1999 A semi-conductor laser driven by a light beam

Christophe LETELLIER

A single-mode class B laser with monochromatic external optical injection is described by Sebastian Wieczorek, Bernd Kraupskopf & Daan Lenstra [1].

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The governing equations are

where B is the rescaled cavity lifetime of photons, F is the rescaled damping rate of the relaxation oscillations and K is the dimensionless injected field strength. Variables x and y are the components of the electric field E inside the laser and z is the normalized population inversion. For parameter values With parameter values K=0.3, \omega=0, \alpha=8, B=0.015 and \Gamma = 0.035, it produces a toroidal structure (Fig. 1) whose Kaplan-Yorke dimension is 2.76.

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Fig. 1. Toroidal chaos solution to a semi-conductor laser driven by a light beam.

A simpler set of equations capturing most of the dynamical characteristics of the previous system was proposed by Konstantinos Chlouverakis & Julian Sprott [2]

With parameter values K=0.4, \alpha = 3 and \epsilon = -0.1, it produces a toroidal chaotic attractor (Figs. 2) whose Kaplan-Yorke dimension is 2.54.

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Fig. 2. Toroidal chaos solution to the simple system with most of the dynamical characteristics observed on the laser system.

[1] S.Wieczorek, B. Krauskopf & D. Lenstra, A unifying view of bifurcations in a semiconductor laser subject to optical injection, Optics Communications, 172, 279295, 1999.

[2] K. E. Chlouverakis & J. C. Sprott, A comparison of correlation and Lyapunov dimensions, Physica D, 200, 156-164, 2004.

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