Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization.

We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electro-optic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator (DPSK-d). The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations (approximately half of the DPSK-d free spectral range), as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup.

Experimental chaotic map generated by picosecond laser pulse-seeded electro-optic nonlinear delay dynamics.

We describe experimental studies of the dynamical behavior of a recently proposed electro-optic discrete time nonlinear delay oscillator. With appropriate choice of the oscillator loop parameters and external forcing of the dynamics using a pulsed laser source, the system allows for the physical realization of a high dimensional mathematical nonlinear mapping. The dynamical features observed with this new class of discrete time delay oscillator differ significantly from those observed with similar continuous time nonlinear delay feedback oscillators and reveal the intrinsic discrete time nature of the dynamics. We also discuss specific applications to chaos communications using regularly clocked binary data.

Demonstration of a chaos generator with two time delays.

We demonstrate a chaos generator involving two time delays and two nonlinear functions. Dynamic behaviors are numerically and experimentally observed. The complexity of the dynamics is discussed in terms of Lyapunov exponents and dimensions. The setup can provide a new architecture for enhancing message security in chaos encryption systems.