Vassilios Kovanis

Predicting Catastrophes in Nonlinear Dynamical Systems by Compressive Sensing

An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.

Instabilities and chaos in optically injected semiconductor lasers

We have experimentally obtained and theoretically analyzed a systematic map of the various instabilities induced in a semiconductor laser subject to strong optical injection as the amount of optical injection power and frequency detuning is varied. Two distinct islands of chaos have been identified in the injection‐locked region. They are separated by regions of period one and period two solutions. Spontaneous emission noise obscures the observation of high periodic orbits.

Period‐doubling route to chaos in a semiconductor laser subject to optical injection

Experimental measurements and a single‐mode analysis of a quantum‐well laser diode subject to strong optical injection are combined to demonstrate that the diode follows a period‐doubling route to chaos. All laser parameters used in this model, including the influence of spontaneous emission noise, were experimentally determined based on the four‐wave mixing technique. The transition to chaos can be used to reduce the uncertainty in the value of the linewidth enhancement factor.

Reconfigurable quantum dot monolithic multi-section passive mode-locked lasers

We investigate the dynamical response of a quantum dot photonic integrated circuit formed with a combination of eleven passive and active gain cells operating when these cells are appropriately biased as a multi-section quantum dot passively mode-locked laser. When the absorber section is judiciously positioned in the laser cavity then fundamental frequency and harmonic mode-locking at repetition rates from 7.2GHz to 51GHz are recorded. These carefully engineered multi-section configurations that include a passive wave-guide section significantly lower the pulse width up to 34% from 9.7 to 6.4 picoseconds, as well increase by 49% the peak pulsed power from 150 to 224 mW, in comparison to conventional two-section configurations that are formed on the identical device under the same average power. In addition an ultra broad operation range with pulse width below ten picoseconds is obtained with the 3rd-harmonic mode-locking configuration. A record peak power of 234 mW for quantum dot mode-locked lasers operating over 40 GHz is reported for the first time.

Time-series-based prediction of complex oscillator networks via compressive sensing

Complex dynamical networks consisting of a large number of interacting units are ubiquitous in nature and society. There are situations where the interactions in a network of interest are unknown and one wishes to reconstruct the full topology of the network through measured time series. We present a general method based on compressive sensing. In particular, by using power series expansions to arbitrary order, we demonstrate that the network-reconstruction problem can be casted into the form X=Ga, where the vector X and matrix G are determined by the time series and a is a sparse vector to be estimated that contains all nonzero power series coefficients in the mathematical functions of all existing couplings among the nodes. Since a is sparse, it can be solved by the standard L1-norm technique in compressive sensing. The main advantages of our approach include sparse data requirement and broad applicability to a variety of complex networked dynamical systems, and these are illustrated by concrete examples of model and real-world complex networks.

PT-symmetric Talbot effects.

We show that complex PT-symmetric photonic lattices can lead to a new class of self-imaging Talbot effects. For this to occur, we find that the input field pattern has to respect specific periodicities dictated by the symmetries of the system. While at the spontaneous PT-symmetry breaking point the image revivals occur at Talbot lengths governed by the characteristics of the passive lattice, at the exact phase it depends on the gain and loss parameter, thus allowing one to control the imaging process.

Analytical stability boundaries for a semiconductor laser subject to optical injection

Abstract We determine analytically the stability boundaries of a semiconductor laser subject to external optical injection. Specifically, we derive the exact conditions for a steady state limit point and a Hopf bifurcation point in terms of the injection strength and the frequency detuning. These conditions are formulated in parametric form and are appropriate for asymptotic approximations. We investigate the limit of a large ratio of the carrier and photon lifetimes and we discuss the resulting expressions in terms of the linewidth enhancement factor. For negative detuning, the unstable domain is bounded by two Hopf bifurcation points which coincide at a critical negative value of the detuning. For positive detunings, all steady state solutions are unstable. Useful scaling laws characterizing different parts of the stability diagram are derived.

Modeling the Injection-Locked Behavior of a Quantum Dash Semiconductor Laser

Using the conventional rate equations describing an injection-locked system, a novel modulation response function is derived, which implicitly incorporates nonlinear gain through the free-running relaxation oscillation frequency and damping rate of the slave laser. In this paper, it is shown that the model presented can be used to extract the characteristic parameters of the coupled system from experimental data. The number of fitting parameters in the model is reduced by determining the fundamental slave parameters through the conventional free-running response function; these parameters are considered to be constant during the curve-fitting of the injection-locked system. Furthermore, in order to reduce the number of possible solutions generated during the least-squares-fitting process, the remaining fitting parameters are tightly constrained based on the physical limits of the coupled system. By reducing the number of unknown fitting parameters and constraining the remaining terms, a stronger confidence in the extracted parameters is achieved. Using a series of response curves measured from an injection-locked quantum dash laser, characteristic parameters of the system are extracted and validity of the model is examined. The verified model is used to analyze the impact of the linewidth enhancement factor on the characteristics of the response function in the microwave domain.

Bragg solitons in nonlinear PT -symmetric periodic potentials

It is shown that slow Bragg soliton solutions are possible in nonlinear complex parity-time (PT ) symmetric periodic structures. Analysis indicates that the PT -symmetric component of the periodic optical refractive index can modify the grating band structure and hence the effective coupling between the forward and backward waves. Starting from a classical modified massive Thirring model, solitary wave solutions are obtained in closed form. The basic properties of these slow solitary waves and their dependence on their respective PT -symmetric gain/loss profile are then explored via numerical simulations.

Linewidth Sharpening via Polarization-Rotated Feedback in Optically Injected Semiconductor Laser Oscillators

Combining optical injection and polarization-rotated optical feedback in a semiconductor laser can induce self-referenced periodic output that is widely tunable by simply varying the dc-bias points of the systems master and slave lasers. We observed a feedback-induced reduction of the fundamental period-one oscillation linewidth by more than two orders of magnitude relative to the injection-only case. Performance was found to be negatively affected by the interference between the external injection signal and the residual feedback in the same polarization. The nonlinear dynamics of the optically injected semiconductor laser can be used to minimize sensitivity to fluctuations in the operating points. However, the use of the nonlinear dynamics at high oscillation frequencies is limited by the decreasing strength of the interaction between the circulating intracavity optical field and the carrier density.