Theoretical seminar | 12 January 2022

Modulational instability (MI) in nonlinear optical fibers occurs conventionally for anomalous group-velocity dispersion (GVD). The phenomenon can be studies by means of the nonlinear Schrödinger equation (NLSE) and its linearization.
Variations of GVD along the propagation direction lead to MI also for normal GVD. The case of random variations modeled by white noise was extensively analyzed.

In this work, we present the effect of colored random GVD fluctuations, of either low-pass or band-pass type. We model the problem as a NLSE where the GVD coefficient fluctuates randomly on top of an average normal value.
Both are physically realizable and give rise to MI sidebands in normal GVD, concentrated for the former at small detuning, similarly to that given by white noise, for the latter around a parametric resonance-like condition, ruled by the modulation carrier. The transition from the two regimes is analyzed by means of two different analytical methods, namely the cumulant expansion and the Furutsu-Novikov-Shapiro-Loginov-Donsker formulas. The reliability and limitations of our estimates is assessed by comparison to numerical results.

Main paper/arXiv, related to the seminar, and other references

1. F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, ``Modulational instability in optical fibers with variable dispersion'' Physics Letters A, 220, (1996), 213–218.
2. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, Elsevier (2007).
3. M. Gitterman, The Noisy Oscillator, The First Hundred Years, From Einstein Until Now, World Scientific (2005)
4. G. Dujardin, A. Armaroli, S. Rota-Nodari, A. Mussot, A. Kudlinski, S. Trillo,
M. Conforti, S. De Bievre, ``Modulational instability in optical fibers with randomly kicked normal dispersion'' Phys. Rev. A, \textbf{103}, (2021), 053521.
5. A. Armaroli, G. Dujardin, A. Kudlinski, A. Mussot, S. Trillo, S. De Bièvre, et M. Conforti, “Stochastic modulational instability in the nonlinear Schrödinger equation with colored random dispersion”, accepted for publication in Phys. Rev. A, arXiv:2111.13691