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6 OPTOINFORMATICS’05 We applied and analyzed five published methods for the identification <strong>of</strong> the time delay from time series generated by a few different types <strong>of</strong> chaos-generating emitters. These methods are: 1. Analysis <strong>of</strong> the return maps <strong>of</strong> the transmitted signal, 2. Analysis <strong>of</strong> the autocorrelation function (ACF) <strong>of</strong> the transmitted signal, 3. Application <strong>of</strong> the average mutual information technique (the AMI-technique), 4. Recovery <strong>of</strong> T by local linear fits in a low-dimensional space [6] , 5. Analysis <strong>of</strong> the time-distribution <strong>of</strong> extrema [7] . We used the numerical models describing a few modifications <strong>of</strong> a communication system based on a DDE-circuit. These are: 1. A system with two feedback loops, one <strong>of</strong> them controlling the source and another one controlling the nonlinearity, 2. A system with two parallel time delays, 3. A system with two parallel time delays and two different filters, 4. A system with two parallel nonlinearities and two time delays, 5. A system with two switching time delays, 6. A system with modulated time delays. We integrated the numerical models with the Runge-Kutta procedure for different sets <strong>of</strong> parameters in the feedback loops. Next, chaotic time series generated by the aforementioned systems were analyzed from the point <strong>of</strong> view <strong>of</strong> the possibility to identify the time delay T. In brief, the main results obtained can be summarized as follows: 1. The communication system based on the chaos-generating circuit with a single feedback containing a time delay and a nonlinearity can be successfully attacked and reconstructed by an eavesdropper, despite the possibility <strong>of</strong> generating hyperchaotic signals. 2. Numerical results obtained show that it is possible to find system architectures that increase the security <strong>of</strong> the cryptosystem up to the necessary level. 3. A simple addition <strong>of</strong> a second feedback loop is not the universal remedy against breaking; the system becomes more secure only with specific choices <strong>of</strong> system architectures and parameters. Acknowledgements: The participation <strong>of</strong> V. S. Udaltsov was supported by the Centre National de la Recherche Scientifique (CNRS), France. 1. V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, Phys. Lett A 308, p. 54, 2003. 2. K. Ikeda and K. Matsumoto, Physica D 29, p. 223, 1987. 3. J. P. Goedgebuer, L. Larger, H. Porte, Phys. Rev. Lett. 80, No. 10, pp. 2249-2252, 1998. 4. V. S. Udaltsov, L. Larger, J. P. Goedgebuer, M. W. Lee, E. Genin, and W. T. Rhodes, IEEE TCAS-1 49, No. 7, pp.1006-1009, 2002. 5. V. S. Udaltsov, J. P. Goedgebuer, L Larger., W. T. Rhodes, Phys. Rev. Lett. 86. No. 9, pp, 1892-1895, 2001. 6. M. J. Bünner, M. Popp, Th. Meyer, A. Kittel, and J. Parisi, Phys. Rev. E 54, p. 3082, 1996. 7. B. P. Bezruchko, A. S. Karavaev, V. I. Ponomarenko, and M. D. Prokhorov, Phys. Rev. E 64, 056216-1, 2001.
SAINT-PETERSBURG, October 17 – 20, 2005 7 INTEGRATED OPTICAL BRAGG GRATINGS FOR FAST ELECTROOPTICAL CONTROL OF SPECTRAL CHANNELS IN OPTICAL TELECOMMUNICATIONS Alexander Shamray, Alexander Kozlov, Igor Ilichev, Mikhail Petrov I<strong>of</strong>fe Physico-Technical Institute, Laboratory <strong>of</strong> Quantum Electronics, 26 Polytekhnicheskaya, St. Petersburg, 194021, Russia Phone: +7-812-2479336, fax: +7-812-247-1017, e-mail: achamrai@mail.i<strong>of</strong>fe.ru A novel method <strong>of</strong> fast electrooptical control <strong>of</strong> the spectral response <strong>of</strong> Bragg gratings has been developed. An integrated optical device for the control <strong>of</strong> spectral channels based on this method has been fabricated and tested. We have developed a novel technique <strong>of</strong> the electrooptical control <strong>of</strong> the spectral response <strong>of</strong> Bragg gratings in LiNbO 3 single-mode channel waveguides. The technique is based on inducing <strong>of</strong> the average refractive index discontinuities which lead to the transformation <strong>of</strong> the shape <strong>of</strong> grating spectral response. An integrated optical device for demonstration <strong>of</strong> the suggested technique has been fabricated. A photorefractive Bragg grating was formed in the LiNbO 3 single mode optical waveguide by holographic recording. Average refractive index discontinuities in the Bragg grating were produced and electrically controlled by application <strong>of</strong> the external electric field with a specified spatial distribution defined by electrodes <strong>of</strong> specially designed configuration. Two modes <strong>of</strong> the device operation and two different regimes <strong>of</strong> its spectral response control have been demonstrated. The first regime is simple tuning <strong>of</strong> the central wavelength <strong>of</strong> the Bragg grating spectral response without changing its shape by application <strong>of</strong> a spatially uniform electric field. The wavelength shift <strong>of</strong> about 0.1 nm has been obtained for an applied electric field <strong>of</strong> 7.5 V/µm. This fast electrooptical tuning can be very attractive for wavelength locking and laser stabilization. The second regime <strong>of</strong> the control is a transformation <strong>of</strong> the shape <strong>of</strong> the Bragg grating spectral response. The application <strong>of</strong> external electric field <strong>of</strong> the same magnitude (7.5 V/µm), but opposite polarity to different halves <strong>of</strong> the grating produces the average refractive index discontinuity that results in maximum transmittance at the central wavelength <strong>of</strong> the grating reflection band. Thus the fast electrooptical switching from the stop-band mode to the pass-band mode has been demonstrated. This mode <strong>of</strong> operation is very attractive for building optical Add/Drop multiplexers, wavelength selective electrically controlled optical attenuators for optical power equalizers, and electrooptical modulators (allowing modulation <strong>of</strong> one specific wavelength channel without affecting the other channels). A high wavelength selectivity (0.1 ÷ 0.01 nm), fast electrooptical control (to 10 ns), relatively low controlling voltages, an integrated optical implementation, compatibility with other components in modern optical networks, and possibility <strong>of</strong> mass production make this device extremely promising as a key building block <strong>of</strong> various optical systems intended for control <strong>of</strong> narrow-band spectral channels in WDM telecommunication systems. The financial support <strong>of</strong> the INTAS (Grant Nr 04-83-3429) and Council <strong>of</strong> the grants <strong>of</strong> President <strong>of</strong> Russian Federation for support <strong>of</strong> young russian scientists and leading scientific schools (Grants NSH-98.2003.2 and MK-1520.2004.9) is gratefully acknowledged.
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