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Revista mexicana de física E

Print version ISSN 1870-3542

Rev. mex. fís. E vol.60 n.1 México Jan. 2014



Bidimensional dynamic maps in optical resonators


V. Aboitesa, Y. Barmenkova, A. Kiryanova and M. Wilsonb


a Centro de Investigaciones en Óptica, Loma del Bosque 115, León, 37150 México. e-mail:

b Universite des Sciences et Technologies de Lille 1, CNRS UMR 8523-UFR de Physique-Batiment P5, 59655 Villeneuve d'Ascq Cedex, France.


Received 29 August 2012
accepted 24 February 2014



In this article an introduction to the dynamical behavior of a beam within a ring phase-conjugated optical resonator is presented and modeled using two dimensional iterative maps. Three well known iterative maps are described: Duffing, Tinkerbell and Henon, and are applied to the description of optical resonators. It is explicitly shown how the difference equations of these maps can be used to describe the dynamic behavior of what we call Tinkerbell, Duffing and Henon beams i.e. beams that behave according to these maps. The matrix of a map generating device are found in terms of the specific map parameters, the state variables and the resonator parameters for each of the three named maps.

Keywords: Resonator; chaotic maps; phase conjugation.



En este artículo se presenta una introducción al comportamiento dinámico de un haz dentro de un resonador óptico de anillo de conjugación de fase el cual es modelado usando mapas iterativos bidimensionales. Tres bien conocidos mapas iterativos son descritos: Duffing, Tinkerbell y Henon, y son utilizados para la descripción de resonadores ópticos. Se muestra explícitamente como las ecuaciones de diferencia de los mapeos anteriores pueden ser utilizados para describir el comportamiento dinámico de lo que llamamos, Haces de Tinkerbell, Duffing y Henon i.e. haces que se comportan siguiendo dichos mapas. La matriz de un dispositivo generador del mapeo se encuentra en términos de los parámetros específicos del mapa, de las variables de estado y de los parámetros del resonador para cada uno de los tres mapas anteriores.

Palabras clave: Resonador; mapeo caótico; resonador de anillo.


PACS: 42.15.-I; 42.60.Da; 42.65.Hw





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