dorsal/arxiv
View SchemaClassical light dispersion theory in a regular lattice
| Authors | M. Marino, A. Carati, L. Galgani |
|---|---|
| Categories | |
| ArXiv ID | physics/0702126 |
| URL | https://arxiv.org/abs/physics/0702126 |
| DOI | 10.1016/j.aop.2006.11.006 |
| Journal | Annals of Physics 322 (2007) 799-823 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
We study the dynamics of an infinite regular lattice of classical charged oscillators. Each individual oscillator is described as a point particle subject to a harmonic restoring potential, to the retarded electromagnetic field generated by all the other particles, and to the radiation reaction expressed according to the Lorentz--Dirac equation. Exact normal mode solutions, describing the propagation of plane electromagnetic waves through the lattice, are obtained for the complete linearized system of infinitely many oscillators. At variance with all the available results, our method is valid for any values of the frequency, or of the ratio between wavelength and lattice parameter. A remarkable feature is that the proper inclusion of radiation reaction in the dynamics of the individual oscillators does not give rise to any extinction coefficient for the global normal modes of the lattice. The dispersion relations resulting from our solution are numerically studied for the case of a simple cubic lattice. New predictions are obtained in this way about the behavior of the crystal at frequencies near the proper oscillation frequency of the dipoles.
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"abstract": "We study the dynamics of an infinite regular lattice of classical charged\noscillators. Each individual oscillator is described as a point particle\nsubject to a harmonic restoring potential, to the retarded electromagnetic\nfield generated by all the other particles, and to the radiation reaction\nexpressed according to the Lorentz--Dirac equation. Exact normal mode\nsolutions, describing the propagation of plane electromagnetic waves through\nthe lattice, are obtained for the complete linearized system of infinitely many\noscillators. At variance with all the available results, our method is valid\nfor any values of the frequency, or of the ratio between wavelength and lattice\nparameter. A remarkable feature is that the proper inclusion of radiation\nreaction in the dynamics of the individual oscillators does not give rise to\nany extinction coefficient for the global normal modes of the lattice. The\ndispersion relations resulting from our solution are numerically studied for\nthe case of a simple cubic lattice. New predictions are obtained in this way\nabout the behavior of the crystal at frequencies near the proper oscillation\nfrequency of the dipoles.",
"arxiv_id": "physics/0702126",
"authors": [
"M. Marino",
"A. Carati",
"L. Galgani"
],
"categories": [
"physics.optics",
"cond-mat.str-el",
"math-ph",
"math.MP",
"physics.class-ph"
],
"doi": "10.1016/j.aop.2006.11.006",
"journal_ref": "Annals of Physics 322 (2007) 799-823",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Classical light dispersion theory in a regular lattice",
"url": "https://arxiv.org/abs/physics/0702126"
},
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