Alternative expression of the Bloch wave group velocity in loss-less periodic media using the electromagnetic field energy

Résultats de recherche: Contribution à un journal/une revueArticle

Résumé

In periodic optical media, the group velocity is defined as the gradient with respect to wave-vector of the corresponding Bloch mode frequency dispersion curve, forming the photonic band structure. Instead of deducing it from the numerically computed photonic crystal band structure, the group velocity can be calculated directly from the integral of the Poynting vector over the crystal unit cell, the physical meaning of which is immediately perceivable. The related formula, which can be regarded as the application of Hellmann–Feynman theorem to electromagnetism, has been reported previously though without proof. We provide hereafter a full derivation of that formula starting from Maxwell’s equations and we discuss its usefulness in photonics.
langueAnglais
Pages213-220
Nombre de pages8
journalJournal of Modern Optics
Volume65
Numéro2
étatPublié - 12 oct. 2017

Empreinte digitale

group velocity
electromagnetic fields
photonics
Hellmann-Feynman theorem
Maxwell equation
crystals
energy
derivation
electromagnetism
gradients
curves
cells

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abstract = "In periodic optical media, the group velocity is defined as the gradient with respect to wave-vector of the corresponding Bloch mode frequency dispersion curve, forming the photonic band structure. Instead of deducing it from the numerically computed photonic crystal band structure, the group velocity can be calculated directly from the integral of the Poynting vector over the crystal unit cell, the physical meaning of which is immediately perceivable. The related formula, which can be regarded as the application of Hellmann–Feynman theorem to electromagnetism, has been reported previously though without proof. We provide hereafter a full derivation of that formula starting from Maxwell’s equations and we discuss its usefulness in photonics.",
author = "Olivier Deparis and Philippe Lambin",
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Alternative expression of the Bloch wave group velocity in loss-less periodic media using the electromagnetic field energy. / Deparis, Olivier; Lambin, Philippe.

Dans: Journal of Modern Optics, Vol 65, Numéro 2, 12.10.2017, p. 213-220.

Résultats de recherche: Contribution à un journal/une revueArticle

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AB - In periodic optical media, the group velocity is defined as the gradient with respect to wave-vector of the corresponding Bloch mode frequency dispersion curve, forming the photonic band structure. Instead of deducing it from the numerically computed photonic crystal band structure, the group velocity can be calculated directly from the integral of the Poynting vector over the crystal unit cell, the physical meaning of which is immediately perceivable. The related formula, which can be regarded as the application of Hellmann–Feynman theorem to electromagnetism, has been reported previously though without proof. We provide hereafter a full derivation of that formula starting from Maxwell’s equations and we discuss its usefulness in photonics.

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