Hamiltonian chaos in a nonlinear polarized optical beam
- 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 Lab., NM (USA)
- 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
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BEAMS
ELECTRIC FIELDS
ELECTROMAGNETIC RADIATION
HAMILTONIANS
LASER RADIATION
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
NONLINEAR OPTICS
OPTICS
PHASE SPACE
PHOTON BEAMS
POLARIZED BEAMS
QUANTUM OPERATORS
RADIATIONS
RANDOMNESS
SPACE
TRAVELLING WAVES
WAVE PROPAGATION