Weak versus strong harmonic-expansion analyses of self-pulsing lasers: I—the Laser Lorenz model

Abstract

We apply a simple harmonic expansion method to the single-mode laser equations to analyze their dynamic properties. First, we extend the well-known small signal analysis to predict the transient pulsations of the relaxation oscillations. Such transients are characteristic of the laser signal relaxing towards its long-term solution, at any level of excitation, both beyond and below the instability threshold. Secondly, we extend the method to a strong harmonic expansion to analyze the properties of the long-term solutions. These properties are derived for typical examples, extending well beyond the boundary region of the instability domain, for which the laser field amplitude undergoes regular pulsations around zero-mean values.