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The scattered field formalism is combined to the particle-in-cell method tomodel relativistic laser-plasma dynamics in complex field configurations.Despite the strong nonlinearity of the interactions, we demonstrate thevalidity of this technique theoretically, by using the semi-linear property ofMaxwell-Vlasov equations, and empirically, by performing a systematicconvergence analysis with simple 1D and 2D examples. Then, we apply this methodto the description of electron acceleration in undercritical plasmas fromtightly focused linear and radially polarized beams. For this purpose, ananalytical solution for a linearly-polarized tightly focused beam is derived.According to our simulations and their analysis, this approach looks verypromising for the optimization of laser-induced relativistic electron beams atultrahigh intensities because it allows for tightly-focused geometries inreduced calculation volumes.

Scattered field formalism in the particle-in-cell method for plasma acceleration in tightly focused ultrashort laser beams