Difference differential equations for a resonator with a very thin nonlinear medium.
We derive from the classic Maxwell-Bloch equations a set of difference-differential equations valid, in general, when the length of the nonlinear medium in the optical cavity is much smaller than a wavelength. Such equations provide an elegant and simple framework in which the case of Fabry-Perot and ring cavity can be discussed in a unified way. We outline a complete scenario for the multimode laser instability in the Fabry-Perot case, illustrating the results for parameter values appropriate to quantum cascade lasers. Our approach can have a relevant impact also on the study of dynamical instabilities in external cavity semiconductor lasers, including multiple quantum well or quantum-dot structures.
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CNISM and Dipartimento di Fisica e Matematica, Università dell'Insubria, Via Valleggio 11, 22100 Como, Italy.
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