Analytical description of the propagation of spatiotemporal solitons in fibers

Abstract

On the basis of the approximate method of the averaged Lagrangian, the propagation modes of spatiotemporal solitons in a graded-index optical fiber with a Kerr nonlinearity and anisotropic transverse distribution of the linear refractive index are investigated. It is shown that within the framework of the proposed approach, the equations for soliton parameters are formally similar to the dynamical equations of a two-dimensional quantum Bose liquid in an external field. Various modes of propagation in the form of light bullets localized in all directions were investigated. The conditions under which ``dancing'' light bullets can form are revealed. The trajectories of such objects are spatial Lissajous figures, turning into helical lines in the case of axially symmetric optical fibers. The fundamental spatiotemporal soliton is a special case of dancing light bullets. Under conditions when the diffraction spreading scale length is much shorter than the dispersion scale length, the transverse dynamics of a soliton does not depend on its longitudinal dynamics. In this case, the principal possibility of forming a wide class of light bullets with different transverse structures is shown. In addition, under these conditions, the spatiotemporal soliton mode of the self-imaging effect is described.