We demonstrate self-similar stable propagation of parabolic optical pulses through a highly nonlinear specialty Bragg fiber at 2.8 μm by a numerical approach. To obtain such propagation characteristics over a longer length of a Bragg fiber, we propose and verify a fiber design scheme that underpins passive introduction of a rapidly varying group-velocity dispersion around its zero dispersion wavelength and modulated nonlinear profile through suitable variation in its diameter. To implement the proposed scheme, we design a segmented and tapered chalcogenide Bragg fiber in which a Gaussian pulse is fed. Transformation of such a launched pulse to a self-similar parabolic pulse with full-width-at-half-maxima of 4.12 ps and energy of ∼39 pJ is obtained at the output. Furthermore, a linear chirp spanning across the entire pulse duration and 3 dB spectral broadening of about 38 nm at the output are reported. In principle, the proposed scheme could be implemented in any chosen set of materials. © 2017 IEEE.