Advertisement

Plasmonics

, Volume 7, Issue 1, pp 13–18 | Cite as

Modified Long Wavelength Approximation for the Optical Response of a Graded-Index Plasmonic Nanoparticle

  • Hung Yi Chung
  • Pui Tak Leung
  • Din Ping Tsai
Article

Abstract

The optical response of graded-index spherical metallic nanoparticles is studied in the modified long wavelength approximation with electrodynamic effects accounted for to the lowest order of the inverse of the wavelength. An effective-medium approach is adopted which leads to the conclusion that the first-order dynamical effects will enter mainly via the polarizability and not the effective dielectric function of the system. Numerical studies using various graded Drude functions show that these effects are not only significant for particles of large sizes but can also be appreciable for smaller particles with varying index profile.

Keywords

Radial inhomogeneous Effective medium Long wavelength approximation 

Notes

Acknowledgments

We would like to thank Professor K. W. Yu of the Chinese University of Hong Kong for useful communications. We also acknowledge the financial support from the National Science Council, Taiwan, ROC, under grant numbers NSC 99-2120-M-002-012, 99-2911-I-002-127, 98-EC-17-A-09-S1-019, and NSC 99-2112-M-231-001-MY3, NSC100-2120-M-002-008, and NSC100-2923-M-002-007-MY3.

References

  1. 1.
    Snyder AW, Love JD (1983) Optical Waveguide Theory. Chapman & Hall, New YorkGoogle Scholar
  2. 2.
    Gomez-Reino C, Perez MV, Bao C (2002) Gradient-index optics, fundamentals and applications. Springer, BerlinGoogle Scholar
  3. 3.
    Cai W, Shalaev VM (2009) Optical metamaterials: fundamentals and applications. Springer, New YorkGoogle Scholar
  4. 4.
    Leonhardt U, Philbin TG (2009) Chapter 2 transformation optics and the geometry of light. Prog Opt 53:69–152CrossRefGoogle Scholar
  5. 5.
    Wegener M, Linden S (2010) Shaping optical space with metamaterials. Phys Today 63(10):32–36CrossRefGoogle Scholar
  6. 6.
    M Yamanouchi, M Koizumi, T Hirai, I Shiota (1990) Proceedings of the first international symposium on functionally graded materials, Sendai, JapanGoogle Scholar
  7. 7.
    Sang ZF, Li ZY (2005) Effective negative refractive index of graded granular composites with metallic magnetic particles. Phys Lett A 334(5–6):422–428CrossRefGoogle Scholar
  8. 8.
    Kong SC, Taflove A, Backman V (2009) Quasi one-dimensional light beam generated by a graded-index microsphere. Opt Exp 17(5):3722–3731CrossRefGoogle Scholar
  9. 9.
    Dong L, Gu GQ, Yu KW (2003) First-principles approach to dielectric response of graded sphere particles. Phys Rev B 67(22):224205CrossRefGoogle Scholar
  10. 10.
    Mie G (1908) Contributions on the optics of turbid media, particularly colloidal metal solutions. Ann Phys 2:377–445CrossRefGoogle Scholar
  11. 11.
    Bhandari R (1965) Scattering coefficients for a multilayered sphere: analytic expressions and algorithms. Appl Opt 24(13):1960–1967CrossRefGoogle Scholar
  12. 12.
    Wu ZS, Wang YP (1991) Eletromagnetic scattering for multilayered sphere: recursive algorithms. Radio Sci 26(6):1393–1401CrossRefGoogle Scholar
  13. 13.
    Johnson BR (1996) Light scattering by a multilayer sphere. Appl Opt 35(18):3286–3296CrossRefGoogle Scholar
  14. 14.
    Johnson BR (1999) Exact theory of electromagnetic scattering by a heterogeneous multilayer sphere in the infinite-layer limit: effective-media approach. J Opt Soc Am A 16(4):845–852CrossRefGoogle Scholar
  15. 15.
    Yang W (2003) Improved recursive algorithm for light scattering by a multilayered sphere. Appl Optics 42(9):1710CrossRefGoogle Scholar
  16. 16.
    Wyatt PJ (1962) Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects. Phys Rev 127(5):1837–1843CrossRefGoogle Scholar
  17. 17.
    Yu KW, Gu GQ (2005) Effective conductivity of composites of graded spherical particles. Phys Lett A 345(4–6):448–452CrossRefGoogle Scholar
  18. 18.
    Kelly KL, Coronado E, Zhao LL, Schatz GC (2003) The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment. J Phys Chem B 107(3):668–677CrossRefGoogle Scholar
  19. 19.
    Meier M, Wokaun A (1983) Enhanced fields on large metal particles: dynamic depolarization. Opt Lett 8(11):581–583CrossRefGoogle Scholar
  20. 20.
    Moroz A (2009) Depolarization field of spheroidal particles. J Opt Soc Am B 26(3):517–527CrossRefGoogle Scholar
  21. 21.
    Meier M, Wokaun A, Liao PF (1985) Enhanced fields on rough surfaces: dipolar interactions among particles of sizes exceeding the Rayleigh limit. J Opt Soc Am B 2(6):931–949CrossRefGoogle Scholar
  22. 22.
    Kullock R, Grafstrom S, Evans PR, Pollard RJ, Eng LM (2010) Metallic nanorod arrays: negative refraction and optical properties explained by retarded dipolar interactions. J Opt Soc Am B 27(9):1819–1827CrossRefGoogle Scholar
  23. 23.
    Chung HY, Leung PT, Tsai DP (2009) Dynamic modifications of polarizability for large metallic spheroidal nanoshells. J Chem Phys 131(12):124122CrossRefGoogle Scholar
  24. 24.
    Chung HY, Guo GY, Chiang HP, Tsai DP, Leung PT (2010) Accurate description of the optical response of a multilayered spherical system in the long wavelength approximation. Phys Rev B 82(16):165440CrossRefGoogle Scholar
  25. 25.
    Mertens H, Koenderink AF, Polman A (2007) Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved Gersten and Nitzan model. Phys Rev B 76(11):115123CrossRefGoogle Scholar
  26. 26.
    Voshchinnikov NV, Mathis JS, (1999) Calculating cross sections of composite interstellar grains. Astrophys Journal 526(1):257–264Google Scholar
  27. 27.
    Li J, Sun G, Chan CT (2006) Optical properties of photonic crystals composed of metal-coated spheres. Phys Rev B 73(7):075117CrossRefGoogle Scholar
  28. 28.
    Xiao JJ, Yahubo K, Yu KW (2010). In: Helsey KN (ed) Plasmonics: theory and applications, chapter 13. Nova Science, HauppaugeGoogle Scholar
  29. 29.
    Huang JP, Yu KW (2004) Optical nonlinearity enhancement of graded metallic films. Appl Phys Lett 85(1):94CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Hung Yi Chung
    • 1
  • Pui Tak Leung
    • 2
    • 3
  • Din Ping Tsai
    • 1
  1. 1.Department of PhysicsNational Taiwan UniversityTaipeiRepublic of China
  2. 2.Department of PhysicsPortland State UniversityPortlandUSA
  3. 3.Institute of Optoelectronic SciencesNational Taiwan Ocean UniversityKeelungRepublic of China

Personalised recommendations