Ikeda Map and Phase Conjugated Ring Resonator Chaotic Dynamics

Authors

V. Aboites, Centro de Investigaciones en ´Optica, Loma del Bosque 115, 37150 Le´on, M´exico.Follow
D. Liceaga, Divisi´on de Ciencias e Ingenier´ıas, Universidad de Guanajuato, Loma del Bosque 107, 37150 Le´on, M´exico.Follow
A. Kiryanov, Centro de Investigaciones en ´Optica, Loma del Bosque 115, 37150 Le´on, M´exico.Follow
M. Wilson, CONACYT - CICESE, Divisi´on de Ciencias de la Tierra, Carretera Ensenada-Tijuana 3918, Zona Playitas, 22860 Ensenada, M´exico.Follow

Author Country (or Countries)

M´exico.

Abstract

The dynamical behavior of a laser beam confined within a ring-phase-conjugated resonator modeled with a chaos generating element based on the Ikeda map is presented. Using the matrix ray optics, explicit expressions are obtained for the elements of the 2x2 dynamical matrix, which is found in terms of the specific map parameters, state variables and resonator parameters. The phase diagrams obtained show that the so called Ikeda map beams present complex dynamics, including critical points and metastability.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100608

Recommended Citation

Aboites, V.; Liceaga, D.; Kiryanov, A.; and Wilson, M. (2016) "Ikeda Map and Phase Conjugated Ring Resonator Chaotic Dynamics," Applied Mathematics & Information Sciences: Vol. 10: Iss. 6, Article 8.
DOI: http://dx.doi.org/10.18576/amis/100608
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss6/8