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Hamiltonian framework for short optical pulses

Please always quote using this URN:urn:nbn:de:0296-matheon-14001
  • Physics of short optical pulses is an important and active research area in nonlinear optics. In what follows we theoretically consider the most extreme representatives of short pulses that contain only several oscillations of electromagnetic field. Description of such pulses is traditionally based on envelope equations and slowly varying envelope approximation, despite the fact that the envelope is not “slow” and, moreover, there is no clear definition of such a “fast” envelope. This happens due to another paradoxical feature: the standard (envelope) generalized nonlinear Schrödinger equation yields very good correspondence to numerical solutions of full Maxwell equations even for few-cycle pulses, a thing that should not be. In what follows we address ultrashort optical pulses using Hamiltonian framework for nonlinear waves. As it appears, the standard optical envelope equation is just a reformulation of general Hamiltonian equations. In a sense, no approximations are required, this is why the generalized nonlinear Schrödinger equation is so effective. Moreover, the Hamiltonian framework greatly contributes to our understanding of “fast” envelope, ultrashort solitons, stability and radiation of optical pulses. Even the inclusion of dissipative terms is possible making the Hamiltonian approach an universal theoretical tool also in extreme nonlinear optics.

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Metadaten
Author:Shalva Amiranashvili
URN:urn:nbn:de:0296-matheon-14001
Referee:Benjamin Kunz
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2016/12/16
Release Date:2016/12/16
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
Project:D Optics and Electronics (Electronic and photonic devices) / D-OT2 Turbulence and extreme events in non-linear optics
MSC-Classification:78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80) / 78-02 Research exposition (monographs, survey articles)
Preprint Number:1118
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