30 October 1998 Computer simulation studies of the speckle correlations of light scattered from a random array of dielectric spheres
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Abstract
The speckle correlations in the light scattered from a volume disordered dielectric medium consisting of a random array of dielectric spheres are studied using computer simulation techniques. The random medium is formed by placing dielectric spheres of radius R and dielectric constant (epsilon) randomly on the vertices of a simple cubic lattice, so that a fixed fraction (rho) of the vertices is occupied by the spheres. The region outside the spheres is vacuum, and the radius of the spheres is assumed to be much smaller than the lattice constant of the cubic lattice. For simplicity the electromagnetic fields are treated in a scalar wave approximation. The scalar wave field equations of this system are integrated numerically to determine the scattered fields, and these fields are used to calculate the speckle correlation function defined by C(vector q, vector kvector q', vector k') equals <{I(vector qvector k) - [I(vector qvector k)]} {I(vector q'vector k') - [I(vector q'vector k')]}>, where I(vector qvector k) is proportional to the differential scattering coefficient for the elastic scattering of light of wavevector vector k into light of wavevector vector q. In implementing our computer simulation we have considered a 9 X 9 X 9 cubic lattice that is occupied by 178 dielectric spheres of dielectric constant (epsilon) equals 9. The lattice constant a of the cubic lattice was taken to satisfy a/(lambda) equals 0.7 where (lambda) is the wavelength of the light in vacuum, and the radius of the dielectric spheres was taken such that R equals 0.0159 (lambda) . Results are presented for C(vector q, vector kvector q', vector k') in the approximation C equals C(1) plus C(10) plus C(1.5), where C(1), C(10) and C(1.5) are terms arising from three distinct scattering processes. The contribution C(1), which contains the memory and time-reversed memory effect terms, has been studied before, and is proportional to (delta) (vector q minus vector k minus vector q' plus vector k'). C(10) is a new term (of the same order of magnitude as C(1)) in the scattering of light from volume disorder, that is found to be proportional to (delta) (vector q minus vector k plus vector q' minus vector k'). C(1.5) is a new term in the scattering of light from volume disorder that exhibits an unrestricted dependence on vector q, vector k, vector q', vector k' and a series of interesting intensity peaks related to the resonant scattering of light by the volume disorder. The contributions C(10) and C(1.5) were considered in the earlier study of the speckle correlation function for the scattering of light from randomly rough surfaces, but have only recently been considered in the scattering of light from volume disorder.
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Arthur R. McGurn, Alexei A. Maradudin, "Computer simulation studies of the speckle correlations of light scattered from a random array of dielectric spheres", Proc. SPIE 3426, Scattering and Surface Roughness II, (30 October 1998); doi: 10.1117/12.328447; https://doi.org/10.1117/12.328447
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