Home page Other articles in this issue | Correlation method for measuring the largest Lyapunov exponent in optical fields Order this article Gavrylyak M.S., Maksimyak A.P. and Maksimyak P.P. We propose an analog interference method for measuring the largest Lyapunov exponent for the optical fields generated by scattering objects and media. The method is further developed to make a device for high-speed real-time measurements of transverse correlation function of the optical fields. Keywords: space-time chaos, the largest Lyapunov exponent, transverse correlation function, nematic liquid crystal, interference method. PACS: 42.25.Hz, 42.25.Fx UDC: 535.36, 535.41 Ukr. J. Phys. Opt. 9 120-127 doi: 10.3116/16091833/9/2/120/2008 Received: 25.03.2008 | | REFERENCES 1. Harrison R. G., Firth W. J. and Al-Saidi I. A. Instabilities and routes to chaos in passive all-optical resonators containing molecular gases. Instabilities and Chaos in Quantum Optics, Arecchi F. T. and Harrison R. G., eds., Berlin: Springer Verlag (1987), 201236. 2. Arecchi F T, Boccaletti S, Giacomelli G, Puccioni G P, Ramazza P L and Residori S, 1992. Patterns, space-time chaos and topological defects in nonlinear optics. Physica D 61: 2539. doi: http://dx.doi.org/10.1016/0167-2789(92)90145-D 3. Asakura T. and Uozumi J. Fractal Optics. Sapporo: Hokkaido Univ. Press (1995). 4. Toronov V Y, Zhang X and Webb A G, 2007. A spatial and temporal comparison of hemodynamic signals measured using optical and functional magnetic resonance imaging during activation in human primary visual cortex. NeuroImage 34: 11361148. doi: http://dx.doi.org/10.1016/j.neuroimage.2006.08.048 5. Barré J and Dauxois T, 2001. Lyapunov exponents as a dynamical indicator of a phase transition. Europhys. Lett. 55: 164170. doi: http://dx.doi.org/10.1209/epl/i2001-00396-3 6. Ebisawa S and Komatsu S, 2007. Message encoding and decoding using an asynchronous chaotic laser diode transmitterreceiver array. Appl. Opt. 46: 43864396. doi: http://dx.doi.org/10.1364/AO.46.004386 7. Politi A, Ginelli F, Yanchuk S and Maistrenko Y, 2006. From synchronization to Lyapunov exponents and back. Physica D 224: 90101. doi: http://dx.doi.org/1016/j.physd.2006.09.032 8. Eckmann J-P and Ruelle D, 1985. Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57: 617656. doi: http://dx.doi.org/10.1103/RevModPhys.57.617 9. Farmer J D and Sidorowich J J, 1987. Predicting chaotic time series. Phys. Rev. Lett. 59: 845848. doi: http://dx.doi.org/10.1103/PhysRevLett.59.845 10. Sano M and Sawada Y, 1985. Measurement of the Lyapunov spectrum from a chaotic time series. Phys. Rev. Lett. 55: 10821085. doi: http://dx.doi.org/10.1103/PhysRevLett.55.1082 11. Wolf A., Swift J B, Swinney H L and Vastano J A, 1985. Determining Lyapunov exponents from a time series. Physica D 16: 285317. doi: http://dx.doi.org/10.1016/0167-2789(85)90011-9 12. Neumark Yu. I. and Landa P. S., Stochastic and Chaotic Fluctuations. Moscow: Nauka (1987). 13. Rosenstein M. T., Collins J. J. and De Luca C. J. A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets. Boston University: MA 02215 (1992). 14. Takens F, 1981. Detecting strange attractors in turbulence. Lect. Notes in Math. 898: 366381. 15. Angelsky O V, Maksimyak P P and Perun T O, 1993. Dimensionality in optical fields and signals. Appl. Opt. 32: 60666071. 16. Rytov S. M., Kravtsov Yu. A. and Tatarsky V. I. Principles of Statistical Radio-physics. Berlin: Springer (1989). 17. Akhmanov S. A., Dyakov Yu. Ye. and Chirkin A. S. Introduction to Statistical Radiophysics and Optics. Moscow: Nauka (1981). (c) Ukrainian Journal of Physical Optics |