Tuning the period of square-wave oscillations for delay-coupled optoelectronic systems

Optical square-wave generation in a semiconductor laser with optoelectronic feedback

We report self-sustained optical square-wave (SW) generation in a semiconductor laser diode subjected to delayed optoelectronic feedback on its injection current (J). This optoelectronic oscillator relies on nonlinear effects present in both the laser diode and in the optoelectronic feedback loop through amplifier saturation. The repetition rate of the SW is an integer multiple of the inverse of the loop delay, while the duty cycle can be tuned with J.

Nonlinear dynamics in an optoelectronic feedback delay oscillator with piecewise linear transfer functions from the laser diode and photodiode

We investigate the nonlinear dynamics of a recent architecture of an optoelectronic oscillator, where the emitting laser and the receiving diode are connected in a head-to-tail configuration via an optical fiber delay line. The resulting nonlinear transfer function is a piecewise linear profile, and its interplay with the delay leads to many complex behaviors such as relaxation oscillations and deterministic chaos. This system belongs to a recent class of optoelectronic oscillators where the nonlinearity does not originate from the sinusoidal transfer function of an imbalanced interferometer, and, in particular, it is a simple optoelectronic oscillator configuration that is capable of displaying a chaotic behavior. The results of the analytic study are confirmed by numerical simulations and experimental measurements.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

In-phase, out-of-phase and T/4 synchronization of square waves in delay-coupled non-identical optoelectronic oscillators

We model two non-identical delay-line optoelectronic oscillators mutually coupled through delayed cross-feedback. The system can generate multi-stable nanosecond periodic square-wave solutions which arise through a Hopf instability. We show that for suitable ratios between self and cross delay times, the two oscillators generate square waves with different amplitude but synchronized in phase, out of phase or with a dephasing of a quarter of the period. We also show that the synchronization is robust to small mismatches in the delay times.

Synchronization of tunable asymmetric square-wave pulses in delay-coupled optoelectronic oscillators

We consider a model for two delay-coupled optoelectronic oscillators under positive delayed feedback as prototypical to study the conditions for synchronization of asymmetric square-wave oscillations, for which the duty cycle is not half of the period. We show that the scenario arising for positive feedback is much richer than with negative feedback. First, it allows for the coexistence of multiple in- and out-of-phase asymmetric periodic square waves for the same parameter values. Second, it is tunable: The period of all the square-wave periodic pulses can be tuned with the ratio of the delays, and the duty cycle of the asymmetric square waves can be changed with the offset phase while the total period remains constant. Finally, in addition to the multiple in- and out-of-phase periodic square waves, low-frequency periodic asymmetric solutions oscillating in phase may coexist for the same values of the parameters. Our analytical results are in agreement with numerical simulations and bifurcation diagrams obtained by using continuation techniques.