Simulation of white light generation and near light bullets using a novel numerical technique

Abstract

An accurate and efficient simulation has been devised, employing a new numerical technique to simulate the derivative generalised non-linear Schrödinger equation in all three spatial dimensions and time. The simulation models all pertinent effects such as self-steepening and plasma for the non-linear propagation of ultrafast optical radiation in bulk material. Simulation results are compared to published experimental spectral data of an example ytterbium aluminum garnet system at 3.1µm 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 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 new physical phenomena based on the interplay of various linear, non-linear and plasma effects that go beyond the experiment and is thus integral to achieving accurate designs of white light generation systems for optical applications. An adaptive error reduction algorithm tailor made for this simulation will also be presented in appendix.

Split-step operators in absolute coordinates for an EFSSM solution method of the generalized nonlinear Schrödinger equation

“…The form of the generalized nonlinear Schrödinger equation used in nonlinear optics for the cases without ionization is [1] (1)…”

“…The numerical solution of this equation is possible using an exponential Fourier split-step method (EFSSM) [1]. The method takes steps in the  direction in order to compute u(+) from u().…”

“…The ordering of the solution operators in step splitting, and the step sizes influence the precision of the solution. The best step size-operator ordering pattern is [1] (…”

“…In order to easily compare the EFSSM solution to experimental data or simulation results from another numerical methods, electric field strength as the function of absolute spatial and temporal coordinates ℰ( , , , ) should be obtained. In [1] we are given the split-step operators and the full EFSSM method for a normalized wavefunction u in normalized coordinates, and the situation is further complicated by the presence of the diffraction length, dispersion length, nonlinear length measures, that depend on both medium and pulse properties. Therefore it is straightforward to derive the corresponding operators in absolute space and time coordinates, that operators give the absolute electric field strength function.…”

“…To derive the operators outlined above, first I substituted the definition of the relative coordinates into (1): = , = , = and = (the latter definition is not present in [1]; sp: pulse e -1 spatial extent).…”