Andreas Karsaklian Dal Bosco

Photonic integrated circuits unveil crisis-induced intermittency

We experimentally investigate an intermittent route to chaos in a photonic integrated circuit consisting of a semiconductor laser with time-delayed optical feedback from a short external cavity. The transition from a period-doubling dynamics to a fully-developed chaos reveals a stage intermittently exhibiting these two dynamics. We unveil the bifurcation mechanism underlying this route to chaos by using the Lang-Kobayashi model and demonstrate that the process is based on a phenomenon of attractor expansion initiated by a particular distribution of the local Lyapunov exponents. We emphasize on the crucial importance of the distribution of the steady-state solutions introduced by the time-delayed feedback on the existence of this intermittent dynamics.

Super-harmonic self-pulsations from a time-delayed phase-conjugate optical system

We provide experimental evidence of super-harmonic self-pulsation in a laser diode with a phase-conjugate optical feedback (PCF), i.e., time-periodic nearly sinusoidal oscillating output power at a frequency being multiple of the external-cavity frequency that corresponds to the long-standing predictions of so-called “external-cavity mode” [G. P. Agrawal and J. T. Klaus, Opt. Lett. 16, 1325–1327 (1991)]. High-harmonic self-pulsations have been so far limited to configurations with long time-delay, hence to relatively small frequencies (<1–2 GHz). By contrast, the reported self-pulsating solutions from PCF are stable in a larger range of feedback strength and with higher-order harmonic number when decreasing the external-cavity time-delay.

Cycles of self-pulsations in a photonic integrated circuit.

We report experimentally on the bifurcation cascade leading to the appearance of self-pulsation in a photonic integrated circuit in which a laser diode is subjected to delayed optical feedback. We study the evolution of the self-pulsing frequency with the increase of both the feedback strength and the injection current. Experimental observations show good qualitative accordance with numerical results carried out with the Lang-Kobayashi rate equation model. We explain the mechanism underlying the self-pulsations by a phenomenon of beating between successive pairs of external cavity modes and antimodes.

Chaos crisis and bistability of self-pulsing dynamics in a laser diode with phase-conjugate feedback

A laser diode subject to a phase-conjugate optical feedback can exhibit rich nonlinear dynamics and chaos. We report here on two bifurcation mechanisms that appear when increasing the amount of light being fed back to the laser. First, we report on a full suppression of chaos from a crisis induced by a saddle-node bifurcation on self-pulsing, so-called external-cavity-mode solutions (ECMs). Second, the feedback-dependent torus and saddle-node bifurcations on ECMs may be responsible for large regions of bistability between ECMs of different and high (beyond gigahertz) frequencies.

Dynamics Versus Feedback Delay Time in Photonic Integrated Circuits: Mapping the Short Cavity Regime

We report a comprehensive experimental investigation of the nonlinear dynamics yielded in five photonic integrated circuits, each consisting of a semiconductor laser with optical feedback from a short external cavity. The external cavity lengths are different for each laser and range from 1.3 to 10.3 mm, allowing analysis of the dependence of the dynamical scenario on the feedback delay time. We draw two-dimensional bifurcation diagrams and study the relative predominance of the different dynamics exhibited in each laser when the feedback strength and the laser injection current are varied. We identify that, in the commonly termed short cavity regime, small variations of the external cavity length can result in totally different dynamical distributions, suggesting the possibility to use the feedback delay time as a means to control laser behaviors.

Random Number Generation From Intermittent Optical Chaos

We propose a method to generate physical random numbers based on intermittent optical chaos. Intermittent chaotic output is produced in a semiconductor laser subjected to optical feedback embedded in a photonic integrated circuit. This dynamics is characterized by a temporal waveform organized in a succession of laminar regions of low amplitude and bursts of high amplitude. The temporal randomness ruling the alternation of successive laminar regions and bursts is used as an entropy source to generate sequences of random bits. We compare the performances of the exclusive OR and reverse methods implemented in the bit generation process and evaluate the quality of the random bits with the Rabbit test of TestU01 for different bit sequences lengths.

Dynamics-dependent synchronization in on-chip coupled semiconductor lasers

Synchronization properties of chaotic dynamics in two mutually coupled semiconductor lasers with optical feedback embedded in a photonic integrated circuit are investigated from the point of view of their dynamical content. A phenomenon in which the two lasers can show qualitatively different synchronization properties according to the frequency range of investigation and their nonlinear dynamics is identified and termed dynamics-dependent synchronization. In-phase synchronization is observed for original signals and antiphase synchronization is observed for low-pass filtered signals in the case where one of the lasers shows chaotic oscillations while the other laser exhibits low-frequency fluctuations dynamics. The experimental conditions causing the synchronization states to vary according to the considered frequency interval are studied and the key roles of asymmetric coupling strength and injection currents are clarified.

Low-frequency fluctuations in a laser diode with phase-conjugate feedback

Optical chaos is easily observed in a laser diode with either conventional (COF) or phase-conjugate optical feedback (PCF). We focus here on the so-called chaotic low-frequency fluctuations (LFF) where the laser exhibits slow power dropouts together with fast picosecond dynamics. We report here on a systematic study of LFF in a laser diode when subjected to PCF for which the bifurcations leading to those LFF remain to be elucidated. Qualitatively different dynamics are observed when increasing the phase-conjugate mirror (PCM) reflectivity or the injection current level. A combination of spectral and temporal measurements unveils the transition to LFF dynamics. The statistical properties of the time between power dropouts -mean dropout time and standard deviation- are studied as a function of the laser and feedback parameters and show that the laser may undergo what we call here a deterministic coherence resonance for a particular value of the PCF ratio. Interestingly, the phase conjugation build-up time here in SPS crystal is around 3 ms, hence is three orders of magnitude faster than what has been reported in previous dynamical studies of chaos in lasers with PCF using BaTiO3 photorefractive crystals. How the phase conjugation time-scale impacts on the laser dynamics remains an interesting question to which we contribute here.