, Acc. Chem. Res. 17, 370 (1984)CrossRefGoogle Scholar
  8. 8.
    M. Moskovits, Rev. Mod. Phys. 57, 783 (1985)ADSCrossRefGoogle Scholar
  9. 9.
    A. Wokaun, Mol. Phys. 56, 1 (1985)ADSCrossRefGoogle Scholar
  10. 10.
    M. Kerker, Enhanced Raman scattering in colloidal systems. No. 45 in Studies in Physical and Theoretical Chemistry (Elsevier, Amsterdam, 1987)Google Scholar
  11. 11.
    M. Kerker, D.S. Wang, H. Chew, App. Opt. 19, 4159 (1980)ADSCrossRefGoogle Scholar
  12. 12.
    G. Mie, Ann. Phys. 25, 377 (1908)zbMATHCrossRefGoogle Scholar
  13. 13.
    H. Chew, P.J. McNulty, M. Kerker, Phys. Rev. A 13, 396 (1976)ADSCrossRefGoogle Scholar
  14. 14.
    H. Chew, M. Kerker, P.J. McNulty, J. Opt. Soc. Am. 66, 440 (1976)ADSCrossRefGoogle Scholar
  15. 15.
    H. Chew, M. Kerker, D.D. Cooke, Phys. Rev. A 16, 320 (1977)ADSCrossRefGoogle Scholar
  16. 16.
    R. Ruppin, J. Chem. Phys. 76, 1681 (1982)ADSCrossRefGoogle Scholar
  17. 17.
    M. Kerker, J. Opt. Soc. Am. B 2, 1327 (1985)ADSCrossRefGoogle Scholar
  18. 18.
    M. Kerker, J. Colloid Interface Sci. 118, 417 (1987)CrossRefGoogle Scholar
  19. 19.
    L.K. Ausman, G.C. Schatz, J. Chem. Phys. 131, 084708 (2009)ADSCrossRefGoogle Scholar
  20. 20.
    S. Zou, N. Janel, G.C. Schatz, J. Chem. Phys. 120, 10871 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    S. Zou, G.C. Schatz, J. Chem. Phys. 121, 12606 (2004)ADSCrossRefGoogle Scholar
  22. 22.
    S. Zou, G.C. Schatz, Chem. Phys. Lett. 403, 62 (2005)ADSCrossRefGoogle Scholar
  23. 23.
    S. Zou, G.C. Schatz,Coupled Plasmonic Plasmon/Photonic Resonance Effects in SERS. No. 103 in Topics in Applied Physics (Springer, Berlin, 2006)Google Scholar
  24. 24.
    S. Zou, G.C. Schatz, Nanotechnology 17, 2813 (2006)ADSCrossRefGoogle Scholar
  25. 25.
    S. Zou, G.C. Schatz, Isreal J. Chem. 46, 293 (2006)Google Scholar
  26. 26.
    L. Quin, S. Zou, C. Xue, A. Atkinson, G.C. Schatz, C.A. Mirkin, Proc. Natl. Acad. Sci. USA 103, 13300 (2006)ADSCrossRefGoogle Scholar
  27. 27.
    J.P. Camden, J.A. Dieringer, Y. Wang, D.J. Masiello, L.D. Marks, G.C. Schatz, R.P. van Duyne, J. Am. Chem. Soc. 130, 12616 (2008)CrossRefGoogle Scholar
  28. 28.
    W. Wei, S. Li, J.E. Millstone, M.J. Banholzer, X. Chen, X. Xu, G.C. Schatz, C.A. Mirkin, Angew. Chem. Int. Edit. 48, 4210 (2009)CrossRefGoogle Scholar
  29. 29.
    J.A. Dieringer, K.L. Wustholz, D.J. Masiello, J.P. Camden, S.L. Kleinman, G.C. Schatz, R.P. van Duyne, J. Am. Chem. Soc. 131, 849 (2009)CrossRefGoogle Scholar
  30. 30.
    K. Kneipp, W. Wang, H. Kneipp, L.T. Perelman, I. Itzkan, R.R. Dasari, M.S. Feld, Phys. Rev. Lett. 78, 1667 (1997)ADSCrossRefGoogle Scholar
  31. 31.
    S. Nie, S. Emory, Science 275, 1102 (1997)CrossRefGoogle Scholar
  32. 32.
    M. Moskovits, L.L. Tay, J. Yang, T. Haslett, SERS and the single molecule. No. 82 in Topics in Applied Physics (Springer, Berlin, 2002)Google Scholar
  33. 33.
    B. Vlčková, M. Moskovits, I. Pavel, K. Šišková, M. Sládková, M. Šlouf, Chem. Phys. Lett. 455, 131 (2008)ADSCrossRefGoogle Scholar
  34. 34.
    Y. Fang, N.H. Seong, D.D. Dlott, Science 321, 388 (2008)ADSCrossRefGoogle Scholar
  35. 35.
    K.E. Shafer-Peltier, C.L. Haynes, M.R. Glucksberg, R.P. van Duyne, J. Am. Chem. Soc. 125, 588 (2003)CrossRefGoogle Scholar
  36. 36.
    X. Zhang, M.A. Young, O. Lyandres, R.P. van Duyne, J. Am. Chem. Soc. 127, 4484 (2005)CrossRefGoogle Scholar
  37. 37.
    N.C. Shah, O. Lyandres, C.R. Yonzon, X. Zhang, R.P. van Duyne, ACS Symposium Series 963, 107 (2007)CrossRefGoogle Scholar
  38. 38.
    S.D. Hudson, G. Chumanov, Anal. Bioanal. Chem. 394, 679 (2009)CrossRefGoogle Scholar
  39. 39.
    D.A. Stuart, K.B. Biggs, R.P. van Duyne, Analyst 131, 568 (2006)ADSCrossRefGoogle Scholar
  40. 40.
    A.V. Whitney, F. Casadio, R.P. van Duyne, App. Spect. 61, 994 (2007)ADSCrossRefGoogle Scholar
  41. 41.
    C.L. Brosseau, A. Gambardella, F. Casadio, C.M. Grzywacz, J. Wouters, R.P. van Duyne, Anal. Chem. 81, 3056 (2009)CrossRefGoogle Scholar
  42. 42.
    S. Malynych, G. Chumanov, J. Am. Chem. Soc. 125, 2896 (2003)CrossRefGoogle Scholar
  43. 43.
    A.S. Kumbhar, M.K. Kinnan, G. Chumanov, J. Am. Chem. Soc. 127, 12444 (2005)CrossRefGoogle Scholar
  44. 44.
    M.K. Kinnan, G. Chumanov, J. Phys. Chem. C 111, 18010 (2007)CrossRefGoogle Scholar
  45. 45.
    Y.D. Suh, G.K. Schenter, L. Zhu, H.P. Lu, Ultramicroscopy 97, 89 (2003)CrossRefGoogle Scholar
  46. 46.
    L. Zhu, G.K. Schenter, M. Micic, Y.D. Suh, N. Klymyshyn, H.P. Lu, Proc. SPIE 4962, 70 (2003)ADSCrossRefGoogle Scholar
  47. 47.
    P.I. Geshev, K. Dickmann, J. Opt. A: Pure Appl. Opt. 8, S161 (2006)ADSCrossRefGoogle Scholar
  48. 48.
    T. Shegai, Z. Li, T. Dadosh, Z. Zhang, H. Xu, G. Haran, Proc. Natl. Acad. Sci. U.S.A. 105, 16448 (2008)ADSCrossRefGoogle Scholar
  49. 49.
    D. Pristinski, E.C. la Ru, S. Tan, S. Sukhishvili, H. Du, Opt. Express 16, 20117 (2008)ADSCrossRefGoogle Scholar
  50. 50.
    C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, Weinheim, 2004)Google Scholar
  51. 51.
    D.W. Mackowski, Proc. R. Soc. London Ser. A 433, 599 (1991)MathSciNetADSzbMATHCrossRefGoogle Scholar
  52. 52.
    D.W. Mackowski, J. Opt. Soc. Am. A 11, 2851 (1994)ADSCrossRefGoogle Scholar
  53. 53.
    D.W. Mackowski, M.I. Mishchenko, J. Opt. Soc. Am. A 13, 2266 (1996)ADSCrossRefGoogle Scholar
  54. 54.
    L.K. Ausman, G.C. Schatz, J. Chem. Phys. 129, 054704 (2008)ADSCrossRefGoogle Scholar
  55. 55.
    C.T. Tai, Dyadic Green’s Functions in Electromagnetic Theory (Intext Educational, Scranton, San Francisco, Toronto, London, 1971)Google Scholar
  56. 56.
    P.B. Johnson, R.W. Christy, Phys. Rev. B 6, 4370 (1972)ADSCrossRefGoogle Scholar
  57. 57.
    D.J. Masiello, G.C. Schatz, Phys. Rev. A 78, 042505 (2008)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of ChemistryNorthwestern UniversityEvanstonUSA

Personalised recommendations