• Kamal Goyal

      Articles written in Pramana – Journal of Physics

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

      D Subbarao R Uma H Singh Kamal Goyal Sanjeev Goyal Ravinder Kumar

      More Details Abstract Fulltext PDF

      It is useful to state propagation laws for a self-focusing laser beam or a soliton in group-theoretical 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.

    • Lie-optic matrix algorithm for computer simulation of paraxial self-focusing in a plasma

      D Subbarao R Uma Kamal Goyal Sanjeev Goyal Karuna Batra

      More Details Abstract Fulltext PDF

      Propagation algorithm for computer simulation of stationary paraxial self-focusing laser beam in a medium with saturating nonlinearity is given in Lie-optic form. Accordingly, a very natural piece-wise continuous Lie transformation that reduces to a restricted Lorentz group of the beam results. It gives rise to a matrix method for self-focusing beam propagation that is constructed and implemented. Although the results use plasma nonlinearities of saturable type, and a gaussian initial beam, these results are applicable for other media like linear optical fibers and to more general situations.

  • Pramana – Journal of Physics | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2017-2019 Indian Academy of Sciences, Bengaluru.