Comparison of different approaches to the numerical calculation of the LMJ focal

Abstract

The beam smoothing in the focal plane of high power lasers is of particular importance to laser- plasma interaction studies in order to minimize plasma parametric and hydrodynamic instabilities on the target. Here we investigate the focal spot structure in different geometrical configurations where standard paraxial hypotheses are no longer verified. We present numerical studies in the cases of single flat top square beam, LMJ quadruplet and complete ring of quads with large azimuth angle. Different calculations are made with Fresnel diffraction propagation model in the paraxial approximation and full vector Maxwell's equations. The first model is based on Fourier transform from near to far field method. The second model uses first spherical wave decomposition in plane waves with Fourier transform and propagates them to the focal spot. These two different approaches are compared with Miro (1) modeling results using paraxial or Feit and Fleck options. The methods presented here are generic for focal spot calculations. They can be used for other complex geometric configurations and various smoothing techniques. The results will be used as boundary conditions in plasma interaction computations. where f(x,y) is the amplitude of the field with a spatial extension size of a and k0 = /c is the wave number of the field. The field expression in the k space (spatial frequencies) with one fast Fourier transform (FFT) requires a large number of points. But for a parabolic phase lens, plane wave decomposition of the electric field in the k space with double FFT allow to reduce the spatial sampling (2048 points instead of 256000 for a = 1.2m and zf = 0.8m). The plane wave decomposition with two FFT is given by: