Modulation instability in nonlinear propagation of pulses in optical fibers

• Published in: Applied mathematics and computation 2013-09, Vol.221, p.177-191
• Main Authors: Muñoz Grajales, Juan Carlos, Quiceno, Julio César
• Format: Article
• Language: English
• Subjects: Computation; Instability; Mathematical analysis; Mathematical models; Modulation; Nonlinearity; Optical fibers; Periodic waves; Spectral numerical method; Stability
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2013.06.058

We consider a generalized system consisting of two coupled Schrödinger-type equations which models nonlinear pulse propagation in a linearly birefringent Kerr optical fiber. An analysis of stability of periodic solutions of the system is performed by using a second-order accurate spectral numerical solver. The main novelty in our study is that we do not assume high or weak birefringence in the fiber and thus the model considered incorporates nonlinear terms which were neglected in the stability analysis performed in previous works. In the case of anomalous dispersion, our numerical simulations indicate that a periodic solution develops a type of modulation instability against small disturbances, given that the perturbation frequency remains within certain range (computed analytically by means of a linear analysis) which depends on the model’s parameters and the amplitude of the perturbing signals. We also find that the gain spectrum of modulation instability is altered by the additional nonlinear terms included in the above-mentioned system.