Mathematics Preprints 2005
Computational Applied Mathematics
05.04 : WALKER, R.P., REES, R., PIERCE, I., SPENCER, P.S. & ROBERTS, G.W.
Analysis of chaos generated by a modulated self-pulsating laser diode
Summary:We have calculated the Lyapunov exponents and plotted bifurcation diagrams for a self pulsating laser diode under periodic current modulation. Different dynamics are obtained dependent on the modulation depth and frequency of the drive current. We show that it is very difficult to distinguish between regimes of high periodicity and true chaos. However by introducing a return map relating the pulse peak height and the inter pulse interval clear differences are observed between these regimes. This has consequences for the use of chaotic self-pulsating laser diodes for data encryption applications.
Published in:IEE Proceedings Optoelectronics, (Special Issue on Semiconductor Optoelectronics), Volume 152, Number 2, April 2005
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05.09 : WALKER, R.P.
Dynamical Analysis of Self-pulsation and Chaos in Semiconductor Laser Models
Abstract:Chaotic semiconductor laser diodes can be used to precipitate secure communications schemes via synchronisation of two such lasers. We study various sets of ordinary differential equations that are used to model such semiconductor laser diodes. We begin by extending the bifurcation analysis of Dubbeldam and Krauskopf to dimensionless equations derived from the Yamada model with terms representative of spontaneous emission and diffusion effects included. We show that the bifurcation diagram changes dramatically at a certain diffusion level, but that the region of self-pulsation is still delineated by the Hopf bifurcation curve. Other models which include recombination effects are also considered.
The excitable region of the parameter space of the dimensionless equations derived from the Yamada model with diffusion effects neglected is considered, and approximations of the excitability threshold are derived. Finally, chaotic behaviour arising from sinusoidal modulation of the pump current is analysed. Lyapunov exponent calculations are supplemented with a return map analysis in order to distinguish between periodic motion and chaos as the modulation depth and frequency are varied. The presence or otherwise of chaos is related to the bifurcation analysis and dominant resonant frequency of the unmodulated laser diode.
Published in:University of Wales, Bangor, PhD thesis (2005)
- gzipped postscript file: walker.ps.gz