The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Avec la technologie émergente des réseaux photoniques, une conception minutieuse devient nécessaire pour tirer le meilleur parti de la capacité de fibre déjà installée. Des outils numériques appropriés sont facilement disponibles. Habituellement, celles-ci sont basées sur la méthode de Fourier à étapes fractionnées (SSFM), employant la transformée de Fourier rapide (FFT). Avec N points de discrétisation, la complexité du SSFM est O(N enregistrer2N). Pour les systèmes réels de multiplexage par répartition en longueur d'onde (WDM), le temps de simulation peut être de l'ordre de quelques jours, donc toute amélioration de la vitesse serait la bienvenue. Nous montrons que le SSFM est un cas particulier de la méthode dite de collocation avec fonctions de base harmonique. Cependant, pour la modélisation de guides d’ondes optiques non linéaires, divers autres systèmes de fonctions de base offrent des avantages significatifs. Pour calculer la propagation d'impulsions uniques de type soliton, une base de Gauss-Hermite adaptée au problème conduit à un temps de calcul fortement réduit par rapport au SSFM. De plus, en utilisant un système de fonctions de base construit à partir d'une fonction de mise à l'échelle, qui génère une ondelette prise en charge de manière compacte, nous avons développé une nouvelle méthode flexible de collocation d'ondelettes en plusieurs étapes (SSWCM). Cette technique est indépendante des formes d'impulsions qui se propagent et offre une complexité de l'ordre de O(N) pour une précision fixe. Pour une situation de modélisation typique avec jusqu'à 64 canaux WDM, le SSWCM conduit à des temps de calcul nettement plus courts que le SSFM standard.
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Tristan KREMP, Alexander KILLI, Andreas RIEDER, Wolfgang FREUDE, "Split-Step Wavelet Collocation Method for Nonlinear Optical Pulse Propagation" in IEICE TRANSACTIONS on Electronics,
vol. E85-C, no. 3, pp. 534-543, March 2002, doi: .
Abstract: With the emerging technology of photonic networks, careful design becomes necessary to make most of the already installed fibre capacity. Appropriate numerical tools are readily available. Usually, these are based on the split-step Fourier method (SSFM), employing the fast Fourier transform (FFT). With N discretization points, the complexity of the SSFM is O(N log2N). For real-world wavelength division multiplexing (WDM) systems, the simulation time can be of the order of days, so any speed improvement would be most welcome. We show that the SSFM is a special case of the so-called collocation method with harmonic basis functions. However, for modelling nonlinear optical waveguides, various other basis function systems offer significant advantages. For calculating the propagation of single soliton-like impulses, a problem-adapted Gauss-Hermite basis leads to a strongly reduced computation time compared to the SSFM . Further, using a basis function system constructed from a scaling function, which generates a compactly supported wavelet, we developed a new and flexible split-step wavelet collocation method (SSWCM). This technique is independent of the propagating impulse shapes, and provides a complexity of the order O(N) for a fixed accuracy. For a typical modelling situation with up to 64 WDM channels, the SSWCM leads to significantly shorter computation times than the standard SSFM.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e85-c_3_534/_p
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@ARTICLE{e85-c_3_534,
author={Tristan KREMP, Alexander KILLI, Andreas RIEDER, Wolfgang FREUDE, },
journal={IEICE TRANSACTIONS on Electronics},
title={Split-Step Wavelet Collocation Method for Nonlinear Optical Pulse Propagation},
year={2002},
volume={E85-C},
number={3},
pages={534-543},
abstract={With the emerging technology of photonic networks, careful design becomes necessary to make most of the already installed fibre capacity. Appropriate numerical tools are readily available. Usually, these are based on the split-step Fourier method (SSFM), employing the fast Fourier transform (FFT). With N discretization points, the complexity of the SSFM is O(N log2N). For real-world wavelength division multiplexing (WDM) systems, the simulation time can be of the order of days, so any speed improvement would be most welcome. We show that the SSFM is a special case of the so-called collocation method with harmonic basis functions. However, for modelling nonlinear optical waveguides, various other basis function systems offer significant advantages. For calculating the propagation of single soliton-like impulses, a problem-adapted Gauss-Hermite basis leads to a strongly reduced computation time compared to the SSFM . Further, using a basis function system constructed from a scaling function, which generates a compactly supported wavelet, we developed a new and flexible split-step wavelet collocation method (SSWCM). This technique is independent of the propagating impulse shapes, and provides a complexity of the order O(N) for a fixed accuracy. For a typical modelling situation with up to 64 WDM channels, the SSWCM leads to significantly shorter computation times than the standard SSFM.},
keywords={},
doi={},
ISSN={},
month={March},}
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TY - JOUR
TI - Split-Step Wavelet Collocation Method for Nonlinear Optical Pulse Propagation
T2 - IEICE TRANSACTIONS on Electronics
SP - 534
EP - 543
AU - Tristan KREMP
AU - Alexander KILLI
AU - Andreas RIEDER
AU - Wolfgang FREUDE
PY - 2002
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E85-C
IS - 3
JA - IEICE TRANSACTIONS on Electronics
Y1 - March 2002
AB - With the emerging technology of photonic networks, careful design becomes necessary to make most of the already installed fibre capacity. Appropriate numerical tools are readily available. Usually, these are based on the split-step Fourier method (SSFM), employing the fast Fourier transform (FFT). With N discretization points, the complexity of the SSFM is O(N log2N). For real-world wavelength division multiplexing (WDM) systems, the simulation time can be of the order of days, so any speed improvement would be most welcome. We show that the SSFM is a special case of the so-called collocation method with harmonic basis functions. However, for modelling nonlinear optical waveguides, various other basis function systems offer significant advantages. For calculating the propagation of single soliton-like impulses, a problem-adapted Gauss-Hermite basis leads to a strongly reduced computation time compared to the SSFM . Further, using a basis function system constructed from a scaling function, which generates a compactly supported wavelet, we developed a new and flexible split-step wavelet collocation method (SSWCM). This technique is independent of the propagating impulse shapes, and provides a complexity of the order O(N) for a fixed accuracy. For a typical modelling situation with up to 64 WDM channels, the SSWCM leads to significantly shorter computation times than the standard SSFM.
ER -