Hamiltonian chaos in a nonlinear polarized optical beam

Conference · Sun Jan 01 00:00:00 EST 1989

OSTI ID:5397587

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

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

This lecture concerns the applications of ideas about temporal complexity in Hamiltonian systems to the dynamics of an optical laser beam with arbitrary polarization propagating as a traveling wave in a medium with cubically nonlinear polarizability. We use methods from the theory of Hamiltonian systems with symmetry to study the geometry of phase space for this optical problem, transforming from C{sup 2} to S{sup 3} {times} S{sup 1}, first, and then to S{sup 2} {times} (J, {theta}), where (J, {theta}) is a symplectic action-angle pair. The bifurcations of the phase portraits of the Hamiltonian motion on S{sub 2} are classified and displayed graphically. These bifurcations take place when either J (the beam intensity), or the optical parameters of the medium are varied. After this bifurcation analysis has shown the existence of various saddle connections on S{sup 2}, the Melnikov method is used to demonstrate analytically that the traveling-wave dynamics of a polarized optical laser pulse develops chaotic behavior in the form of Smale horseshoes when propagating through spatially periodic perturbations in the optical parameters of the medium. 20 refs., 7 figs.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: DOE/ER
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 5397587
• Report Number(s): LA-UR-89-3337; CONF-8906239-1; ON: DE90002437; TRN: 89-029490
• Resource Relation: Conference: Santa Fe Institute summer school on complex systems, Santa Fe, NM (USA), 5-30 Jun 1989
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
PHOTON BEAMS
NONLINEAR OPTICS
ELECTRIC FIELDS
HAMILTONIANS
LASER RADIATION
PHASE SPACE
POLARIZED BEAMS
RANDOMNESS
TRAVELLING WAVES
WAVE PROPAGATION
BEAMS
ELECTROMAGNETIC RADIATION
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
OPTICS
QUANTUM OPERATORS
RADIATIONS
SPACE
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics