Manipulation of geometric parametric sidebands via elliptical Gaussian beam in graded-index multimode fibers

Geometric parametric instability is a class of processes where the revival of optical beam in a nonlinear multimode graded-index fiber induces a spatial index modification and in turn generates frequency sidebands due to space-time coupling. While current studies have been focusing on breathing Gaussian beams in such settings, the evenly spaced eigenvalue in parabolic fiber indicates that any input condition will experience self-imaging effects under linear conditions. Here we investigate the nonlinear propagation and the corresponding geometric parametric instability sidebands generation associated with elliptical Gaussian beams where the long- and short- axis of the beam oscillates with different phases. We show that, depending on the initial conditions, there are four possible propagation regimes: over-trapping, self-trapping, under-trapping and self-focusing. As a result, the spacing and strength of generated sidebands can be judiciously tuned by the elliptical ratio of elliptical Gaussian beams. At certain conditions, missing-order effect occurs where a set of sidebands completely disappear. We experimentally observed the multiple and a few sidebands of the Gaussian beam and elliptical Gaussian beam in a standard graded-index multimode fiber. In addition, experiments show that GPI sidebands have well-defined and stable bell-shaped near-field profiles. These results pave the way for developing tunable light sources and ultra-broadband supercontinuum generation.