We examine similarities and differences between high-power parabolic pulse generation in an active medium and in tapered fiber with decreasing normal dispersion. Using a realistic tapered fiber design, we demonstrate the possibility of parabolic pulse generation without an external pump and determine the limitations of this approach. © 2007 Optical Society of America OCIS codes: 060.2280, 060.4370, 060.5530, 320.5540. High-power pulse propagation in optical fiber is strongly affected by nonlinear phenomena. Mastering these nonlinear effects can result in the development of new attractive techniques for optical signal generation, processing, and manipulation. In the normal dispersion regime, nonlinear-dominated optical pulse broadening generally leads to wave breaking that manifests itself as waveform steepening with subsequent growing oscillations at the pulse tails. However, there is an interesting class of breakingfree pulses with a parabolic profile in the energycontaining core that can propagate in a stable selfsimilar manner, holding a certain relation (scaling) among changing pulse power, width, and chirp. 1 Such a parabolic pulse can be analytically described as an approximate solution of the nonlinear Schrödinger equation (NLSE) with normal dispersion and gain in the large-amplitude (or small-dispersion) limit. [1][2][3][4][5] Note that the self-similar parabolic approximation is applied only in the central part of the pulse. A more accurate mathematical description that matches the parabolic core with the pulse tails has been presented in Ref. 6. Parabolic pulses (PPs) have recently attracted a great deal of attention because of their potential importance for high-power femtosecond lasers, 7-9 applications in spectral broadening and supercontinuum generation, 10,11 and all-optical signal processing and regeneration. 12,13 Generation of PPs by using an optical fiber amplifying medium (e.g., Er-doped fiber amplifiers, Ybdoped fiber, or passive optical fibers with distributed Raman amplification) has been successfully demonstrated in a number of recent publications (see, e.g., Refs. 14 and 15 and references therein). Breakingfree optical pulse amplification is beneficial for highpower lasers and similar applications. However, there is a range of physical and technical problems (e.g., telecommunication signal processing) where high signal power is not required and the most valuable features are the specific parabolic pulse shape and chirp. An active medium, inevitably, introduces amplified spontaneous emission noise. Therefore, taking into account a variety of possible applications, it is of interest to examine other approaches to PP generation. A simple alternative method for generation of PPs in a passive device by means of a dispersion-decreasing fiber (DDF) was proposed in Ref. 16. The first experiments 17,18 confirmed the possibility of PP generation in DDF. It was pointed out in Ref. 16 that in a system described by the ideal lossless NLSE with dispersion decreasing as D͑z͒ = D͑0͒ / ͑1+⌫ 0 z͒ (hyp...