Experimental observation of self-accelerating beams in quadratic nonlinear media

We present the experimental observation of 1D and 2D self-accelerating nonlinear beams in quadratic media, which are also the first nonlinear self-accelerating beams in any symmetric nonlinearity. Notably, we show that the intensity peaks of the first and second harmonics are asynchronous with respect to one another, but the coupled harmonics exhibit joint acceleration within the nonlinear medium. Finally, we demonstrate the impact of self-healing effects on the jointly accelerating first and second harmonics.