DocumentCode :
3259353
Title :
New approaches to modeling the dynamics of misaligned beams in nonlinear gradient waveguides
Author :
Bychenkov, A.I. ; Derbov, V.L. ; Serov, V.V.
Author_Institution :
Dept. of Phys., Saratov State Univ., Russia
fYear :
2001
fDate :
2001
Firstpage :
349
Lastpage :
352
Abstract :
The propagation of a misaligned paraxial beam through a nonlinear waveguide medium can be presented as a nonlinear dynamical problem, where the longitudinal coordinate z plays the role of time, while the transverse pattern of the field is the dynamical system evolving with z. The reduction to a finite-dimensional system is possible within the framework of the approximate method using Gaussian probe functions whose parameters are determined by Galerkin´s criterion in the basis of a small number of flexible Gaussian modes. This method is referred as the modified generalized method of moments (MGMM). Using the MGMM we studied the dynamics of an off-axis initially Gaussian beam propagating through a Kerr nonlinear parabolic waveguide and revealed stationary, periodic and quasiperiodic regimes, as well as nontrivial phenomena, such as phase locking, cycle generation, etc. In particular, the behavior of the beam variables in the vicinity of the stationary states was analyzed. However, direct numerical modeling shows significant non-Gaussian distortions of the beam caused by Kerr nonlinearity, so MGMM is expected to describe correctly the dynamics of the beam moments rather than the field transverse pattern itself. To check this idea alternative approaches are desirable. The method proposed here involves the exact numerical calculation of nonlinear modes followed by the linear analysis of small nonstationary perturbations of these modes based on Bogoliubov´s equations
Keywords :
Galerkin method; Gaussian processes; method of moments; nonlinear media; nonlinear optics; optical Kerr effect; optical waveguide theory; optical waveguides; Bogoliubov´s equations; Galerkin´s criterion; Gaussian beam propagation; Gaussian modes; Gaussian probe functions; Kerr nonlinear parabolic waveguide; MGMM; approximate method; cycle generation; dynamical system; exact numerical calculation; linear analysis; longitudinal coordinate; misaligned beams dynamics; misaligned paraxial beam propagation; modified generalized method of moments; nonGaussian distortions; nonlinear dynamical problem; nonlinear gradient waveguides; nonlinear optics; nonlinear waveguide medium; nonstationary perturbations; phase locking; stationary states; transverse field pattern; Frequency; Moment methods; Nonlinear dynamical systems; Nonlinear equations; Optical waveguides; Oscillators; Physics; Probes; Quantum mechanics; Stationary state;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Transparent Optical Networks, 2001. Proceedings of 2001 3rd International Conference on
Conference_Location :
Cracow
Print_ISBN :
0-7803-7096-1
Type :
conf
DOI :
10.1109/ICTON.2001.934788
Filename :
934788
Link To Document :
بازگشت