Pulse-train solutions and excitability in an optoelectronic oscillator

We study an optoelectronic time-delay oscillator with bandpass filtering for different values of the filter bandwidth. Our experiments show novel pulse-train solutions with pulse widths that can be controlled over a three-order–of–magnitude range, with a minimum pulse width of ∼150 ps. The equations governing the dynamics of our optoelectronic oscillator are similar to the FitzHugh-Nagumo model from neurodynamics with delayed feedback in the excitable and oscillatory regimes. Using a nullclines analysis, we derive an analytical proportionality between pulse width and the low-frequency cutoff of the bandpass filter, which is in agreement with experiments and numerical simulations. Furthermore, the nullclines help to describe the shape of the waveforms.