Third-order laser-field-expansion analysis of the Lorenz–Haken equations

This paper revisits a few aspects of laser-dynamics with a strong-harmonic expansion analysis from which new analytical information, within the intrinsic pulsing regime that characterizes the non-linearly coupled differential Lorenz–Haken equations, is extracted. The analysis is expected to provide clearer insights to the physics involved in the laser-dynamics issue. Carried out to third-order in electric field amplitude, the procedure allows for the derivation of a closed form expression which describes the permanent-oscillation frequency of the unstable periodic state. Comparison between the frequency values evaluated from the literal formula and those obtained through direct numerical simulations shows a realistic fit inside the control parameters space that displays symmetric period-one pulsing solutions.