In optical communication, pulses have approximately a rectangular shape with smooth boundaries. In order to understand the dynamics of these pulses: (A) the generic dynamics of singular quantum mechanics’ wave functions was applied to sharp-boundaries pulses propagation in short dispersive medium and (B) an analytical expression for the propagation of a smooth rectangular pulse in dispersive medium was derived. This analytical expression consists of a couple of complex error functions and can be applied in good approximation to most rectangular pulses propagations in dispersive medium. (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 approximations can be used in other systems where the Schrödinger dynamics hold, such as the paraxial approximation.
© 2012 Optical Society of America
Fiber Optics and Optical Communications
Original Manuscript: October 24, 2011
Revised Manuscript: December 24, 2011
Manuscript Accepted: December 30, 2011
Published: March 26, 2012
Er’el Granot, Eitam Luz, and Avi Marchewka, "Generic pattern formation of sharp-boundaries pulses propagation in dispersive media," J. Opt. Soc. Am. B 29, 763-768 (2012)