We analyze the physical processes in the nonlinear wavelength conversion stages of a recently demonstrated red–green–blue (RGB) laser source, which generated $⩾8\mathrm{W}$ of average power in each color. The system is based on an infrared femtosecond mode-locked laser and contains a frequency doubler, a parametric generator, a parametric amplifier, and two sum-frequency conversion stages. It does not require any resonant cavities, external laser amplifiers, or nonlinear crystals operated at elevated temperatures; therefore it appears to be more practical than other previously demonstrated RGB laser sources. However, the optimization of the overall system is nontrivial, because pump depletion, birefringence, and temporal walk-off in the first conversion stages lead to spatial and temporal distortion of the interacting beams in the subsequent nonlinear conversion stages. This leads to the interaction of spatially and temporally distorted beams in the later conversion stages. By using a numerical simulation of the nonlinear conversion processes based on a Fourier-space method in one temporal and two transverse spatial dimensions, we can fully take into account these effects. We analyze and discuss the physical effects in the different conversion stages and describe the optimization of the overall system performance.