@mastersthesis {9998,
	title = {Simulation and analysis of a soliton perturbation by a truncated Airy in Kerr media},
	year = {2012},
	type = {masters},
	abstract = {The simulation and analysis of a temporal soliton perturbation (interaction) with a\&nbsp;dispersive truncated Airy pulse traveling in a nonlinear fiber at the same center\&nbsp;wavelength (or frequency). True Airy pulses remain self-similar while propagating\&nbsp;along a ballistic trajectory. However, they are infinite in energy due to the infinite tail\&nbsp;that prevents the energy integral from converging. In order to be realized, Airy pulses\&nbsp;must therefore, be truncated. The truncation is carried out by apodizing the infinite\&nbsp;Airy tail. Despite the truncation Airy pulses remain self-similar over extended ranges\&nbsp;while the ballistic trajectory is completely preserved. This allows them to interact with\&nbsp;a nearby soliton on account of the accelerating wavefront property.The interactions are governed by the Nonlinear Schr{\"o}dinger equation for\&nbsp;which no analytical solution currently exists for these initial conditions. Therefore,\&nbsp;numerical simulations are required. The numerical method chosen is the split step\&nbsp;Fourier method which is a mathematical algorithm for propagation of the pulses. By\&nbsp;providing the simulation program with the initial launch conditions we are able to\&nbsp;follow the interactions as they progress.Analysis of the simulation is carried out by tracking the fundamental\&nbsp;parameters of the emergent soliton during propagation{\textemdash}time position, amplitude,\&nbsp;phase and frequency{\textemdash}that alter due to the primary collision with the Airy main lobe\&nbsp;and the continuous co-propagation with the dispersed Airy background. Following the\&nbsp;collision, the soliton intensity oscillates as it relaxes in the dispersed Airy background,\&nbsp;trying to settle in to a new soliton state. Further, by varying the initial parameters of\&nbsp;the Airy pulse such as initial phase, amplitude and time position, different outcomes\&nbsp;are witnessed which allows for a broader understanding of the interaction.Due to the spectral repositioning of the Airy spectrum by dispersion, the\&nbsp;interaction is found to resemble coherent interactions at times and incoherent at\&nbsp;others. The results indicate that in certain cases permanent change in frequency and\&nbsp;intensity occurs, depending on the configuration of the initial parameters chosen.\&nbsp;These changes are made apparent through changes in time position and in the\&nbsp;accumulated phase of the soliton. Furthermore, according to the perturbation theory\&nbsp;local changes in time position and phase can also occur independently from the\&nbsp;frequency change and intensity change, respectively.},
	url = {http://hufind.huji.ac.il/Record/HUJ001748140},
	author = {Amitay Rudnick}
}
