Polarization Smoothing efficacy for SBS mitigation in different configurations for quadruplet architectures

Polarization Smoothing is one of the smoothing techniques that may be used to mitigate parametric instabilities in laser-plasma experiments, and which is currently implemented on NIF. Due to the quadruplet architecture of NIF- and LMJ- type beams, Polarization Smoothing can be implemented in different ways, depending on how the polarizations are split between the beams. We compare the efficacy of those different configurations regarding the mitigation of stimulated Brillouin back-scattering. SBS reflectivity has been experimentally shown to depend on both the average power contained in a speckle for each polarization, and an "anamorphosis coefficient" depending on average transverse and longitudinal speckle dimensions. We analytically derive the mean speckle dimensions using a pseudo-modal expansion of Schell-model beams in various configurations, and establish that the optimal configuration, along with intra-beam Polaization Smoothing, is to arrange the polarizations diagonally. The same analysis is also applied to hypothetical configurations outside of the quadruplet architecture.