Modulation instability is one of the most ubiquitous phenomena in physics. Here we investigate the phase-sensitive properties of modulation instability with harmonic seeding in passive fiber resonators. Theoretical investigations based on the Lugiato−Lefever equation with time dependent pump and a three-wave truncation show that the dynamics of the system is sensitive to the relative phase between input signal, idler, and pump waves. The modulation instability gain can even vanish for a peculiar value of the initial relative phase. An advanced multi-heterodyne measurement technique had been developed to record the real time evolution, round-trip to round-trip, of the power and phase of the output cavity field to confirm these theoretical predictions.
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This work was partly supported by the Agence Nationale de la Recherche through the Equipex Fibers optiques pour les hauts flux (FLUX) through the Program Investisse-ments d’Avenir, by the Ministry of Higher Education and Research, Hauts de France Council, and European Regional Development Fund (ERDF) through the Contrat de Projets Etat-Region (CPER Photonics for Society, P4S), HEAFISY project and I-SITE through the VERIFICO, FUHNKC and EXAT projects and H2020 Marie Skodowska-Curie Actions (MSCA)(713694).