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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 12 — Jun. 16, 2014
  • pp: 14505–14516

Chaotic dynamics in coupled resonator sequences

M. Mancinelli, M. Borghi, F. Ramiro-Manzano, J. M. Fedeli, and L. Pavesi  »View Author Affiliations


Optics Express, Vol. 22, Issue 12, pp. 14505-14516 (2014)
http://dx.doi.org/10.1364/OE.22.014505


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Abstract

Optically induced thermal and free carrier nonlinearities in silicon micro-ring resonator influence their behavior. They can be either deleterious by making them instable and by driving their resonances out of the designed wavelengths, or enabler of different applications. Among the most interesting one, there are optical bistability and self induced oscillations. These lead to all optical logic, signal modulation, optical memories and applications in neural networks. Here, we theoretically and experimentally demonstrate that when many resonators are coupled together, thermal and free carrier nonlinearities induce also chaos. The chaotic dynamics are deeply analyzed using experimentally reconstructed phase space trajectories and the tool of Lyapunov exponents.

© 2014 Optical Society of America

OCIS Codes
(190.3100) Nonlinear optics : Instabilities and chaos
(230.4555) Optical devices : Coupled resonators
(130.4815) Integrated optics : Optical switching devices

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: March 11, 2014
Revised Manuscript: May 13, 2014
Manuscript Accepted: May 21, 2014
Published: June 5, 2014

Citation
M. Mancinelli, M. Borghi, F. Ramiro-Manzano, J. M. Fedeli, and L. Pavesi, "Chaotic dynamics in coupled resonator sequences," Opt. Express 22, 14505-14516 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-12-14505


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References

  1. V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29, 2387–2389 (2004). [CrossRef] [PubMed]
  2. P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005). [CrossRef] [PubMed]
  3. M. Borselli, T. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13, 1515–1530 (2005). [CrossRef] [PubMed]
  4. Q. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express 15, 924–929 (2007). [CrossRef] [PubMed]
  5. T. J. Johnson, M. Borselli, and O. Painter, “Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator,” Opt. Express 14, 817–831 (2006). [CrossRef] [PubMed]
  6. G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, “Optical bistability and pulsating behaviour in silicon-on-insulator ring resonator structures,” Opt. Express 13, 9623–9628 (2005). [CrossRef] [PubMed]
  7. T. Van Vaerenbergh, M. Fiers, P. Mechet, T. Spuesens, R. Kumar, G. Morthier, B. Schrauwen, J. Dambre, and P. Bienstman, “Cascadable excitability in microrings,” Opt. Express 20, 20292–20308 (2012). [CrossRef] [PubMed]
  8. T. Van Vaerenbergh, M. Fiers, P. Mechet, T. Spuesens, R. Kumar, G. Mortier, K. Vandoorne, B. Schneider, B. Schrauwen, J. Dambre, and P. Bienstman, “Self-pulsation and excitability mechanism in silicon-on-insulator microrings,” in Asia Communications and Photonics Conference, J. Opt. Soc. Am. (2012).
  9. T. Van Vaerenbergh, M. Fiers, J. Dambre, and P. Bienstman, “Simplified description of self-pulsation and excitability by thermal and free-carrier effects in semiconductor microcavities,” Phys. Rev. A 86, 063808 (2012). [CrossRef]
  10. A. Armaroli, S. Malaguti, G. Bellanca, S. Trillo, A. de Rossi, and S. Combrié, “Oscillatory dynamics in nanocavities with noninstantaneous kerr response,” Phys. Rev. A 84, 053816 (2011). [CrossRef]
  11. J. Petráček, Y. Ekşioğlu, and A. Sterkhova, “Simulation of self-pulsing in kerr-nonlinear coupled ring resonators,” Opt. Commun. 318, 147–152 (2014). [CrossRef]
  12. B. Maes, M. Fiers, and P. Bienstman, “Self-pulsing and chaos in short chains of coupled nonlinear microcavities,” Phys. Rev. A 80, 033805 (2009). [CrossRef]
  13. A. Argyris, M. Hamacher, K. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100, 194101 (2008). [CrossRef] [PubMed]
  14. A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nature Photon. 2, 728–732 (2008). [CrossRef]
  15. 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]
  16. M. Mancinelli, R. Guider, M. Masi, P. Bettotti, M. Vanacharla, J. Fedeli, and L. Pavesi, “Optical characterization of a SCISSOR device,” Opt. Express 19, 13664–13674 (2011). [CrossRef] [PubMed]
  17. Y. M. Landobasa, S. Darmawan, and M.-K. Chin, “Matrix analysis of 2-d microresonator lattice optical filters,” IEEE J. Quantum Electron. 41, 1410–1418 (2005). [CrossRef]
  18. M. Mancinelli, PhD Thesis, “Linear and non linear coupling effects in sequence of microresonators,” http://eprints-phd.biblio.unitn.it/1050/ (2013).
  19. A.A. Kumar, Fundamentals of Digital Circuits (Prentice Hall, 2012).
  20. F. Takens, “Detecting strange attractors in turbulence,” in Dynamical systems and turbulence, Warwick 1980, (Springer, 1981), pp. 366–381. [CrossRef]
  21. J.-P. Eckmann and D. Ruelle, “Ergodic theory of chaos and strange attractors,” Reviews of Modern Physics 57, 617 (1985). [CrossRef]
  22. M. Cencini, F. Cecconi, and A. Vulpiani, Chaos: From Simple Models to Complex Systems (World Scientific Publishing, 2010).
  23. S. Chen, L. Zhang, Y. Fei, and T. Cao, “Bistability and self-pulsation phenomena in silicon microring resonators based on nonlinear optical effects,” Opt. Express 20, 7454–7468 (2012). [CrossRef] [PubMed]
  24. H. A. Haus, Waves and Fields in Optoelectronics, vol. 1 (Prentice-Hall1984).
  25. Y. F. Xiao, X. B. Zou, W. Jiang, Y. L. Chen, and G. C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007). [CrossRef]
  26. L. F. Shampine and M. W. Reichelt, “The matlab ode suite,” SIAM journal on scientific computing 18, 1–22 (1997). [CrossRef]

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