Nonlinear dynamics of spatial and temporal patterns in lasers and atom optics: Kerr-lens mode-locked laser, Zeeman laser and Bose-Einstein atomic condensate

Abstract

Nonlinear dynamics оf spatial and temporal behaviour of laser and atom optical systems is investigated numerically. Systems with nearly one scalar transverse mode (Kerr-lens mode-locked laser), with large number of vectorial transverse modes (Zeeman laser with large Fresnel number and anisotropic cavity), and non-ground collective states of Bose-Einstein condensate of trapped neutral atoms are considered. Attempts to classify the complex transverse polarization pattern dynamics are made basing on the vectorial Karhunen-Loeve modes and their singularity points character, including catastrophes and Newton diagrams. Excitation оf non-ground states оf atomic Bose-Einstein condensate via resonant perturbation is analyzed.