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Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator
Vicente Aboites1, David Liceaga2, Rider Jaimes-Reátegui3
1Centro de Investigaciones en Óptica, Loma del Bosque 115, 37150 León, Mexico.
Abstract:
In this paper, we propose using paraxial matrix optics to describe a ring-phase conjugated resonator that includes an intracavity chaos-generating element; this allows the system to behave in phase space as a Bogdanov Map. Explicit expressions for the intracavity chaos-generating matrix elements were obtained. Furthermore, computer calculations for several parameter configurations were made; rich dynamic behavior among periodic orbits high periodicity and chaos were observed through bifurcation diagrams. These results confirm the direct dependence between the parameters present in the intracavity chaos-generating element.
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