Abstract

Efficient high energy Ti:Al₂O₃ lasers are currently of interest as coherent sources for a variety of applications, such as laser atmospheric sensing. Furthermore, the output of such lasers can be converted to visible and UV wavelengths through frequency conversion processes. We report here on a novel method for modeling these lasers. The exact cavity equations of motion coupled with realistic time-dependent laser kinetics are solved numerically to obtain the 2-D radially-symmetric time-dependent electric field inside the optical cavity of an injection-seeded Ti:Al₂O₃ laser with an unstable resonator. The analytical model is an extension of our previous gain-loaded laser cavity model¹ to predict pulsed laser performance. It is used here to model Ti:Al₂O₃ lasers; however, it can also be used to predict the performance of any pulsed laser, such as CO₂ or Q-switched Nd:YAG. In this method, the electric field inside the cavity is expanded in terms of the diffractive transverse (Fox-Li) stationary eigenmodes of the optical cavity, with expansion coefficients that depend on time and axial distance. In this way, the electric field is guaranteed to satisfy all the boundary conditions inside the optical cavity at all times. The expansion coefficients are further expanded in a Fourier series of longitudinal modes. Even though the laser is injection seeded, we find that the inclusion of many longitudinal modes is necessary to maintain energy conversation and to appropriately model the spatial and temporal buildup of the laser pulse.

© 1991 Optical Society of America