Analytical and numerical solutions to the amplifier with incoherent pulse temporal overlap

Serious pulse temporal overlap in amplifiers would result in the decrease of energy extraction efficiency and the increase of pulse-shape distortion (PSD). Precisely predicting pulse temporal overlap is of significance to an effective amplifier design. In this work, the analytical expressions with complete pulse overlap are derived and a numerical method is proposed to solve the case with partial temporal overlap for a double-pass Nd:YAG amplifier. Our studies, in which pulse temporal overlap is taken into account, can precisely predict the output energy and temporal shape, compared to the results from Hirano and other experiments. In addition, our numerical routes could provide the applicable range of analytical solutions to conventional Frantz–Nodvik equations in the case of pulse overlap, further extending the applicability and reducing computational costs. For given conditions, energy reduction and PSD are mainly determined by the overlap degree. For step-shaped pulse, we demonstrate that avoiding overlap in the peak pulse and allowing overlap in the foot pulse have small impacts on the energy extraction and PSD, which extends the range of duration of the pulse for a designed amplifier. Our investigations might provide an efficient way to carefully design a pulsed amplifier with controllable temporal overlap.