Chaotic behavior in nonlinear polarization dynamics

Conference · Sat Dec 31 23:00:00 EST 1988

DOI:https://doi.org/10.1007/978-1-4613-9033-6_3· OSTI ID:5592289

David, D; Holm, D D; Tratnik, M V ^[1]

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1. Los Alamos National Lab., NM (USA)

We analyze the problem of two counterpropagating optical laser beams in a slightly nonlinear medium from the point of view of Hamiltonian systems; the one-beam subproblem is also investigated as a special case. We are interested in these systems as integrable dynamical systems which undergo chaotic behavior under various types of perturbations. The phase space for the two-beam problem is C{sup 2} {times} C{sup 2} when we restricted the the regime of travelling-wave solutions. We use the method of reduction for Hamiltonian systems invariant under one-parameter symmetry groups to demonstrate that the phase space reduces to the two-sphere S{sup 2} and is therefore completely integrable. The phase portraits of the system are classified and we also determine the bifurcations that modify these portraits; some new degenerate bifurcations are presented in this context. Finally, we introduce various physically relevant perturbations and use the Melnikov method to prove that horseshoe chaos and Arnold diffusion occur as consequences of these perturbations. 10 refs., 7 figs., 1 tab.

• Research Organization: Los Alamos National Lab., NM (USA)
• Sponsoring Organization: DOE/ER
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 5592289
• Report Number(s): LA-UR-89-1664; CONF-891151--1; ON: DE89013453
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC RADIATION
EQUATIONS
EQUATIONS OF MOTION
FIBERS
HAMILTONIANS
LASER RADIATION
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
NONLINEAR OPTICS
NONLINEAR PROBLEMS
OPTICAL FIBERS
OPTICS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
POLARIZATION
QUANTUM OPERATORS
RADIATIONS
SPACE
TRAVELLING WAVES
WAVE PROPAGATION