Generic propagation dynamics of pulses with sharp-boundaries or singularities in dispersive media

Er'el Granot, Eitam Luz and Avi Marchewka

Department of Electrical and Electronics Engineering, Ariel University Center of Samaria, Ariel, Israel

Abstract:

In optical communication pulses often have sharp boundaries. In order to understand the dynamics of these pulses in dispersive fibers: A) The generic dynamics of singular Quantum Mechanics' wavefunctions was applied to the propagation of pulses with singularities in short fibers, B) An analytical expression for the propagation of a smooth rectangular pulse in dispersive medium was derived. This analytical expression can be applied in good accuracy to most rectangular pulses. C) An analytical approximation was derived for the propagation of any pulse with sharp boundaries. This approximation, despite being analytical, can be applied to any sharp boundaries pulse with any given shape.

These exact expressions and approximation can also be implemented in other systems, which are governed by the Schrödinger dynamics, such as the paraxial approximation.