Simple model for the study of period-doubling instabilities in the nonlinear ring cavity

In the good cavity limit, the two-dimensional Ikeda map [K. Ikeda, Opt. Commun. 30, 257 (1979)] representing the evolution of the field in a nonlinear ring cavity may be approximated by a set of two coupled-differential equations for the description of the dynamics of the period-2 regime of Ikeda instability. Our theory, which constitutes a generalization, to period doubling, of the single-mode mean-field theory of passive nonlinear cavities, provides a new insight of Ikeda instabilities in these devices.