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Symmetry-Breaking Bifurcations in Laser Systems with All-to-All Coupling

In: Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Author

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  • Juancho A. Collera

    (University of the Philippines Baguio, Department of Mathematics and Computer Science)

Abstract

We consider a system of n semiconductor lasers with all-to-all coupling that is described using the Lang-Kobayashi rate equations. The lasers are coupled through their optical fields with delay arising from the finite propagation time of the light from one laser to another. As a consequence of the coupling structure, the resulting system of delay differential equations is equivariant under the symmetry group S n ×S 1. Since symmetry gives rise to eigenvalues of higher multiplicity, implementing a numerical bifurcation analysis to our laser system is not straightforward. Our results include the use of the equivariance property of the laser system to find symmetric solutions, and to correctly locate steady-state and Hopf bifurcations. Additionally, this method identifies symmetry-breaking bifurcations where new branches of solutions emerge.

Suggested Citation

  • Juancho A. Collera, 2016. "Symmetry-Breaking Bifurcations in Laser Systems with All-to-All Coupling," Springer Books, in: Jacques Bélair & Ian A. Frigaard & Herb Kunze & Roman Makarov & Roderick Melnik & Raymond J. Spiteri (ed.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pages 81-88, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30379-6_8
    DOI: 10.1007/978-3-319-30379-6_8
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