The simulation and analysis of a temporal soliton perturbation (interaction) with a dispersive truncated Airy pulse traveling in a nonlinear fiber at the same center wavelength (or frequency). True Airy pulses remain self-similar while propagating along a ballistic trajectory. However, they are infinite in energy due to the infinite tail that prevents the energy integral from converging. In order to be realized, Airy pulses must therefore, be truncated. The truncation is carried out by apodizing the infinite Airy tail. Despite the truncation Airy pulses remain self-similar over extended ranges while the ballistic trajectory is completely preserved. This allows them to interact with a nearby soliton on account of the accelerating wavefront property.
The interactions are governed by the Nonlinear Schrödinger equation for which no analytical solution currently exists for these initial conditions. Therefore, numerical simulations are required. The numerical method chosen is the split step Fourier method which is a mathematical algorithm for propagation of the pulses. By providing the simulation program with the initial launch conditions we are able to follow the interactions as they progress.
Analysis of the simulation is carried out by tracking the fundamental parameters of the emergent soliton during propagation—time position, amplitude, phase and frequency—that alter due to the primary collision with the Airy main lobe and the continuous co-propagation with the dispersed Airy background. Following the collision, the soliton intensity oscillates as it relaxes in the dispersed Airy background, trying to settle in to a new soliton state. Further, by varying the initial parameters of the Airy pulse such as initial phase, amplitude and time position, different outcomes are witnessed which allows for a broader understanding of the interaction.
Due to the spectral repositioning of the Airy spectrum by dispersion, the interaction is found to resemble coherent interactions at times and incoherent at others. The results indicate that in certain cases permanent change in frequency and intensity occurs, depending on the configuration of the initial parameters chosen. These changes are made apparent through changes in time position and in the accumulated phase of the soliton. Furthermore, according to the perturbation theory local changes in time position and phase can also occur independently from the frequency change and intensity change, respectively.