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Point scatterers for classical waves

Pedro de Vries, David V. van Coevorden, and Ad Lagendijk

Pedro de Vries

  • Van der Waals–Zeeman Institute, University of Amsterdam, Valckenierstraat 65-67, 1018 XE Amsterdam, The Netherlands

David V. van Coevorden

  • FOM-Institute for Atomic and Molecular Physics, Kruislaan 407, 1098 SJ Amsterdam, The Netherlands

Ad Lagendijk

  • Van der Waals–Zeeman Institute, University of Amsterdam, Valckenierstraat 65-67, 1018 XE Amsterdam, The Netherlands

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Rev. Mod. Phys. 70, 447 – Published 1 April, 1998

DOI: https://doi.org/10.1103/RevModPhys.70.447

Abstract

The authors present a closed formulation of resonant point scatterers for classical-wave propagation problems. A Green’s-function approach is employed in which all the small-distance singularities are regularized. Application of point scatterers considerably simplifies multiple-scattering calculations needed, for instance, for understanding the optical properties of dense cold gases and optical lattices. In the case of the vector description of light, it is shown that two different regularization parameters are required in order to obtain physically meaningful results. One parameter is related to the physical size of the pointlike scattering particle, while the other is connected to its dynamic properties. All parameters involved are defined in terms of physical observables leading to a complete and self-consistent treatment. The applicability of the point-scatterer model to several physical models is demonstrated. We calculate the local density of states of waves in the presence of one resonant point scatterer. For the vector case, the bare polarizability is shown to enter the local density of states. For a collection of resonant point dipoles, the Lorentz-Lorenz relation for the dielectric constant is derived for cubic lattices and for disordered arrangements.

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Rev. Mod. Phys. 70, 447– Published 1 April, 1998

    © 1998 American Physical Society

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