Laser Plasmas : Lie-optics, geometrical phase and nonlinear dynamics of self-focusing and soliton evolution in a plasma

Pramana

Sanjeev Goyal1¹  D Subbarao¹  R Uma¹  H Singh1¹  Kamal Goyal1¹  Ravinder Kumar1¹ 

[1] Plasma Science and Technology Program, Center for Energy Studies, Indian Institute of Technology, New Delhi 110 016, India$$

关键词: Potential approximation in quantum mechanics;    paraxial refractive index;    group theory in optics;    geometrical phase;    methods in classical mechanics;    nonlinear optics;    self-focusing;    solitons.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

It is useful to state propagation laws for a self-focusing laser beam or a soliton in grouptheoretical form to be called Lie-optical form for being able to predict self-focusing dynamics conveniently and amongst other things, the geometrical phase. It is shown that the propagation of the gaussian laser beam is governed by a rotation group in a non-absorbing medium and by the Lorentz group in an absorbing medium if the additional symmetry of paraxial propagation is imposed on the laser beam. This latter symmetry, however, needs care in its implementation because the electromagnetic wave of the laser sees a different refractive index profile than the laboratory observer in this approximation. It is explained how to estimate this non-Taylor paraxial power series approximation. The group theoretical laws so-stated are used to predict the geometrical or Berry phase of the laser beam by a technique developed by one of us elsewhere. The group-theoretical Lie-optic (or ABCD) laws are also useful in predicting the laser behavior in a more complex optical arrangement like in a laser cavity etc. The nonlinear dynamical consequences of these laws for long distance (or time) predictions are also dealt with. Ergodic dynamics of an ensemble of laser beams on the torus during absorptionless self-focusing is discussed in this context. From the point of view of new physics concepts, we introduce a stroboscopic invariant torus and a stroboscopic generating function in classical mechanics that is useful for long-distance predictions of absorptionless self-focusing.

【 授权许可】

Unknown