The objective of my work was the realization of an experimental optical bench on the quadratic propagations which can lead to a mutual trapping (spatial and temporal) beams at fundamental and second harmonic frequencies. The originality of these researches has been to demonstrate, for the first time, the appearance and disappearance of one or more 2D quadratic spatial soliton / extreme events, as a function of the monotonic rise of the initial pump power. These spatial nonlinear phenomena are accompanied by a spectral broadening as well as a temporal compression, followed by the deterioration of the initial pulse. Two applications have been realized, one on ultrafast temporal remodeling of short pulses, the other using quadratic supercontinuum to demonstrate CARS Multiplex imaging.