IJPAM: Volume 36, No. 4 (2007)


Vicente Aboites
Centro de Investigaciones en Optica A.C.
Loma del Bosque 115
Col. Lomas del Campestre, 37150, Leon, Guanajuato, MEXICO
e-mail: aboites@cio.mx

Abstract.The dynamics of a laser resonator is presented. It is shown that a non-linear dynamic behaviour takes place when a chaos generating element is introduced within the resonator. The analysis of a laser resonator using ABCD matrix formalism is showed for the case where these elements are present in the resonator. Assuming a ray inside the resonator with parameters $y(z)$ and $\theta (z)$ for the effective distance to the optical axis $z$ and angle to the same axis confined in the resonator we obtain expressions for the $n$-th trip $y(z)_{n}$ and $\theta (z)_{n}$. In particular an expression for $y(z)_{n + 1}$ of the form: $y_{n + 1} = ay_{n}(l - y_{n})$ is obtained. Chaotic regions are shown in a simple bifurcation diagram. The dynamics of the resonator can be modified by the change of the resonator parameters. Finally the characteristics of the chaos generating elements is discussed and the matrix elements of a chaos generating matrix $[a, b, c, e]$ are presented.

Received: August 16, 2006

AMS Subject Classification: 78A60

Key Words and Phrases: laser dynamics, laser, resonator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 4