Advertisement

Applied Physics B

, 93:21 | Cite as

Propagation of the fundamental whispering gallery modes in a linear chain of microspheres

  • L. I. DeychEmail author
  • C. Schmidt
  • A. Chipouline
  • T. Pertsch
  • A. Tünnermann
Article

Abstract

Multi-sphere Mie theory is used to analyze the resonance response and the spatial distribution of the electromagnetic field in a system of a linear chain of microspheres. We assume that the system is coupled to a monochromatic source that would have excited a fundamental whispering gallery mode in a single sphere, and study the modification of the resonance frequencies and the spatial distribution of the field induced by optical coupling between spheres. We find that the coupled-mode approach does not give an adequate description of this situation, and that the excitations of the chain cannot be presented as linear combinations of the single-sphere fundamental modes. In the case of chains with an odd number of microspheres, there exists a single collective mode with frequency equal to that of the single-sphere resonance, which reproduces the field pattern of a single-sphere fundamental mode without distortion in every odd-numbered sphere of the chain.

PACS

42.60.Da 42.25.Bs 42.82.Et 

References

  1. 1.
    S.M. Spillane, T.J. Kippenberg, K.J. Vahala, Nature 415, 621 (2002) CrossRefADSGoogle Scholar
  2. 2.
    T.M. Benson, S.V. Boriskina, P. Sewell, A. Vukovic, S.C. Greedy, A.I. Nosich, Micro-optical resonators for microlasers and integrated optoelectronics, in Frontiers of Planar Lightwave Circuit Technology: Design, Simulation and Fabrication, ed. by S. Janz, J. Ctyroky, S. Tanev. NATO Sci. Ser. II: Math. Phys. Chem., vol. 216 (Springer, Dordrecht, 2006) CrossRefGoogle Scholar
  3. 3.
    V.M. Braginsky, M.L. Gorodetsky, V.S. Ilchenko, Phys. Lett. A 137, 393 (1989) CrossRefADSGoogle Scholar
  4. 4.
    V.R. Almeida, C.A. Barrios, R.R. Panepucci, M. Lipson, Nature 431, 1081 (2004) CrossRefADSGoogle Scholar
  5. 5.
    V.S. Ilchenko, M.L. Gorodetsky, X.S. Yao, L. Maleki, Opt. Lett. 26, 256 (2001) CrossRefADSGoogle Scholar
  6. 6.
    M. Bayer, T. Gutbrod, J.P. Reithmaier, A. Forchel, T.L. Reinecke, P.A. Knipp, Phys. Rev. Lett. 81, 2582 (1998) CrossRefADSGoogle Scholar
  7. 7.
    Y.P. Rakovich, J.F. Donegan, M. Gerlach, A.L. Bradley, T.M. Connolly, J.J. Boland, N. Gaponik, A. Rogach, Phys. Rev. A 70, 051801 (2004) CrossRefADSGoogle Scholar
  8. 8.
    T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999) CrossRefADSGoogle Scholar
  9. 9.
    H. Miyazaki, Y. Jimba, Phys. Rev. B 62, 7976 (2000) CrossRefADSGoogle Scholar
  10. 10.
    S.V. Boriskina, Opt. Lett. 31, 338 (2006) CrossRefADSGoogle Scholar
  11. 11.
    A. Yariv, Y. Xu, R.K. Lee, A. Scherer, Opt. Lett. 24, 711 (1999) CrossRefADSGoogle Scholar
  12. 12.
    S.M. Spillane, T.J. Kippenberg, O.J. Painter, K.J. Valhala, Phys. Rev. Lett. 91, 043902 (2003) CrossRefADSGoogle Scholar
  13. 13.
    A. Naweed, G. Farca, S.I. Shopova, A.T. Rosenberger, Phys. Rev. A 71, 043804 (2005) CrossRefADSGoogle Scholar
  14. 14.
    M.L. Povinelli, S.G. Johnson, M. Lonc̆ar, M. Ibanescu, E.J. Smythe, F. Capasso, J.D. Joannopoulos, Opt. Express 13, 8286 (2005) CrossRefADSGoogle Scholar
  15. 15.
    M.I. Mishchenko, L.D. Travis, A.A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, Cambridge, 2002) Google Scholar
  16. 16.
    K.A. Fuller, Appl. Opt. 30, 4716 (1991) ADSCrossRefGoogle Scholar
  17. 17.
    O. Cruzan, Q. Appl. Math. 20, 33 (1962) zbMATHMathSciNetGoogle Scholar
  18. 18.
    S. Stein, Q. Appl. Math. 19, 15 (1961) zbMATHGoogle Scholar
  19. 19.
    L. Deych, A. Roslyak, Phys. Rev. E 73, 036606 (2006) CrossRefADSGoogle Scholar
  20. 20.
    Y. Hara, T. Mukaiyama, K. Takeda, M. Kuwata-Gonokami, Phys. Rev. Lett. 94, 203905 (2005) CrossRefADSGoogle Scholar
  21. 21.
    V. Astratov, J. Franchak, S. Ashili, Appl. Phys. Lett. 85, 5508 (2004) CrossRefADSGoogle Scholar
  22. 22.
    B.M. Moeller, U. Woggon, M. Artemeyev, Opt. Lett. 30, 2116 (2005) CrossRefADSGoogle Scholar
  23. 23.
    K. Totsuka, N. Kobayashi, M. Tomita, Phys. Rev. Lett. 98, 213904 (2007) CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • L. I. Deych
    • 1
    Email author
  • C. Schmidt
    • 2
  • A. Chipouline
    • 2
  • T. Pertsch
    • 2
  • A. Tünnermann
    • 3
  1. 1.Physics Department, Queens CollegeCity University of New YorkFlushingUSA
  2. 2.Institute of Applied PhysicsFriedrich Schiller University JenaJenaGermany
  3. 3.Fraunhofer Institute for Applied Optics and Precision EngineeringJenaGermany

Personalised recommendations