A technique developed to accurately simulate the amplification of back-reflected light through a multi-petawatt laser system is presented. Using the Frantz–Nodvik equation, we developed an iterative algorithm to simulate the amplification of the main beam as it propagates through solid-state multipass amplifiers, while also accounting for back-reflections from experimental targets and the residual gain within the crystals. Our technique builds on the theoretical model by estimating the energy levels after multiple passes through all amplifiers and refining the simulated data using a brute-force optimization algorithm. We also demonstrate an application of this tool aimed at evaluating machine safety: optimizing the laser system to minimize crystal gain in the post-pulse regime and, consequently, the amplification of back-reflections, while taking advantage of the B-integral.
