Cylinders, scattering finite

In Chapter 8 we shall derive the field scattered by an infinite cylinder of arbitrary radius and refractive index we shall also consider scattering by a finite cylinder in the diffraction theory approximation. Although the finite cylinder scattering problem is not exactly soluble, we can obtain analytical expressions for the amplitude scattering matrix elements in the Rayleigh-Gan s approximation. 

Scattering factors have been calculated for a variety of more complicated particles e.g., oblate and prolate ellipsoids, cylinders of finite thickness, shells of different forms, particles of nonuniform density, and assemblages of simple geometrical shapes (see Ref. 19 and citations therein). 

Equation (8.43) provides us with an approximate criterion, subject to the limitations of diffraction theory, for when a finite cylinder may be regarded as effectively infinite if R > 10, say, there will be comparatively little light scattered in directions other than those in a plane perpendicular to the cylinder axis. The greater is R, the more the scattered light is concentrated in this plane in the limit of indefinitely large R, no light is scattered in directions other than in this plane. We may show this as follows. The phase function may be written in the form p(0, ) = G(0, )F(0, ), where... 

Fig. 3.18. Normalized differential scattering cross-sections of an oblate cylinder with ksb = 15 and 2ksa = 7.5. The cmves are computed with the TAXSYM routine, discrete somces method (DSM), multiple multipole method (MMP), discrete dipole approximation (DDA) and finite integration technique (CST)...

M.I. Mishchenko, L.D. Travis, A. Macke, Scattering of light by polydisperse, randomly oriented, finite circular cylinders, Appl. Opt. 35, 4927 (1996)... 

Figure 4 shows Nakamura and Norisuye s theoretical curves for KP cylinders with IL=1 and different Xd values. As the chain becomes thicker (for a fixed 2 ), the scattering curve lowers with a broad peak at a small k. This feature of the curve is similar to what was shown for flexible HW chains by Nagasaka et Another model for a polymer with finite thickness is a touched-bead chain, whose P k] is given exactly by the product of Po(fe) for the chain contour and the scattering function F(fedb) for spheres of diameter db, that is, by... 

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