Nonlinear dynamics in a Fabry-Perot resonator |
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Authors: | L A Lugiato L M Narducci |
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Institution: | (1) Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, I-10129 Torino, Italy;(2) Physics Department, Drexel University, 19104 Philadelphia, PA, USA |
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Abstract: | We develop a general formalism to describe the dynamical behavior of an ensemble of two-level systems in a Fabry-Perot cavity. Our main result is a set of space and time-dependent, integro-differential equations for the slowly varying radiation and atomic variables, which we derive through a precise analysis of the slowly-varying amplitude approximation in the presence of counter-propagating fields. With the help of new and properly chosen variables we recast these equations in a form that makes their boundary conditions formally identical to those of an ideal Fabry-Perot resonator, and introduce in a natural way a modal structure even for systems with arbitrary mirror reflectivity. We derive simplified forms of these equations in the uniform field limit and within the more general single-frequency approximation. Finally, we extend our formulation to include driven systems such as optically bistable devices and the laser with an injected signal. |
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