Novel self-accelerating pulses generation via soliton pulses with cubic temporal phases in optical fibers

A novel self-accelerating pulse whose shape and spectrum consist of one main lobe and a series of weak decayed side ones is revealed numerically by a hyperbolic-secant soliton pulse with the cubic temporal phase (CTP). This novel self-accelerating pulse is somewhat similar to but never the same as the Airy one. The temporal main lobe is approximate sectioned parabolic curve and its bending direction may change more than once. Depending on different CTPs and soliton orders, the temporal trajectory bending directions, bending angles, bending ranges, bending times, and the concrete trajectory routes are also different. Depending on different CTPs, the spectra may be red- or blue-shifted. For the larger soliton order case, the spectral main lobe may vary its position. The results enable us to engineer the temporal trajectories and the corresponding spectra of the soliton pulses via introducing appropriate CTPs besides the conventional cubic spectral ones. Besides, the soliton order can be an auxiliary control parameter which can compress or stretch some of the temporal lobes.