Straight line shifts of time-domain trajectories of soliton pulses with initial first-order phase modulation in optical fibers

The nonlinear propagation of hyperbolic secant soliton optical pulses with initial first-order phase modulation in the anomalous dispersion regions of optical fibers are investigated numerically. The corresponding evolutions of pulse shapes and spectra are provided for different soliton order and phase modulation parameters. The results show that, in the time domain, the initially first-order phase modulation can make the soliton pulse shift towards the pulse leading or trailing edges along a straight line with the pulse shape profile and its breather evolution behavior unchanged. Correspondingly, in the frequency domain, the initial first-order phase modulation can make the pulse spectrum exhibit red-shifting or blue-shifting phenomenon with the pulse spectrum profile and its breather evolution behavior unchanged. The larger the absolute value of the phase modulation parameter, the larger the shifting. While for the same phase modulation parameter, both the fundamental- and higher-order solitons exhibit the same shifting. These results may be potentially applied in manipulating the time-domain trajectories of the solitons as well as their corresponding frequency-domain positions by engineering the initial first-order phase modulation parameters of the solitons.