Scattering matrix theory for stochastic scalar fields

Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.
Physical Review E (Impact Factor: 2.29). 06/2007; 75(5 Pt 2):056609. DOI: 10.1103/PhysRevE.75.056609
Source: PubMed


We consider scattering of stochastic scalar fields on deterministic as well as on random media, occupying a finite domain. The scattering is characterized by a generalized scattering matrix which transforms the angular correlation function of the incident field into the angular correlation function of the scattered field. Within the accuracy of the first Born approximation this matrix can be expressed in a simple manner in terms of the scattering potential of the scatterer. Apart from determining the angular distribution of the spectral intensity of the scattered field, the scattering matrix makes it possible also to determine the changes in the state of coherence of the field produced on scattering.

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    • "Xin et al presented a model describing the outline of QH electromagnetic beams scattered by a QH medium in the three-dimensional rectangular coordinate system [18] [19]. On the other hand, the theory of the scalar light field scattered from a collection of anisotropic particles has been well developed by Sahin and Korotkova [20], by utilizing a generalized scattering matrix [21]. Very recently, Wang and Zhao deduced the condition that, for the case that a completely coherent scalar plane wave incident on a random medium, the corresponding spectral degree of coherence of the scattered field may remain invariant in the entire scattering 2040-8978/11/115702+08$33.00 © 2011 IOP Publishing Ltd Printed in the UK & the USA process [22]. "
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    ABSTRACT: Within the accuracy of the first-order Born approximation, the fourth-order correlation statistics of an electromagnetic plane wave scattering from a quasi-homogeneous (QH) medium is studied. Under the assumption that the fluctuations of the scattering potential obey Gaussian statistics, the moment theorem for a complex Gaussian random process is utilized to formulate fourth-order correlations for the case of an electromagnetic plane wave incident on a QH medium. The effects of the polarization of the incident plane waves and the scattering azimuth angles on the correlation properties are discussed by numerical examples. It is verified that, in general, the numerical values of the correlations between intensity fluctuations for the electromagnetic case cannot exceed those for the scalar case. Only when a certain limitation to the scattering angles or initial polarization is imposed are the values for the two cases equal to one another.
    Journal of optics 10/2011; 13(11):115702. DOI:10.1088/2040-8978/13/11/115702 · 2.06 Impact Factor
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    ABSTRACT: Using the angular spectrum representation of fields and the first Born approximation we develop a theory of scattering of scalar waves with any spectral composition and any correlation properties from collections of particles which have either deterministic or random distributions of the index of refraction and locations. An example illustrating the far-field intensity and the far-field spectral degree of coherence produced on scattering of a model field from collections of several particles with Gaussian potentials is considered.
    Physical Review A 12/2008; 78(6). DOI:10.1103/PhysRevA.78.063815 · 2.81 Impact Factor
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    ABSTRACT: Using scattering matrices and the angular spectrum representation of waves, we develop the analytical theory of scattering of random scalar waves from random collections of particles, valid under the first Born approximation. We demonstrate that in the calculation of far-field statistics, such as the spectral density and the spectral degree of coherence, the knowledge of the pair-structure factor of the collection is crucial. We illustrate our analytical approach by considering a numerical example involving scattering of two partially correlated plane waves from a random distribution of spheres.
    Optics Letters 07/2009; 34(12):1762-4. DOI:10.1364/OL.34.001762 · 3.29 Impact Factor
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