Bistable dissipative soliton in cubic-quintic nonlinear medium with multiphoton absorption and gain dispersion

We studied the propagation of optical pulse in a dissipative cubic-quintic nonlinear medium with multiphoton absorption and gain dispersion. Variational method in conjugation with Rayleigh dissipative function is used to analytically solve the governing complex cubic-quintic Ginzburg–Landau equation. Three cases of multiphoton absorption are studied: (i) two-photon absorption (TPA), (ii) three-photon absorption (3PA) and (iii) both TPA and 3PA. For all three cases, the pulse intensity decays and width broadens. The greater the gain dispersion, the wider the pulse. Increasing quintic nonlinearity marginally affects pulse amplitude but significantly reduces pulse broadening. TPA and 3PA, which are functions of positive imaginary parts of, respectively, third- and fifth-order susceptibility, individually cause pulse decay and pulse broadening. Thus, their combination only expedites pulse degradation. Conversely, negative imaginary part of fifth-order susceptibility may lead to an effect that impedes pulse degradation. Matching numerical results are obtained that validates the entire analytical outcome. A suitable gain can arrest both pulse broadening and decay. Such dissipative solitonic pulses, bistable owing to quintic nonlinearity, are found for all cases.