Pedestal-free pulse compression in nonlinear fibers and nonlinear fiber Bragg gratings

Abstract

Recently, a technique known as self-similar analysis has been utilized to study linearly chirped pulses in optical fibers and fiber amplifiers. The self-similar pulses have attracted much attention since the linear chirp facilitates efficient pulse compression. In addition, these pulses can propagate without pulse break-up at high powers. However, because of the relatively small dispersion of optical fibers, this scheme requires long fiber lengths, and only a few dispersion profiles are practically feasible. A more attractive solution consists of pulse compression in a highly dispersive nonlinear medium such as a fiber Bragg grating (FBG). Grating dispersion just outside the stop band is up to six orders of magnitude larger than that of silica fiber and can be tailored simply by changing the grating profile. This potential suggests utilizing this huge dispersion to construct a short compressor. Through the self-similar analysis, we have theoretically investigated the linearly chirped Bragg soliton near the photonic bandgap (PEG) structure of FBG. Efficient Bragg soliton compression can be achieved with the exponentially decreasing dispersion. The stepwise approximation of exponentially decreasing dispersion is carried out by concatenation of grating segments with constant dispersion. For the proposed compression scheme, the input pulse must be pre-chirped in a prescribed manner, and a simple pre-chirper, such as a linear fiber or grating, is used to add the required chirp profile to initial chirp-free hyperbolic secant or Gaussian pulse. The comparisons between nonlinear Schrodinger (NLS) equation, pulse parameter evolution equations, and nonlinear coupled-mode equations are given. Higher order nonlinearities must be considered if the optical pulse intensity is high or the nonlinear coefficients of the materials are large, for instance, in semiconductor doped glasses. Therefore, we have investigated the existence of chirped solitary wave solutions in the cubic-quintic nonlinear media with exponentially decreasing dispersion. We numerically show that competing cubic and quintic nonlinearities stabilize the chirped solitary wave propagation against perturbations of initial pulse parameters. In addition, we studied the possibility of rapid compression of Townes solitons by the collapse phenomenon in the exponentially decreasing dispersion. We also found that the collapse could be postponed if the dispersion increases exponentially.