Daniel M. Heffernan

Multistability, intermittency and remerging Feigenbaum trees in an externally pumped ring cavity laser system

Abstract We study a Fabry-Perot cavity containing a saturable absorber and driven by an external laser. It is shown that the output field as a function of the input field and bistability parameter exhibits multistability, intermittency and remerging Feigenbaum trees.

Characterization of chaos

We give a brief introduction to chaos and its characterization. We examine some standard systems in detail from the perspective of chaos and review their properties. Concepts necessary to understand them, such as dimension, are also reviewed. To illustrate the main ideas, we choose three examples which have served as paradigms for the study of chaos in physical systems, namely, the Hénon discrete mapping, the Lorenz system of coupled ordinary differential equations, and the Mackey-Glass infinite-dimensional delay differential equation.

Bistability by induced waveguiding in coupled semiconductor lasers

Recently, McInerney, Reekie, and Bradley observed bistability in twin diode GaAs/GaAlAs injection lasers in an external cavity when both diodes were above threshold. We show that this bistability may be explained by a form of self-focusing which is produced by induced waveguiding in the wide stripe lasers. A detailed analysis is performed on a standard model of these diodes in an external cavity. We have found very good agreement between theory and experiment.

Three-frequency Chaos in an External Cavity Injection Laser

Abstract We report fixed-frequency interactions in a modulated delay system. In particular, we have observed frequency locking, quasiperiodicity and the progression to a chaotic state by the collapse of a three-frequency quasiperiodic attractor, characteristic of the Ruelle-Takens-Newhouse scenario, in a modulated two-sided external cavity injection laser. While the temporal and spectral characteristics of the laser emission suggest that the laser has progressed to a chaotic state, dimensionality testing of the laser output is inconclusive.

Optical bistability and switching by nonlinear waveguiding in semiconductor lasers and laser amplifiers

Two schemes for sub-nanosecond bistable switching using nonlinear waveguiding in coupled semiconductor lasers are described and analyzed. Using longitudinally coupled lasers in an external cavity gives rise to photon lifetime limited switching, but the system is cumbersome and susceptible to low-frequency self-pulsations and noise. Laterally coupled twin stripe lasers offer a monolithically integrated alternative, in which switching times are limited by carrier diffusion.

Long switching times in absorptive bistable systems

Abstract We study the switching characteristics of a Fabry-Perot cavity containing a saturable absorber and driven by an external laser. It is shown how long switching times can arise in such a system and an expression is given for the switching time.

Transient degenerate four wave mixing in saturable absorbers

Abstract The transient behaviour of degenerate four wave mixing (DFWM) in a three-level saturable absorber is analysed. We discuss two cases which are relevant to present day experiments. We obtain the transient reflectivity in the cases where the pump beams consist of (a) a single pulse and (b) a train of pulses.

The formation and evolution of fractal structure within chaotic attractors

In this paper we examine in detail the formation and evolution of fractal structure in the chaotic attractors of nonlinear dynamical systems. We explicitly obtain the fractal structure of the underlying chaotic attractors of low-dimensional systems and study their evolution as a system parameter is varied. Using periodic enumeration, dimensional, andf(α) spectral techniques, we obtain a detailed characterization of the multifractal structure.

Frequency Locking, Quasiperiodicity and Chaos in Modulated External Cavity Injection Lasers

All physical processes can be considered from the standpoint of frequency interactions. Thus a good understanding of such interactions is desirable for an increased comprehension of many physical processes. More importantly if the physical processes involved are nonlinear, a variety of interesting phenomena which are absent in linear or quasilinear systems may appear; some of which are not well understood. In this paper we are only concerned with nonlinear frequency interactions and in particular interactions between fixed frequencies. Specifically we consider the dynamic behaviour of modulated external cavity diode lasers where the frequency interaction occurs between the fixed round trip frequencies of the external cavity and an applied modulation frequency. We report frequency locking, quasiperiodicity and chaos in these systems.

Single-parameter characterization of bistability in double contact injection lasers

Abstract We show that for the Lasher-Basov model of a double contact injection laser the hysteresis in the light output as a function of the driving current in the gain region can be characterized by a single parameter.