Four-dimensional treatment of frequency conversion and the effect of smoothing by spectral dispersion

Orion is a new laser facility under construction at AWE for studying high energy density physics whose design has been underwritten by modelling various aspects of the beamlines. For the long pulse beams this has included the frequency conversion process from the first to the third harmonic. The need to take account of the effect of the phase modulation applied for Smoothing (of the output focal spot) by Spectral Dispersion (SSD) has led to the development of a four-dimensional (x,y,z,t) frequency conversion code. The code uses a split-step approach, considering diffraction, walk-off, coupled waves, wavefront error, angular dispersion, self-phase modulation, and group velocity dispersion. The code's performance is demonstrated using an idealised input beam and the Orion frequency conversion crystal design. Without the presence of phase modulation, the code reports a third harmonic conversion efficiency of 79.2%. With phase modulation, a conversion efficiency of between 70.3% and 71.6% is reported, depending on the directions of applied angular dispersion. The smoothing of the focal spot as a function of time using a kinoform phase plate is also demonstrated based on the 2D-SSD system to be used on Orion. The contrast ratio of the focal spot is shown to reduce by a factor of 5 within the first 0.2 ns, and to reach 7% by the end of the 1.25 ns time window.