טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentToroker Zeev
SubjectStudying Pulse Propagation through Nonlinear Fiber Bragg
Gratings
DepartmentDepartment of Electrical Engineering
Supervisor Professor Moshe Horowitz
Full Thesis textFull thesis text - English Version


Abstract

Nonlinear fiber Bragg gratings (FBGs) have been studied theoretically and experimentally. The nonlinear Kerr effect in FBGs makes it possible to obtain pulse compression, optical switching, optical gates, and solitons having a slow group velocity. Due to large dispersion these gratings are ideal for studying nonlinear pulse propagation in a length scale of few centimeters.


Pulse propagation in such nonlinear FBGs is modeled by the nonlinear coupled mode equations (NLCME).

In the first part of the thesis we present a new split-step numerical method for solving NLCME. This new method, as opposed to the previous method, does not impose that the temporal and spatial step sizes will be connected via the group velocity. We found that the spatial step-size can be increased substantially in some problems without adversely affecting the accuracy of the results. Hence, in some practical problems we could decrease the run-time by a factor of up to a hundred.


The second part of the thesis is devoted to analyze the collision of two Bragg solitons in uniform FBGs. Collisions of two Bragg solitons have been studied numerically. However, there is no known explicit function that describes the collision of two Bragg solitons. When two Bragg solitons collide, they may emerge from the interaction with a change in their energy or momentum or may even disappear. However, in broad soliton parameters, an elastic collision between two Bragg solitons is obtained. In this work, we show that under certain soliton parameters the NLCME can be analyzed by transforming the solution of the massive Thirring model (MTM), which is solvable by the inverse scattering transform (IST).


We present, for the first time, an approximate solution of an elastic collision between two Bragg solitons by transforming the solution to interaction between two Thirring solitons. This means that two Bragg solitons can collide as Thirring-like solitons. Particularly, we have found that two Bragg solitons can interchange their roles after a collision and overlap during interaction, as do two Thirring solitons. Also, we have found that the approximate solution enables, to explicitly describe the collision of two Bragg solitons in most of the important region of soliton parameters that can be realized experimentally.

We could analytically study the interaction between Bragg solitons and its asymptotic behavior. For example, the explicit function enables one to calculate the shift in locations and phases that occur in the collision of Bragg solitons.