Highly chirped dissipative solitons as a one-parameter family of stable solutions of the cubic–quintic Ginzburg–Landau equation

In this paper, the stability of the analytical solutions of the cubic–quintic Ginzburg–Landau equation (CQGLE) in the high-chirp approximation has been studied numerically. The existence domain for the stable solution in the CQGLE parameter set has been found. A temporal and spectral shape of the stable solution as dependent of the cavity parameters has been analyzed. Direct comparison of the spectra with numerical calculations has been performed, demonstrating 10−2–10−4 accuracy of the analytical solution for chirp parameter f>10. The stable solutions represent the dissipative soliton family with only one composite parameter. Inside this family, the pulse shape in the time domain evolves from the conventional soliton shape, sech−2, to a rectangular one in the opposite limit with a parabolic shape as an intermediate one. The obtained theoretical results make it possible to classify experimentally observed highly chirped pulses and to optimize experimental schemes with an all-normal-dispersion cavity.