Theoretical and experimental study of the optoelectronic oscillators cascaded by nonlinear electronic components

Abstract

This thesis aims at the theoretical and experimental study of optoelectronic oscillators cascaded by nonlinear electronic components. For this purpose, two (02) nonlinear electronics components have been used, namely: the self-sustained Colpitts oscillator and the nonlinear filter. We first study numerically and experimentally the self-sustained Colpitts oscillator which generates an electrical signal at high frequency and exhibits dynamic behaviors such as periodic, bursting, and mixed-mode oscillations which can be obtained using a potentiometer contained in the electronic circuit of the oscillator. Subsequently, this Colpitts oscillator is inserted into the electronic part of the optoelectronic oscillator (Colpitts-OEO). In this way, we put forward the interaction between optical nonlinearity and electronic nonlinearity to obtain also complex dynamic behaviors of the system thus constituted. It is shown that a wide variety of periodic and chaotic states can be excited and that there is an amplification of the signal frequencies. The temporal dynamics of the Colpitts-OEO system with and without delay is studied experimentally. In addition, we make an analytical and numerical study of the optoelectronic oscillator cascaded by a nonlinear filter (CN-OEO). This nonlinear filter is designed from a non-linear capacitor and a coil. We thus provide a spectral analysis of the phenomena of multi-periodicity, crenelated, mixed-mode oscillations, and chaos when the bandwidth and the cubic nonlinear term of the filter vary in the CN-OEO. On the one hand, when the high and low cut-off frequencies are sufficiently far apart, it is both analytically and numerically proved that the presence of the cubic nonlinear term (CNT) reveals the frequency combs generation with a free spectral range equal to the inverse of the time delay. Likewise, the width of the central peak narrows with the increase of the CNT, showing that the system becomes more and more selective in terms of oscillation frequencies. On the other hand, when the cut-off frequencies are sufficiently close, harmonic and sub-harmonic frequencies are recorded. In either case, CN-OEO displays oscillations whose frequencies remain greater than those of a standard optoelectronic oscillator.