Hamiltonian Framework for Short Optical Pulses

  • Shalva AmiranashviliEmail author
Part of the Lecture Notes in Physics book series (LNP, volume 908)


Physics of short optical pulses is an important and active research area in nonlinear optics. In this Chapter 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, the 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 contributes greatly to our understanding of “fast” envelopes, 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.


Poisson Bracket Canonical Variable Optical Pulse Ultrashort Pulse Rogue Wave 
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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

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