Highly Anomalous Propagation of Pseudo-Gaussian Pulse

Hiroyuki HOSONO; Toshio HOSONO

doi:10.1093/ietele/e90-c.2.224

Highly Anomalous Propagation of Pseudo-Gaussian Pulse

Hiroyuki HOSONO, Toshio HOSONO

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Gaussian pulse has no beginning point, so has no Laplace transform and is non-physical. We propose sinⁿt pulse (referred to as pseudo-Gaussian pulse or PGP) as an approximation of the Gaussian pulse. PGP has the Laplace transform and approaches the Gaussian pulse as n→∞. The propagation of PGP-modulated wave packet in the highly anomalous dispersion band of a Lorentz medium is investigated by numerical inversion of Laplace transform. Our results are greatly different from the conventional results obtained by the saddle point method. Our results show that the velocity of a Gaussian wave packet cannot be explained only by the concept of the group velocity as has been done so far.

Publication: IEICE TRANSACTIONS on Electronics Vol.E90-C No.2 pp.224-230

Publication Date: 2007/02/01

Publicized

Online ISSN: 1745-1353

DOI: 10.1093/ietele/e90-c.2.224

Type of Manuscript: Special Section PAPER (Special Section on Recent Progress in Electromagnetic Theory and Its Application)

Category: Fundamental Theory of Electromagnetic Fields

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Hiroyuki HOSONO, Toshio HOSONO, "Highly Anomalous Propagation of Pseudo-Gaussian Pulse" in IEICE TRANSACTIONS on Electronics, vol. E90-C, no. 2, pp. 224-230, February 2007, doi: 10.1093/ietele/e90-c.2.224.
Abstract: Gaussian pulse has no beginning point, so has no Laplace transform and is non-physical. We propose sinⁿt pulse (referred to as pseudo-Gaussian pulse or PGP) as an approximation of the Gaussian pulse. PGP has the Laplace transform and approaches the Gaussian pulse as n→∞. The propagation of PGP-modulated wave packet in the highly anomalous dispersion band of a Lorentz medium is investigated by numerical inversion of Laplace transform. Our results are greatly different from the conventional results obtained by the saddle point method. Our results show that the velocity of a Gaussian wave packet cannot be explained only by the concept of the group velocity as has been done so far.
URL: https://globals.ieice.org/en_transactions/electronics/10.1093/ietele/e90-c.2.224/_p

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@ARTICLE{e90-c_2_224,
author={Hiroyuki HOSONO, Toshio HOSONO, },
journal={IEICE TRANSACTIONS on Electronics},
title={Highly Anomalous Propagation of Pseudo-Gaussian Pulse},
year={2007},
volume={E90-C},
number={2},
pages={224-230},
abstract={Gaussian pulse has no beginning point, so has no Laplace transform and is non-physical. We propose sinⁿt pulse (referred to as pseudo-Gaussian pulse or PGP) as an approximation of the Gaussian pulse. PGP has the Laplace transform and approaches the Gaussian pulse as n→∞. The propagation of PGP-modulated wave packet in the highly anomalous dispersion band of a Lorentz medium is investigated by numerical inversion of Laplace transform. Our results are greatly different from the conventional results obtained by the saddle point method. Our results show that the velocity of a Gaussian wave packet cannot be explained only by the concept of the group velocity as has been done so far.},
keywords={},
doi={10.1093/ietele/e90-c.2.224},
ISSN={1745-1353},
month={February},}

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TY - JOUR
TI - Highly Anomalous Propagation of Pseudo-Gaussian Pulse
T2 - IEICE TRANSACTIONS on Electronics
SP - 224
EP - 230
AU - Hiroyuki HOSONO
AU - Toshio HOSONO
PY - 2007
DO - 10.1093/ietele/e90-c.2.224
JO - IEICE TRANSACTIONS on Electronics
SN - 1745-1353
VL - E90-C
IS - 2
JA - IEICE TRANSACTIONS on Electronics
Y1 - February 2007
AB - Gaussian pulse has no beginning point, so has no Laplace transform and is non-physical. We propose sinⁿt pulse (referred to as pseudo-Gaussian pulse or PGP) as an approximation of the Gaussian pulse. PGP has the Laplace transform and approaches the Gaussian pulse as n→∞. The propagation of PGP-modulated wave packet in the highly anomalous dispersion band of a Lorentz medium is investigated by numerical inversion of Laplace transform. Our results are greatly different from the conventional results obtained by the saddle point method. Our results show that the velocity of a Gaussian wave packet cannot be explained only by the concept of the group velocity as has been done so far.
ER -