Numerical modeling of the interaction of light pulses in nonlinear medium

Author: Daviti Kobaidze
Keywords: optical pulse, nonlinear schrodinger equation, soliton, modulational instability
Annotation:

The main purpose of the bachalor’s thesis is studying elastic and inelastic collisions of optical pulses and solitons. Processing such issues by theoretical and numerical methods is important in problems of management of optical pulses. Management of optical pulses means to control number of solitons and their amplitudes, to change their group velocity. If the pulse does not change its shape during the collision , there is an elastic collison, which characterizes solitons. In an inelastic collision, the parameters of solitons are changed. In the thesis, to control solitons, we used method of variation of dispersion. Namely, there is used variation of a diameter of a fiber; in this case coefficient of dispersion depends on a coordinate, which leads to a number of effects, with which a propagation of a light pulses in such variable dispersive medium are characterized. We used the Nonlinear Schrodinger Equation to study above mentioned properties of solitons, which is widely used for studying the propagation of elecrtomagnetic waves in nonlinear dispersive medium. However, besides the solitary solutions, we have also discussed an issue of stability of ligth pulses, for which we used perturbative analysis and as a result of numerical experiments a possibility of a modulational instability is shown. Also, there is studied a behavior of pulses in a regime of the modulational instability.