Generation of self-similar parabolic pulse is analytically and numerically demonstrated by designing parabolic index normal dispersion decreasing fiber (NDDF) amplifiers. The pulse transmission is extensively studied for NDDFs in presence of physical gain as well as virtual gain induced by two different dispersion profiles corresponding to two different physical gain coefficients. Here, we introduce the virtual gain arising from the unavoidable spatial nonlinear variation, which helps to obtain the self-similar parabolic pulses at smaller optimum length in comparison to NDDF with constant nonlinearity. The output power profiles resemble with a perfect parabolic shape giving rise to self-similar pulses with very small misfit parameters. Pulse propagation in presence of spatial gain variation is also studied. To avoid fabrication difficulties, we propose equivalent staircase dispersion profiles consisting of a number of constant dispersion fibers (CDFs), which are simple to manufacture and show performances excellently close to that of the proposed NDDF.
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