IJPAM: Volume 65, No. 2 (2010)

HÉNON BEAMS

Vicente Aboites$^1$, Mario Huicochea$^2$
$^1$Center for Research in Optics
Loma del Bosque 115, Lomas del Campestre
37150, León, Guanajuato, MÉXICO
e-mail: aboites@cio.mx
$^2$Center for Research in Mathematics
Jalisco s/n, Col. Valenciana, 36240, Guanajuato, Gto., MEXICO
e-mail: dym@cimat.mx


Abstract.The behavior of a laser beam within a ring phase conjugated resonator is studied. It is shown that assuming ray optics the two beam parameters may be described by a Hénon map and the necessary conditions for this occurrence are discussed. In particular it is shown that the introduction of a specific optical chaos generating element within the ring phase-conjugated resonator may produce chaotic beams described by a Hénon map, which we call ``Hénon beams''. The matrix formalism is used to analyze the dynamical behavior for the ring cavity when a Hénon chaos generating element is introduced. Finally the specific matrix elements of the Hénon chaos generating matrix are obtained for the first time to our knowledge.

Received: June 10, 2009

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

Key Words and Phrases: chaos, tinkerbell, resonator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 65
Issue: 2