Integrability and chaos in nonlinearly coupled optical beams
This paper presents a study, using dynamical systems methods, of the equations describing the polarization behavior of two nonlinearly coupled optical beams counterpropagating in a nonlinear medium. In the travelling-wave regime assumption, this system possesses a Lie-Poisson structure on the manifold C{sup 2} {times} C{sup 2}. In the case where the medium is assumed to be isotropic, this system exhibits invariance under the Hamiltonian action of two copies of the rotation group, S{sup 1}, and actually reduces to a lower-dimensional system on the two-sphere, S{sup 2}. We study the dynamics on the reduced space and examine the structure of the phase portrait by determining the fixed points and infinite-period homoclinic and heteroclinic orbits; we concentrate on presenting some exotic behaviour that occurs when some parameters are varied, and we also show special solutions associated with some of the above-mentioned orbits. Last, we demonstrate the existence of complex dynamics when the system is subject to certain classes of Hamiltonian perturbations. To this end, we make use of the Melnikov method to analytically show the occurrence of either horseshoe chaos, or Arnold diffusion. 19 refs.
- Research Organization:
- Los Alamos National Lab., NM (USA)
- Sponsoring Organization:
- DOE/DP
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 6980972
- Report Number(s):
- LA-UR-90-537; CONF-8910365--1; ON: DE90007540
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BEAMS
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC FIELDS
EQUATIONS
EQUATIONS OF MOTION
FUNCTIONS
HAMILTONIAN FUNCTION
NONLINEAR OPTICS
OPTICS
PARTIAL DIFFERENTIAL EQUATIONS
PHOTON BEAMS
POLARIZATION
TRAVELLING WAVES