We present the theory of modulation instability induced by spectrally dependent losses (optical filters) in passive driven nonlinear fiber ring resonators. Starting from an Ikeda map description of the propagation equation and boundary conditions, we derive a mean-field model - a generalized Lugiato-Lefever equation - which reproduces with great accuracy the predictions of the map. The effects on instability gain and comb generation of the different control parameters such as dispersion, cavity detuning, filter spectral position, and bandwidth are discussed.
Bibliographical noteFunding Information:
This study was partly supported by IRCICA, by the French government through the Programme Investissement d'Avenir (I-SITE ULNE/ANR-16-IDEX-0004 ULNE, projects VERIFICO, EXAT, FUNHK) managed by the Agence Nationale de la Recherche. The work of A.M.P. was supported by the Royal Academy of Engineering under the Research Fellowship scheme.
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