High-amplitude dissipative solitons in the normal and anomalous dispersion regimes

Abstract

In this work, using the method of moments and starting from a singularity found by Akhmediev and co-workers, very high-amplitude solitons of the cubic-quintic complex Ginzburg–Landau equation are predicted in both the normal and anomalous dispersion regimes. The propagation and the main characteristics of such very high-amplitude solitons are investigated in both dispersion regimes. Moreover, the region of existence of these pulses is numerically found in the plane defined by the dispersion and the nonlinear gain saturation parameters. In general, numerical computations are in good agreement with the predictions based on the method of moments when a quartic trial function is assumed. We show that choosing an appropriate signal for the reactive quintic nonlinearity parameter can provide an extension of the region of existence of the above pulses. High-energy ultrashort pulses are found mainly in the normal dispersion region, which is in agreement with the experimental observations reported by other authors.