Theoretical Analysis of Partial-Spatial Q-Switching Dynamics Using a Two-Level ${\rm CO}_{2}$ Laser Model

A detailed numerical study of the dynamic behavior of a Q-switched CO₂ laser under partial spatial modulation conditions is presented. The Q-switching performance is strongly related to the switching speed and modulation depth of the modulator. The switching speed of most of the modulator principles are typically limited by one or more geometrical dimensions of the modulator. For example, the modulation bandwidth of an acousto-optic modulator is transition time limited. The switching speed is therefore strongly dependent on the optical beam size seen by the modulator along the axis of acoustic wave propagation. This paper is concerned with the impact of transit-time limited modulators with reduced spatial dimensions as compared to the laser beam size, on the Q-switching performance. Numerical simulations on a slit modulated laser beam show that depending on the boundary conditions and the transverse lasing mode, similar or higher Q-switch peak powers can be realized as compared to full-beam modulation.