Ultrafast Nonlinear Dynamics in Mesoscopic Oscillators

  • Chee Wei WongEmail author
  • Shu-Wei Huang
  • Jiagui Wu
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 6)


Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to cryptography. Recently our team has examined two types of mesoscopic nonlinear oscillators—in optomechanics and frequency combs—that provide new platforms to uncover quintessential architectures of chaos generation and the underlying physics. In the first section, we will describe the measurements of deterministic chaos formation at 60 fJ intracavity energies, through coupled Drude electron-hole plasma and radiation pressure. Statistical and entropic characterization quantifies the complexity of the chaos, including a correlation dimension D2 approximately 1.67 for the chaotic attractor, reminiscent of Lorenz chaos, along with the Lyapunov exponents. The dynamical maps demonstrate the plethora of subharmonics and bifurcations, with distinct transitional routes into chaotic states. In the second section, we will describe the measurements of spontaneous Turing pattern formation in nonlinear oscillators from background noise. Transitional states of breathers, chaos, soliton molecules are involved, in addition to the Turing patterns. Our observed threshold-dependent stationary Turing pattern has a RF tone tunable between 1.14 to 1.57 THz. Local mode hybridizations in the nonlinear ring oscillator seeds the pattern formation and phase matching, with a record high conversion efficiency of 45% and strong asymmetry in the Turing roll pattern. By heterodyne beating against a 1-Hz stabilized frequency reference, we show a fractional frequency sideband non-uniformity measured at 6.6 × 10−16, potentially serving as a high-performance chip-scale frequency reference.


Lyapunov Exponent Turing Pattern Kolmogorov Entropy Photonic Crystal Cavity Optomechanical Cavity 
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.


  1. 1.
    H. Poincaré, Science and Hypothesis (Courier Dover Publications, 2013)Google Scholar
  2. 2.
    Y. Li (Wong) et al., Design of dispersive optomechanical coupling and cooling in ultrahigh-Q/V slot-type photonic crystal cavities. Opt. Express 18, 23844 (2010)Google Scholar
  3. 3.
    X. Luan (Wong) et al., An integrated low phase noise radiation-pressure-driven optomechanical oscillator chipset. Nat. Sci. Rep. 4, 6842 (2014)Google Scholar
  4. 4.
    J. Yang (Wong) et al., Radio-frequency regenerative oscillations in monolithic high-Q/V heterostructured photonic crystal cavities. Appl. Phys. Lett. 104, 061104 (2014)Google Scholar
  5. 5.
    J. Wu (Wong) et al., Dynamical chaos in mesoscopic optomechanical oscillators, manuscript under review (2016)Google Scholar
  6. 6.
    J.C. Sprott, Chaos and time-series analysis (Oxford University Press, Oxford, UK, 2003)zbMATHGoogle Scholar
  7. 7.
    E. Ott, Chaos in dynamical systems (Cambridge Press, Cambridge, England, 2002)CrossRefzbMATHGoogle Scholar
  8. 8.
    P. Grassberger, I. Procaccia, Phys. Rev. Lett. 50, 346 (1983)MathSciNetCrossRefGoogle Scholar
  9. 9.
    S. Kondo, T. Miura, Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329, 1616 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    R. Sheth, L. Marcon, M.F. Bastida, M. Junco, L. Quintana, R. Dahn, M. Kmita, J. Sharpe, M.A. Ros, Hox genes regulate digit patterning by controlling the wavelength of a Turing-type mechanism. Science 338, 1476 (2012)CrossRefGoogle Scholar
  11. 11.
    J. Horváth, I. Szalai, P. De Kepper, An experimental design method leading to chemical Turing patterns. Science 324, 772 (2009)CrossRefGoogle Scholar
  12. 12.
    A.M. Turing, Phil. Trans. R. Soc. Lond. 237, 37 (1952)CrossRefGoogle Scholar
  13. 13.
    T. Bánsági Jr., V.K. Vanag, I.R. Epstein, Tomography of reaction-diffusion microemulsions reveals three-dimensional Turing patterns. Science 331, 1309 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    A. Liehr, Dissipative Solitons In Reaction Diffusion Systems: Mechanisms, Dynamics Interactions (Springer series in Synergetics, New York, 2013)Google Scholar
  15. 15.
    S.-W. Huang (Wong) et al., Spontaneous tunable Turing pattern formation for coherent high-power THz radiation, manuscript under review (2016).

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Mesoscopic Optics and Quantum Electronics LaboratoryUniversity of California Los AngelesLos AngelesUSA
  2. 2.College of Electronic and Information Engineering, Southwest UniversityChongqingChina

Personalised recommendations