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Transverse limits on the uni-directional pulse propagation approximation

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 Added by Paul Kinsler
 Publication date 2012
  fields Physics
and research's language is English
 Authors P. Kinsler




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I calculate the limitations on the widely-used forward-only (uni-directional) propagation assumption by considering the effects of transverse effects (e.g. diffraction). The starting point is the scalar second order wave equation, and simple predictions are made which aim to clarify the forward-backward coupling limits on diffraction strength. The result is unsurprising, being based on the ratio of transverse and total wave vectors, but the intent is to present a derivation directly comparable to a recently published emph{nonlinearity} constrained limits on the uni-directional approximation [Kinsler, J. Opt. Soc. Am. B (2007)].



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I apply the method of characteristics to both bi-directional and uni-directional pulse propagation in dispersionless media containing nonlinearity of arbitrary order. The differing analytic predictions for the shocking distance quantify the effects of the uni-directional approximation used in many pulse propagation models. Results from numerical simulations support the theoretical predictions, and reveal the nature of the coupling between forward and backward waves.
288 - P. Kinsler 2010
I present an overview of pulse propagation methods used in nonlinear optics, covering both full-field and envelope-and-carrier methods. Both wideband and narrowband cases are discussed. Three basic forms are considered -- those based on (a) Maxwells equations, (b) directional fields, and (c) the second order wave equation. While Maxwells equations simulators are the most general, directional field methods can give significant computational and conceptual advantages. Factorizations of the second order wave equation complete the set by being the simplest to understand. One important conclusion is that that envelope methods based on forward-only directional field propagation has made the traditional envelope methods (such as the SVEA, and extensions) based on the second order wave equation utterly redundant.
109 - Paul Kinsler 2014
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Generically, spectral statistics of spinless systems with time reversal invariance (TRI) and chaotic dynamics are well described by the Gaussian Orthogonal ensemble (GOE). However, if an additional symmetry is present, the spectrum can be split into independent sectors which statistics depend on the type of the groups irreducible representation. In particular, this allows the construction of TRI quantum graphs with spectral statistics characteristic of the Gaussian Symplectic ensembles (GSE). To this end one usually has to use groups admitting pseudo-real irreducible representations. In this paper we show how GSE spectral statistics can be realized in TRI systems with simpler symmetry groups lacking pseudo-real representations. As an application, we provide a class of quantum graphs with only $C_4$ rotational symmetry possessing GSE spectral statistics.
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