Dependence of beating dynamics on the ellipticity of a Gaussian beam in graded-index absorbing nonlinear fibers

Using the collective variable approach technique, we analyze propagation of elliptical Gaussian beams in nonlinear waveguides with a parabolic graded-index (GRIN) profile. We considered both saturable and cubic-quintic models to describe the nonlinearity, taking into account both linear and nonlinear absorption. For lossless media, we construct diagrams, which define regions of self-focusing and self-diffractive beam propagation for both models in GRIN waveguides and compare them with those for nongraded waveguides. The widths of the propagating elliptic beam exhibit an oscillatory pattern, similar to the "breathing" and "beating" behavior found in nongraded media. Two types of beating oscillations are observed in both models. We calculate the dependence of L_beat/L_br, the ratio of the "beating" to "breathing" oscillation periods, on the beam ellipticity ρ and the GRIN index g. We find that there is a remarkable difference in this dependence between saturable and cubic-quintic media: in the saturable model, L_beat/L_br is a monotonic function of ρ, whereas in the cubic-quintic model, it is characterized by singularities, which correspond to transitions between the types of beat oscillations. For lossy media, we discuss the difference between the breathing behavior in nongraded and GRIN waveguides.