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Advances in Optical Technologies
Volume 2011 (2011), Article ID 989515, 8 pages
http://dx.doi.org/10.1155/2011/989515
Research Article

Ultrashort Optical Pulse Propagation in terms of Analytic Signal

1Division of Laser Dynamics, Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany
2Invalidenstrasse 114, 10115 Berlin, Germany

Received 26 May 2011; Revised 9 August 2011; Accepted 9 August 2011

Academic Editor: Ci-Ling Pan

Copyright © 2011 Sh. Amiranashvili and A. Demircan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We demonstrate that ultrashort optical pulses propagating in a nonlinear dispersive medium are naturally described through incorporation of analytic signal for the electric field. To this end a second-order nonlinear wave equation is first simplified using a unidirectional approximation. Then the analytic signal is introduced, and all nonresonant nonlinear terms are eliminated. The derived propagation equation accounts for arbitrary dispersion, resonant four-wave mixing processes, weak absorption, and arbitrary pulse duration. The model applies to the complex electric field and is independent of the slowly varying envelope approximation. Still the derived propagation equation posses universal structure of the generalized nonlinear Schrödinger equation (NSE). In particular, it can be solved numerically with only small changes of the standard split-step solver or more complicated spectral algorithms for NSE. We present exemplary numerical solutions describing supercontinuum generation with an ultrashort optical pulse.