OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijin de Sterke
  • Vol. 19, Iss. 7 — Mar. 28, 2011
  • pp: 6923–6937

Effect of size disorder on the optical transport in chains of coupled microspherical resonators

Chao-Sheng Deng, Hui Xu, and Lev Deych  »View Author Affiliations


Optics Express, Vol. 19, Issue 7, pp. 6923-6937 (2011)
http://dx.doi.org/10.1364/OE.19.006923


View Full Text Article

Enhanced HTML    Acrobat PDF (1154 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We investigate statistical properties of collective optical excitations in disordered chains of microspheres using transfer-matrix method based on nearest-neighbors approximation. Radiative losses together with transmission and reflection coefficients of optical excitations are studied numerically. We found that for the macroscopically long chain, the transmission coefficient demonstrates properties typical for a one dimensional strongly localized system: log-normal distribution with parameters obeying standard scaling relation. At the same time, we show that the distribution function of the radiative losses behaves very differently from other lossy optical systems. We also studied statistical properties of the optical transport in short chains of resonators and demonstrated that even small disorder results in significant drop of transmission coefficient acompanied by strong enhancement of the radiative losses.

© 2011 OSA

OCIS Codes
(290.4020) Scattering : Mie theory
(230.4555) Optical devices : Coupled resonators

ToC Category:
Scattering

History
Original Manuscript: January 18, 2011
Revised Manuscript: March 3, 2011
Manuscript Accepted: March 7, 2011
Published: March 25, 2011

Citation
Chao-Sheng Deng, Hui Xu, and Lev Deych, "Effect of size disorder on the optical transport in chains of coupled microspherical resonators," Opt. Express 19, 6923-6937 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-7-6923


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. B. Matsko and V. S. Ilchenko, “Optical Resonators With Whispering-Gallery Modes—Part I: Basics,” IEEE J. OF Sel. Topics in Q. El. 12, 3–14 (2006). [CrossRef]
  2. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999). [CrossRef]
  3. V. N. Astratov, J. P. Franchak, and S. P. Ashili, “Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder,” Appl. Phys. Lett. 85, 5508–5510 (2004). [CrossRef]
  4. Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, “Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres,” Phys. Rev. Lett. 94, 203905 (2005). [CrossRef] [PubMed]
  5. B. M. Möller, U. Woggon, and M. V. Artemyev, “Bloch modes and disorder phenomena in coupled resonator chains,” Phys. Rev. B 75, 245327 (2007). [CrossRef]
  6. K. Grujic and O. G. Hellesø, “Dielectric microsphere manipulation and chain assembly by counter-propagating waves in a channel waveguide,” Opt. Express 15, 6470–6477 (2007). [CrossRef] [PubMed]
  7. J. Goeckeritz and S. Blair, “Optical characterization of coupled resonator slow-light rib waveguides,” Opt. Express 18, 18190–18199 (2010). [CrossRef] [PubMed]
  8. S. Yang and V. N. Astratov, “Photonic nanojet-induced modes in chains of size-disordered microspheres with an attenuation of only 0.08 db per sphere,” Appl. Phys. Lett. 92, 261111 (2008). [CrossRef]
  9. M. L. Cooper, G. Gupta, M. A. Schneider, W. M. J. Green, S. Assefa, F. Xia, Y. A. Vlasov, and S. Mookherjea, “Statistics of light transport in 235-ring silicon coupled-resonator optical waveguides,” Opt. Express 18, 26505–26516 (2010). [CrossRef] [PubMed]
  10. V. N. Astratov, “Fundamentals and Applications of Microsphere Resonator Circuits,” in Photonic Microresonator Research and Applications , I. Chremmos, O. Schwelb, and N. Uzunoglu, eds., (Springer Series in Optical Sciences156, 2010), pp. 423–457. [CrossRef]
  11. L. I. Deych and O. Roslyak, “Photonic band mixing in linear chains of optically coupled microspheres,” Phys. Rev. E 73, 036606 (2006). [CrossRef]
  12. Z. Chen, A. Taflove, and V. Backman, “Highly efficient optical coupling and transport phenomena in chains of dielectric microspheres,” Opt. Lett. 31, 389–391 (2006). [CrossRef] [PubMed]
  13. G. S. Blaustein, M. I. Gozman, O. Samoylova, I. Y. Polishchuk, and A. L. Burin, “Guiding optical modes in chains of dielectric particles,” Opt. Express 15, 17380–17391 (2007). [CrossRef] [PubMed]
  14. M. Gozman, I. Polishchuk, and A. Burin, “Light propagation in linear arrays of spherical particles,” Phys. Lett. A 372, 5250 – 5253 (2008). [CrossRef]
  15. A. Petrov, M. Krause, and M. Eich, “Backscattering and disorder limits in slow light photonic crystal waveguides,” Opt. Express 17, 8676–8684 (2009). [CrossRef] [PubMed]
  16. D. P. Fussell, S. Hughes, and M. M. Dignam, “Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides,” Phys. Rev. B 78, 144201 (2008). [CrossRef]
  17. S. Mookherjea and A. Oh, “Effect of disorder on slow light velocity in optical slow-wave structures,” Opt. Lett. 32, 289–291 (2007). [CrossRef] [PubMed]
  18. S. Mookherjea, “Spectral characteristics of coupled resonators,” J. Opt. Soc. Am. B 23, 1137–1145 (2006). [CrossRef]
  19. P. Pradhan and N. Kumar, “Localization of light in coherently amplifying random media,” Phys. Rev. B 50, 9644–9647 (1994). [CrossRef]
  20. V. Freilikher, M. Pustilnik, and I. Yurkevich, “Effect of absorption on the wave transport in the strong localization regime,” Phys. Rev. Lett. 73, 810–813 (1994). [CrossRef] [PubMed]
  21. J. Heinrichs, “Transmission, reflection and localization in a random medium with absorption or gain,” J. Phys.: Condens. Matter 18, 4781 (2006). [CrossRef]
  22. J. C. J. Paasschens, T. S. Misirpashaev, and C. W. J. Beenakker, “Localization of light: Dual symmetry between absorption and amplification,” Phys. Rev. B 54, 11887–11890 (1996). [CrossRef]
  23. V. Freilikher and M. Pustilnik, “Phase randomness in a one-dimensional disordered absorbing medium,” Phys. Rev. B 55, R653–R655 (1997). [CrossRef]
  24. S. K. Joshi, D. Sahoo, and A. M. Jayannavar, “Modeling of stochastic absorption in a random medium,” Phys. Rev. B 62, 880–885 (2000). [CrossRef]
  25. D. V. Savin and H.-J. Sommers, “Distribution of reflection eigenvalues in many-channel chaotic cavities with absorption,” Phys. Rev. E 69, 035201 (2004). [CrossRef]
  26. C.-S. Deng, H. Xu, and L. Deych, “Optical transport and statistics of radiative losses in disordered chains of microspheres,” Phys. Rev. A 82, 041803 (2010). [CrossRef]
  27. M. Mishchenko, L. Travis, and A. Lacis, Scattering, absorption, and emission of light by small particles (Cambridge University Press, Cambridge, 2002).
  28. H. Miyazaki and Y. Jimba, “Ab initio tight-binding description of morphology-dependent resonance in a bi-sphere,” Phys. Rev. B 62, 7976–7997 (2000). [CrossRef]
  29. A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Collective emission and absorption in a linear resonator chain,” Opt. Express 17, 15210 (2009). [CrossRef] [PubMed]
  30. A. D. Stone, J. D. Joannopoulos, and D. J. Chadi, “Scaling studies of the resistance of the one-dimensional anderson model with general disorder,” Phys. Rev. B 24, 5583–5596 (1981). [CrossRef]
  31. Z.-Q. Zhang, “Light amplification and localization in randomly layered media with gain,” Phys. Rev. B 52, 7960–7964 (1995). [CrossRef]
  32. X. Jiang and C. M. Soukoulis, “Transmission and reflection studies of periodic and random systems with gain,” Phys. Rev. B 59, 6159–6166 (1999). [CrossRef]
  33. G. Czycholl, B. Kramer, and A. MacKinnon, “Conductivity and localization of electron states in one dimensional disordered systems: Further numerical results,” Z. Phys. B 43, 5–11 (1981). [CrossRef]
  34. B. Kramer and A. MacKinnon, “Localization: theory and experiment,” Rep. Prog. Phys. 56, 1469 (1993). [CrossRef]
  35. B. Derrida and E. Gardner, “Lyapounov exponent of the one dimensional Anderson model : weak disorder expansions,” J. Phys. France 45, 1283–1295 (1984). [CrossRef]
  36. F. M. Izrailev, S. Ruffo, and L. Tessieri, “Classical representation of the one-dimensional Anderson model,” J. Phys. A: Math. Gen. 31, 5263 (1998). [CrossRef]
  37. A. V. Kanaev, V. N. Astratov, and W. Cai, “Optical coupling at a distance between detuned spherical cavities,” Appl. Phys. Lett. 88, 111111 (2006). [CrossRef]
  38. C. Schmidt, A. Chipouline, T. Käsebier, E.-B. Kley, A. Tünnermann, T. Pertsch, V. Shuvayev, and L. I. Deych, “Observation of optical coupling in microdisk resonators,” Phys. Rev. A 80, 043841 (2009). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited