Modeling Q-switched Laser Dynamics by State Space Methods

Q-switched lasers are prevalent in applications that require high intensity laser in ultra-short pulses. In a solid state laser Q-switching regime, the laser rate equations are a set of nonlinear coupled differential equations involving photon flux $\phi_a$, instantaneous population inversion density $n_s$, and the absorption center density $n_a$. In this paper, the Q-switched laser is modeled by a system theoretic approach called state space method, where the three physical quantities: $\phi_a$, $n_a$, and $n_s$ are defined as the state variables of the system, the modulation function of the cavity losses, $\alpha(t)$ as the input function, and the laser output power as the output function of the system. First the system is Taylor linearized and the linearized system is simulated by MATLAB Simulink software. The full nonlinear system is also simulated in Simulink. The contribution to the output from the nonlinear components of the system is obtained from the difference between the outputs of the two models.