Investigation of low pulse repetition passively mode-locked Nd:YVO₄ lasers via multi-pass periodic trajectories in a confocal cavity

We derive the parametric equations for the geometric rays of a periodic orbit inside a confocal cavity. Based on the derived formula, we demonstrate a passively mode-locked solid-state laser with a low pulse repetition rate to obtain a pulse train traveling along zigzag multi-pass trajectories. We achieve a stable mode-locked pulse train with a pulse repetition rate of 18 MHz by designing the cavity to satisfy the dual-M trajectory. Furthermore, by precisely adjusting cavity mirrors under the same experimental setup, we can reach pulse repetition rates of 12 and 9 MHz for the mode-locked laser. It is believed that the numerical calculation and the developed experiment can provide a straightforward and convenient way to achieve a low pulse repetition rate for passively mode-locked lasers.