19 May 2008 Third-order harmonic-expansion analysis of the Lorenz-Haken equations
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This paper aims at revisiting the basic Lorenz-Haken equations with two-fold harmonic-expansion approaches, yielding new analytical information on both the transient and the long term characteristics of the system pulse-structuring. First, we extend the well-known Casperson Hendow-Sargent weak-sideband analysis to derive a general formula that gives the value of the transient frequencies, characteristic of the laser relaxing towards its long-term state, either stable or unstable. Its validity is shown to apply with a remarkable precision at any level of excitation, both beyond and below the instability threshold. Second, we put forward a strong-harmonic expansion scheme to analyse the system long-term solutions. Carried up to third order in field amplitude, the method allows for the derivation of a closed form expression of the system eigen-frequency (derived here for the first time in three decades of laser dynamics) that naturally yields an iterative algorithm to build, analytically, the regular pulsing solutions of the Lorenz-Haken equations. These solutions are constructed for typical examples, extending well beyond the boundary region of the instability domain, inside which the laser field amplitude undergoes regular pulsations around zero-mean values.
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S. Ayadi, S. Ayadi, B. Meziane, B. Meziane, "Third-order harmonic-expansion analysis of the Lorenz-Haken equations", Proc. SPIE 6997, Semiconductor Lasers and Laser Dynamics III, 69971D (19 May 2008); doi: 10.1117/12.775174; https://doi.org/10.1117/12.775174

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