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Abstract

An accurate simulation has been devised, employing a new numerical technique to simulate the generalised non-linear Schrödinger equation in all three spatial dimensions and time. The simulations model all pertinent higher order effects such as self-steepening and plasma for the non-linear propagation of ultrafast optical radiation in bulk material. Simulation results are accurate and the novel numerical technique uses reduced computational resources. Simulation results are compared to published experimental data of an example ytterbium aluminum garnet (YAG) system at 3.1um radiation and fits to within a factor of 5. The simulation shows that there is a stability point near the end of the 2 mm crystal where the pulse is both collimated at a reduced diameter (factor of ~2) and there exists a near temporal soliton at the optical center. The temporal intensity profile within this stable region is compressed by a factor of ~4 compared to the input. This explains the reported stable regime found in the experiment. It is shown that the simulation highlights new physical phenomena based on the interplay of various linear, non-linear and plasma effects that go beyond the experiment and would help in the design of white-light generation systems for optical applications. This justifies the use of such accurate and efficient computational tools.