Coated sphere, scattering

The classical method of solving scattering problems, separation of variables, has been applied previously in this book to a homogeneous sphere, a coated sphere (a simple example of an inhomogeneous particle), and an infinite right circular cylinder. It is applicable to particles with boundaries coinciding with coordinate surfaces of coordinate systems in which the wave equation is separable. By this method Asano and Yamamoto (1975) obtained an exact solution to the problem of scattering by an arbitrary spheroid (prolate or oblate) and numerical results have been obtained for spheroids of various shape, orientation, and refractive index (Asano, 1979 Asano and Sato, 1980). 

The mathematical form of all the scattering functions for a coated sphere—efficiencies and matrix elements—have the same form as those for a homogeneous sphere. Only the scattering coefficients (8.2) are different these may be written in a form more suitable for computations ... 

They found, that for a concentric sphere with a variable coating, the scattering was not sensitive to the form of the variation in the shell whenever there was a constant amount of refractive material (m = 1.0738). For inhomogeneous spheres with either a Cauchy or parabolic distribution, the forward scattering... 

Heng RL, Sy KC, Pilon L Absorption and scattering by bispheres, quadspheres, and circular rings of spheres and their equivalent coated spheres, J Opt Soc Am A 32(l) 46-60, 2015. 

Figure 18.4 shows the results obtained from such SLS experiments. The scattering intensity is plotted as a )/ R ) as a function of the molar water-to-surfactant ratio, co. The experimental data are compared with a coated sphere model containing two adjustables, with one being the proportionality constant L entering equation (18.25), and the second the polydispersity index of the droplets e. The former parameter only causes a vertical shift of the curve, while its shape is entirely determined by the polydispersity. Three different polydispersity indices were used to predict this curve, and the results turn out to be very sensitive to these values. Thus, the polydispersity index can be determined from such an experiment with good confidence, and the result yields the values 0.12 and L 2 0.15 nm. 

Figure 18.8. Dynamic light scattering measurements of the apparent hydrodynamic radii of water-in-oil microemulsion droplets with the surfactant sodium bis(2-ethylhexyl) sulfos-uccinate (AOT) as a function of the water-to-surfactant molar ratio 0). The continuous lines are calculated with a coated sphere model for different polydispersity indices (20)...

W. Sun, N. G. Loeb and Q. Fu, Light scattering by coated sphere immersed in absorbing medium a comparison between the FDTD and analytic solutions. Journal of Quantitative Spectroscopy Radiative Transfer 83 (2004), 483- 492. 

Kaiser, T., Schweiger, G., Stable Algorithm for the Computation of Mie Coefficients for Scattered and Transmitted Fields ofa Coated Sphere, Comput Phys., 1993, 7, 682-686. 

K.A. Fuller, Scattering of light by coated spheres. Opt. Lett. 18, 257 (1993) K.A. Fuller, Scattering and absorption cross sections of compounded spheres. 

Goudonnet J.P., Begun G.M., Arakawa E.T., Surface-enhanced Raman-scattering on silver-coated Teflon sphere substrates, Chem. Phys. Lett. 1982 92 197-201. 

Silica has been used both as a core and shell material. For example, monodis-persed silica spheres were coated with titania by decomposing titanyl sulfate, TiOS04, in acidic solutions at 90°C (146). The particles so produced showed good hiding power, to be useful as paper whiteners (147). Due to the uniformity of the cores and shells, the optical properties of such dispersions were predictable and reproducible, as shown in Figure 1.1.22, which compares the scattering coefficient,... 

I he field scattered by any spherically symmetrical particle composed of materials described by the constitutive relations (2.7)-(2.9) has the same form as that scattered by the homogeneous sphere considered in Chapter 4. However, the functional form of the coefficients an and bn depends on the radial variation of e and ju. In this section we consider the problem of scattering by a homogeneous sphere coated with a homogeneous layer of uniform thickness, the solution to which was first obtained by Aden and Kerker (1951). This is one of the simplest examples of a particle with a spatially variable refractive index, and it can readily be generalized to a multilayered sphere. 

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... 

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