Classical light dispersion theory in a regular lattice
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 LorentzDirac 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.
 Authors:
 Dipartimento di Matematica, Universita di Milano, via Saldini 50, I20133 Milan (Italy). Email: Massimo.Marino@unimi.it
 Dipartimento di Matematica, Universita di Milano, via Saldini 50, I20133 Milan (Italy). Email: carati@mat.unimi.it
 Dipartimento di Matematica, Universita di Milano, via Saldini 50, I20133 Milan (Italy). Email: galgani@mat.unimi.it
 Publication Date:
 OSTI Identifier:
 20976744
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Annals of Physics (New York); Journal Volume: 322; Journal Issue: 4; Other Information: DOI: 10.1016/j.aop.2006.11.006; PII: S00034916(06)002569; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CRYSTALS; CUBIC LATTICES; DIPOLES; DIRAC EQUATION; DISPERSION RELATIONS; ELECTROMAGNETIC FIELDS; EXACT SOLUTIONS; LATTICE PARAMETERS; OSCILLATIONS; OSCILLATORS; POTENTIALS; WAVELENGTHS
Citation Formats
Marino, M., Carati, A., and Galgani, L.. Classical light dispersion theory in a regular lattice. United States: N. p., 2007.
Web. doi:10.1016/j.aop.2006.11.006.
Marino, M., Carati, A., & Galgani, L.. Classical light dispersion theory in a regular lattice. United States. doi:10.1016/j.aop.2006.11.006.
Marino, M., Carati, A., and Galgani, L.. Sun .
"Classical light dispersion theory in a regular lattice". United States.
doi:10.1016/j.aop.2006.11.006.
@article{osti_20976744,
title = {Classical light dispersion theory in a regular lattice},
author = {Marino, M. and Carati, A. and Galgani, L.},
abstractNote = {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 LorentzDirac 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.},
doi = {10.1016/j.aop.2006.11.006},
journal = {Annals of Physics (New York)},
number = 4,
volume = 322,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}

The dependence of the nonlinear refractive index of an optical medium on the optical wave frequency in the classical theory of dispersion of highintensity light is shown to have the same form as in the quantum theory if a structural unit of substance in the Lorentz model is considered as two parametrically coupled nonlinear oscillators rather than one oscillator. 13 refs.

Lack of dispersion cancellation with classical phasesensitive light
Shapiro recently argued that nonlocal dispersion cancellation using entangled pairs of photons is essentially classical in nature, based on a comparison with a classical model in which two stationary, chaotic beams of light have phases and frequencies that are anticorrelated, which he refers to as 'phasesensitive' light [J. H. Shapiro, Phys. Rev. A 81, 023824 (2010)]. It is shown here that there is no physical cancellation of dispersion for classical light of that kind and Shapiro's results merely reflect the fact that identical dispersion occurs in both beams. The origin of the cross correlations between the intensities of the twomore »