Directed Electromagnetic Pulse Dynamics: Projecting Operators Method

In this article, we consider a one-dimensional model of electromagnetic pulse propagation in isotropic media, taking into account a nonlinearity of the third order. We introduce a method for Maxwell's equation transformation on the basis of a complete set of projecting operators. The operators...

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Bibliographic Details
Published in:Journal of the Physical Society of Japan 2011-02, Vol.80 (2), p.024002-024002-5
Main Author: Kuszner, Mateusz
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Nonlinear optics
Optics
Physics
Ultrafast processes
optical pulse generation and pulse compression
Wave optics
Wave propagation, transmission and absorption
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Summary:In this article, we consider a one-dimensional model of electromagnetic pulse propagation in isotropic media, taking into account a nonlinearity of the third order. We introduce a method for Maxwell's equation transformation on the basis of a complete set of projecting operators. The operators correspond to wave dispersion branches including the direction of propagation. As the simplest result of applying the method, we derive a system of equations describing one-dimensional dynamics of pulses of opposite directions of propagation without dispersion account. The corresponding self-action equations are extracted. Next we introduce a dispersion and show how the operators change. Through applications in such a manner, the generalized short pulse equations (SPE) of Shafer and Wayne are obtained for both propagation directions. The effects of the unidirectional pulse interaction are discussed.
ISSN:0031-9015
1347-4073
DOI:10.1143/JPSJ.80.024002