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Anisotropic sphere, scattering

The reason for the intractability of the anisotropic sphere scattering problem is the fundamental mismatch between the symmetry of the optical constants and the shape of the particle. For example, the vector wave equation for a uniaxial material is separable in cylindrical coordinates that is, the solutions to the field equations are cylindrical waves. But the bounding surface of the... [Pg.184]

In this chapter we consider theories of scattering by particles that are either inhomogeneous, anisotropic, or nonspherical. No attempt will be made to be comprehensive our choice of examples is guided solely by personal taste. First we consider a special example of inhomogeneity, a layered sphere. Then we briefly discuss anisotropic spheres, including an exactly soluble problem. Isotropic optically active particles, ones with mirror asymmetry, are then considered. Cylindrical particles are not uncommon in nature—spider webs, viruses, various fibers—and we therefore devote considerable space to scattering by a right circular cylinder. [Pg.181]

We have discussed intrinsically anisotropic particles—ones with anisotropy originating in their optical constants rather than their shape—in previous chapters. In Section 5.6 we gave the solution to the problem of scattering by an anisotropic sphere in the Rayleigh approximation. From the results of that section and Section 5.5 it follows that the average cross section (C) (scattering or absorption) of a collection of randomly oriented, sufficiently small, anisotropic spheres is... [Pg.184]

A special anisotropic particle scattering problem has been treated by Roth and Dignam (1973), who considered an isotropic sphere coated with a uniform film with constitutive relations... [Pg.185]

Scattering media to which this matrix applies include randomly oriented anisotropic spheres of substances such as calcite or crystalline quartz (uniaxial) or olivine (biaxial). Also included are isotropic cylinders and ellipsoids of substances such as glass and cubic crystals. An example of an exactly soluble system to which (13.21) applies is scattering by randomly oriented isotropic spheroids (Asano and Sato, 1980). Elements of (13.21) off the block diagonal vanish. Some degree of alignment is implied, therefore, if these matrix elements... [Pg.413]

To find a value for the radius R of the spherulites the angle 6 corresponding to the maxima of scattered intensity for crossed polarisers is measured. If it is assumed that the spherulite can be approximated by an isolated anisotropic sphere embedded in an isotropic matrix, a detailed theoretical treatment then shows that... [Pg.135]

The scattering from such structures may be described surprisingly well by the idealised model of isolated anisotropic sphere having radial and tangential polarisabilities a, and at and radius R which is imbedded in an isotropic uniform matrix of polarisability a,. This leads to the equations ... [Pg.121]

Figure 123 Variation of H, scattered light intensity at 45° for (a) optically anisotropic spheres, (b) optically isotropic spheres in each case u = (4imr/Ao)sin(0/2). (a) Reprinted with permission from Macromolecules, 1982, IS, 1004 (b) reprinteid with permission from [53]. Copyright 1982 and 1993 American Chemical Society... Figure 123 Variation of H, scattered light intensity at 45° for (a) optically anisotropic spheres, (b) optically isotropic spheres in each case u = (4imr/Ao)sin(0/2). (a) Reprinted with permission from Macromolecules, 1982, IS, 1004 (b) reprinteid with permission from [53]. Copyright 1982 and 1993 American Chemical Society...
Meeten GH, Navard P. Small-angle scattering of polarized light. 1. Comparison of theoretical predictions for isotropic and anisotropic spheres. J Polym Sci B 1989 27 2023-2035. [Pg.177]

K. L. Wong, H.T. Chen, Electromagnetic scattering by a uniaxially anisotropic sphere, Proc. IEEE 139, 314 (1992)... [Pg.315]

Refractive Index and Orientation Fluctuations in Semicrystalline Polymers. The crystals of semicrystalline pol5nners are optically anisotropic. The simplest spherulite-based model for predicting light scattering is a sphere of radius r with a different polarizability in the radial direction Uj. than in the tangential direction (25). Assuming vertically polarized incident light, the intensities of the two scattered components (vertical and horizontal) are... [Pg.5351]

F IZJ Contour plots of scattered light intensity from (a) optically anisotropic sfriieres (b) optically isotroi c spheres x — r sin, y = rcos, where r is the radius of the sphere... [Pg.301]

The same incoherent quasi-elastic neutron scattering methods have been used to probe the molecular dynamics of more complex systems. Fatty acid salts of copper form a disk-like molecule comprising a binuclear core with four chains extending from it, and these can form a columnar mesophase where the disks are stacked. Copper palmi-tate has been examined in its crystalline phase and in a columnar mesophase. The quasi-elastic scattering was interpreted in terms of the motion of the alkyl chains. Each methylene group explored a spherical volume and the radius of the sphere increased with distance from the copper core [68], A later experiment on oriented fibers of copper laurate [69] showed that this motion was anisotropic with a greater amplitude in the plane perpendicular to the columns. [Pg.727]

This expression can be very considerably simplified, as explained in more detail by Degiorgio, et al. whose discussion is followed here(lO). If, as is the case in the experiments discussed below, the scattering particles are mechanically spherical but internally optically anisotropic, the orientations of pairs of spheres are uncorrelated, so the product aj(0)ak(t) causes the distinct (j 7 k) terms to average to zero, leading to... [Pg.298]


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See also in sourсe #XX -- [ Pg.152 , Pg.153 , Pg.184 , Pg.185 ]




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