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An accurate and efficient simulation has been devised, employing a newnumerical technique to simulate the derivative generalised non-linearSchr\"odinger equation in all three spatial dimensions and time. The simulationmodels all pertinent effects such as self-steepening and plasma for thenon-linear propagation of ultrafast optical radiation in bulk material.Simulation results are compared to published experimental spectral data of anexample ytterbium aluminum garnet system at 3.1um radiation and fits to withina factor of 5. The simulation shows that there is a stability point near theend of the 2 mm crystal where a quasi-light bullet (spatial temporal soliton)is present. Within this region, the pulse is collimated at a reduced diameter(factor of ~2) and there exists a near temporal soliton at the spatial center.The temporal intensity within this stable region is compressed by a factor of~4 compared to the input. This study shows that the simulation highlights newphysical phenomena based on the interplay of various linear, non-linear andplasma effects that go beyond the experiment and is thus integral to achievingaccurate designs of white light generation systems for optical applications. Anadaptive error reduction algorithm tailor made for this simulation will also bepresented in appendix.

Simulation of White Light Generation and Near Light Bullets Using a Novel Numerical Technique