Vladimir S. Udaltsov

Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations

Abstract We report that signal encoding with high-dimensional chaos produced by delayed feedback systems with a strong nonlinearity can be broken. We describe the procedure and illustrate the method with chaotic waveforms obtained from a strongly nonlinear optical system that we used previously to demonstrate signal encryption/decryption with chaos in wavelength. The method can be extended to any systems ruled by nonlinear time-delayed differential equations.

Dynamics of non-linear feedback systems with short time-delays

Abstract We report a study of optical systems with delayed non-linear feedback when the ratio T / τ of the time-delay T and the response time τ of the system ranges from 10 to 0.01. Results of numerical simulations and experiments including the statistics, the bifurcation diagrams, the power-spectra and the correlation parameters are reported and show that the dynamics evolves from high-dimensional chaos to quasi-periodic oscillations and multistability. The frequency of the P-2 regime is shown to differ from 1/2 T when T / τ decreases.

Recording and reconstruction of femtosecond light pulses using volume holograms

Abstract Recording and reconstruction of the temporal profile of femtosecond laser pulses is realized by holography using the volume photorefractive polymer medium Reoxan. This medium is characterized by a rather high sensitivity and the ability to create holograms with high diffraction efficiency. After some theoretical consideration the principles and properties of the recording medium are discussed, the experimental setup is described, and the main results of the experiments are presented.

Experimental chaotic map generated by picosecond laser pulse-seeded electro-optic nonlinear delay dynamics

We describe experimental studies of the dynamical behavior of a recently proposed electro-optic discrete time nonlinear delay oscillator. With appropriate choice of the oscillator loop parameters and external forcing of the dynamics using a pulsed laser source, the system allows for the physical realization of a high dimensional mathematical nonlinear mapping. The dynamical features observed with this new class of discrete time delay oscillator differ significantly from those observed with similar continuous time nonlinear delay feedback oscillators and reveal the intrinsic discrete time nature of the dynamics. We also discuss specific applications to chaos communications using regularly clocked binary data.

RF-Interferences Generate Chaotic GHz FM—Carrier for Communications

Following the principle of a highly nonlinear delay oscillator, we demonstrate the generation of an RF chaotic frequency modulated carrier, which could be used in chaos based communication systems. The nonlinear process is provided by the transfer function of an RF interferometer, modulating the amplitude of an FM signal; for this purpose, the path difference required for the interference process, as well as a long delay required for complex chaotic oscillation, are designed through the use of optical fibers. The RF signal used to produce interferences is transposed in the optical domain by a direct laser modulation with the gigahertz chaotic FM signal. The interference is obtained at fiber outputs terminated by photodiodes for backconversion of the RF signal into the electrical domain. Experimental results reporting the particular dynamical behavior of the nonlinear delay RF oscillator are presented, and also discussed in terms of chaos communication applications

Delayed optoelectronic RF-interferences for chaos communications

Abstract Chaotic waveforms demonstrated in the past 10 years their ability to synchronize (Pecora and Carroll, 1990), and thus to be involved in various transmission configurations, from CDMA-like digital modulations (Penaud et al. , 2000), to analog chaotic masking of high speed digital data. Following the principle of a highly nonlinear delay dynamics, we demonstrate the possibility for the generation of a taylored RF band limited chaotic carrier, which could be used in chaos based communication systems. The nonlinear process is provided by the RF interference filtering of an FM signal. The optical path difference of the interferences, as well as the delay, are produced through the use of optical fibers, while the RF signal is optically converted by a laser direct modulation by a GHz chaotic FM signal. Experimental results as well as discussion of potential applications are reported.

Three-dimensional holography of femtosecond laser pulses

The results of the holographic recording and reconstruction of the time-domain profile of femtosecond laser pulses in the polymer volume medium named Reoxan are presented. The experimental data show the possibility of the effective spectral filtering to control the shape of ultrashort pulses.

Spectral vision: production of longitudinal images of diffusely scattered objects by spectral interferometric method

The spectral interferometric method of the objects longitudinal spatial structure observation is developed. It is based on spectral distribution correlation analysis of the radiation scattered by diffusely scattering objects. For this reason the developed method is called a spectral vision.