International audienceThe forthcoming laser installations related to inertial confinement fusion, Laser Mégajoule (LMJ) (France) and National Ignition Facility (NIF) (USA), require multidimensional numerical simulation tools for interpreting current experimental data and to perform predictive modeling for future experiments. Simulations of macroscopic plasma volumes of the order of 1 mm^3 and laser exposure times of the order of hundreds of picoseconds are necessary. We present recent developments in the PARAX code towards this goal. The laser field is treated in a standard paraxial approximation in three dimensions. The plasma response is described by single-fluid, two-temperature, fully nonlinear hydrodynamical equations in the plane tran...