Since the seminal works by A. Hasegawa and co-workers in the 1980s, the modulation instability phenomenon has been widely studied and used in optical fibers, in particular for generating high-repetition-rate soliton trains and for parametric amplification of weak signals. Modulation instability is also known as a general precursor of highly localized wave structures through amplification of perturbations. We review here our recent experiments performed in conservative physical systems based on nonlinear fiber optics [4], that evidence a large class of exact pulsating solutions of the nonlinear Schrödinger equation, called breathers and rogue wave solutions. Based on the coherent seeding of the modulation instability process in scalar and vector fiber systems, we confirm the existence of super-regular breathers and dark vector rogue waves. These results have shed new lights on extreme nonlinear dynamics and related analogies between optics and hydrodynamics.

Moreover, we present our recent investigations into the modulation instability process in dissipative systems based on a nonlinear fiber ring cavity [5]. In this special case, the cavity boundary conditions are known to play, in addition to the fiber nonlinearity and dispersion, a crucial role in the propagation dynamics. We show that such systems exhibit complex spatiotemporal dynamics that lead to the emergence of extreme events for very simple parameters.

References

[1] B. Frisquet et al., Phys. Rev. A 89, 023821 (2014)

[2] B. Kibler et al., Phys. Rev. X 5, 041026 (2015)

[3] B. Frisquet et al., Phys. Rev. A 92, 053854 (2015)

[4] B. Frisquet et al., Sci. Rep. 6, 20785 (2016)

[5] A. Bendahmane et al., SPIE Photonics Europe, 9894-10 (2016)

[6] A. Bendahmane et al., in preparation (2016)