IJPAM: Volume 54, No. 3 (2009)

TINKERBELL CHAOS IN A RING
PHASE-CONJUGATED RESONATOR

Vicente Aboites$^1$, Mario Wilson$^2$
$^{1,2}$Center for Research in Optics
Loma del Bosque 115, Lomas del Campestre
Guanajuato, León, 37150, MÉXICO
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.The dynamics of an optical ring phase conjugated resonator with Tinkerbell chaos is presented. It is shown that a non-linear behavior takes places when a chaos generating element is introduced on the resonator. The matrix formalism is used in order to carry out the analysis of the resonator in his full-round trip when all the optical resonator elements are involved. Assuming ray optics inside the cavity with parameters $y(z)$ and $\theta(z)$ for the effective distance to the optical axis and the angle to the same axis respectively, the expressions for the $n$-th trip are obtained. The matrix of an optical chaos generating element $[a,b,c,e]$ able to produce Tinkerbell chaos in an ideal ring phase conjugation resonator are obtained for the first time to our knowledge.

Received: June 27, 2009

AMS Subject Classification: 37N20, 78A05, 78A60, 37E99

Key Words and Phrases: chaos, Tinkerbell cahos, resonator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 3