-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.
Copyright c EPLA, 2011Introduction. -Excitability is an essential characteristic of many biological systems, such as neural networks and the heart [1]. The FitzHugh-Nagumo (FHN) model [2] is a canonical model of excitability, which exhibits a variety of dynamics ranging from spiking to relaxation oscillations. The study of excitability in optics and electronics is of great current interest [3][4][5][6].There is also great interest in developing devices that produce periodic trains of optical pulses, which correspond to distinct comb lines in the frequency domain, for applications ranging from metrology [7] to frequency conversion and signal broadcasting [8]. Narrow pulses, with correspondingly large bandwidths, are particularly useful. Therefore, the ability to tune pulse widths to short time scales is very desirable.In this letter, we describe novel pulse-train solutions generated by a time-delay optoelectronic oscillator (OEO). Using nullclines corresponding to solutions that are periodic with the time delay, we find an analytic expression relating the pulse width to the low-frequency cutoff of the bandpass filter in our system. The analytic expression is in good agreement with experiments and numerical simulations. We also apply a similar analysis to the oscillatory regime, where we can control the duty cycle of the limit-cycle oscillations. Again, the nullclines make analytical studies of the waveforms of these solutions possible.