Observation of stability of Gaussian beams and off-axis beam-cleaning in graded-index rods

While nonlinear effects in graded-index (GRIN) multimode fibers have been studied extensively, little is known about nonlinear effects in larger GRIN waveguides, where the number of modes approaches infinity and modal dispersion becomes negligible. Here we show that Gaussian beams remain nearly invariant even with large nonlinear phase accumulation and on- or off-axis trajectories in GRIN rods. In addition, spatially-complex beams can undergo self-cleaning to single-lobed profiles for both on- and off-axis trajectories. Numerical simulations exhibit the features observed in experiments, and a qualitative interpretation of these results that makes connection to beam-cleaning phenomena observed in GRIN fibers is proposed.