Paul M. Alsing

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.

Subharmonic transition in an optically injected semiconductor laser: theory and experiments

The equations for a semiconductor laser subject to detuned optical injection are analysed using asymptotic methods. We derive a third-order equation for the phase of the laser field which is then investigated for small injection but arbitrary frequency detuning. The long-time solution is a small amplitude time-periodic solution with a frequency close to the detuning except if the detuning is close to a multiple of the free-running laser relaxation frequency (resonance). We examine the case of subharmonic resonance, injecting at twice the relaxation resonance frequency, in detail. In addition to period-doubling bifurcations, we show the coexistence of bifurcation and isolated branches of solutions. Our approximate results are in good agreement with the numerical bifurcation diagram obtained from the original laser equations. Our analysis motivated a series of new experiments on laser diodes operating in the weak injection but large detuning regime. The experimental spectra show clearly the period-doubling bifurcation as well as the shifting of the slave-laser frequency predicted by our analysis.

Controlling chaos may induce new attractors in an optical device

Abstract The logistic map has been used to describe period doubling bifurcations for periodically modulated lasers. It also represents an asymptotic approximation of Ikedas map for a passive ring cavity. Because various control methods have been used recently to stabilize branches of periodic solutions in lasers, we investigate the logistic map with a standard Ott, Grebogi and Yorke (OGY) control. We explore the structure of this map plus perturbations and find considerable modifications to its bifurcation diagram. In addition to the original fixed points, we find a new fixed point and new period doubling bifurcations. We show that for certain values of small perturbations the new fixed point of the perturbed logistic map is stable, while its original fixed point becomes unstable. Our analysis suggests that new branches of solutions may exist in lasers as a result of the feedback control.

Lang and Kobayashi phase equation and its validity for low pump

An asymptotic theory of Lang and Kobayashi (LK) equations describing a semiconductor laser subject to optical feedback is investigated in detail. We obtain a simple third order, nonlinear, delay-differential equation for the phase of the laser field which admits multiple branches of time-periodic intensity solutions. The theory is based on typical values of LK dimensionless parameters and assumes that the pump parameter is not too small. In this paper, we examine the validity of this assumption by considering the small pump limit. We find the same phase equation as the leading problem of our asymptotic analysis but now with a stronger damping coefficient. This phase equation fails as a correct asymptotic approximation only for very low pump, close to the lasing threshold. The approximation for this case is more complicated and reveals a stronger influence of the laser intensity.

Synchronization of chaos using proportional feedback

We have demonstrated experimentally a proportional feedback algorithm for the synchronization of chaotic time signals generated from a pair of independent diode resonator circuits. Synchronization was easily obtained and occurred for relative feedback levels between three and eight percent of the driving voltage. Once established, the synchronization persisted throughout the whole range of the resonator bifurcation diagram without varying the gain of the feedback.

Controlling chaos in semiconductor laser devices

In most encounters, chaos is considered a nuisance, if not a down right detriment to system performance, especially in laser devices. However, the presence of chaos in a system can act as a rich source of complex frequencies if one only had a way of accessing them. In this work we present a discussion of the recent work of Ott, Grebogi and Yorke on controlling chaos as applied to a semiconductor diode laser subject to optical feedback via an external mirror. In the regime in which the laser is chaotic, stabilization can be achieved by sampling the output intensity and feeding back minuscule amounts of a correcting signal on the pumping current at the appropriate time interval. We present the results of our numerical investigations.

Using neural networks for controlling chaos

A feed-forward backpropagating neural network is trained to achieve and maintain control of the unstable periodic orbits embedded in a chaotic attractor. The controlling algorithms used for training the network are based on the now standard scheme developed by Ott, Gregogi and Yorke, including variants that utilize previous perturbations and/or delayed time series data.

Experimental synchronization of chaotic attractors

We have experimentally synchronized chaotic diode laser resonators using occasionally applied feedback. We have also synchronized and controlled a unidirectionally coupled array of diode resonators.

Effects of charge accumulation and biasing on resonant tunneling energies and tunneling dynamics

We introduce charge accumulation in quantum wells through the use of a nonlinear Schrodinger equation. Looking first at infinite and finite square wells allows us to calculate the new energy spectrum including the separate effects of a biasing electric field and charge accumulation. This gives us insight into the new resonant tunneling energies that arise due to the quasibound states being shifted by either the external field or the reaction field built up through the accumulation of charge. Using a double barrier potential, we calculate the transmission coefficient with and without the external bias field and then with charge accumulation. To study the tunneling dynamics, we first start with a single barrier in an infinite well and discover a fractal-like character to the probability for finding an electron wavepacket in one side of the structure. Finally we numerically integrate the full time- dependent nonlinear Schrodinger equation with various barrier potentials to obtain the dynamics of a wavepacket incident on the structures.

Dynamics of optical switching phenomena in dense media

The ultrafast optical switching phenomena in a dense medium of two-level atoms induced by arbitrary varying pulses are explained in terms of the adiabatic cancellation of the pulse by the induced polarization. The final population inversion of the medium after the passage of the pulse is found to depend on the number of oscillations the inversion exhibits during the time interval when the normalized pulse amplitude exceeds the maximum allowed value of the atomic polarization. If the inversion undergoes an integer number of oscillations in this region, then the final state of the system returns to the ground state. On the other hand, if the inversion undergoes a half integer number of oscillations in this region, the final state of the system is fully inverted. This behavior is explored analytically and illustrated numerically for the constant, sine and secant pulse shapes.