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With the advent of PW class lasers, the very large laser intensitiesattainable on-target should enable the production of intense high order Dopplerharmonics from relativistic laser-plasma mirrors interactions. At present, themodeling of these harmonics with Particle-In-Cell (PIC) codes is extremelychallenging as it implies an accurate description of tens of harmonic orders ona a broad range of angles. In particular, we show here that standard FiniteDifference Time Domain (FDTD) Maxwell solvers used in most PIC codes partlyfail to model Doppler harmonic generation because they induce numericaldispersion of electromagnetic waves in vacuum which is responsible for aspurious angular deviation of harmonic beams. This effect was extensivelystudied and a simple toy-model based on Snell-Descartes law was developed thatallows us to finely predict the angular deviation of harmonics depending on thespatio-temporal resolution and the Maxwell solver used in the simulations. Ourmodel demonstrates that the mitigation of this numerical artifact with FDTDsolvers mandates very high spatio-temporal resolution preventing doingrealistic 3D simulations. We finally show that non dispersive pseudo-spectralanalytical time domain solvers can considerably reduce the spatio-temporalresolution required to mitigate this spurious deviation and should enable inthe the near future 3D accurate modeling on supercomputers in a realistictime-to-solution.

Pseudo-spectral Maxwell solvers for an accurate modeling of Doppler harmonic generation on plasma mirrors with Particle-In-Cell codes