Thesis Type:MSc thesis
An Airy pulse, a solution of the dispersion equation, manifests two unique properties while propagating in linear media. One is self-similarity, meaning the pulse has the same envelope throughout propagation in dispersive media and the second is acceleration in time- namely moving in parabolic trajectory with respect to a time frame that moves with the group velocity of the pulse.
We simulate and analyze the propagation of truncated temporal Airy pulses in a single mode fiber in the presence of self-phase modulation (Kerr effect) and anomalous dispersion. Due to the presence of the nonlinear effect, the Airy is no longer a valid solution, such that the pulse evolution is no more predictable.
By gradually increasing the launched Airy power we examine the nonlinearity influence on the Airy pulse evolution. For sufficient large launched intensity we observe soliton pulse shedding from the Airy main lobe, with the emergent soliton parameters dependent on the launched Airy pulse characteristics. The emergent soliton performs "breathing"- periodic oscillations of its parameters along the propagation distance due to interaction with background radiation, with the periodicity increasing with the launched power. Additionally, the soliton mean temporal position shifts to earlier times with higher launched powers due to an earlier shedding event and with greater energy in the Airy tail due to collisions with the accelerating lobes. In spite of the Airy energy loss to the shed Soliton, the Airy pulse continues to exhibit the unique property of acceleration in time and the main lobe recovers from the energy loss (healing property of Airy waveforms), but performs decaying oscillations of its peak power according to the interplay between the dispersion and the nonlinear effect.
The influence of the truncation coefficient—required for limiting the Airy pulse to finite energy—on the Airy nonlinear propagation is also investigated. Small truncation degree increases the Airy tail energy, which has considerable influence on the soliton shedding distance, the soliton mean temporal position, and on the residual accelerating energy.