Power spectrum analysis of time-delayed optoelectronic oscillators with wide and narrow band nonlinear filters

In this paper, we use the fourth-order Runge-Kutta and fast Fourier transform-based spectral analysis to study the power spectrum of the phenomena of multi-periodicity, crenelated, mixed-mode oscillations, and chaos when the values of the bandwidth and the cubic-nonlinear term (CNT) of the filter vary in the cubic-nonlinear optoelectronic oscillator (CN-OEO). On the one hand, when the high and low cut-off frequencies are sufficiently far apart, it is numerically proved that the presence of the 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.