Refractive indices wave scattering

Several theories have been developed to explain the rainbow phenomena, including the Lorenz-Mie theory, Airy s theory, the complex angular momentum theory that provides an approximation to the Lorenz-Mie theory, and the theory based on Huy gen s principle. Among these theories, only the Lorenz-Mie theory provides an exact solution for the scattering of electromagnetic waves by a spherical particle. The implementation of the rainbow thermometry for droplet temperature measurement necessitates two functional relationships. One relates the rainbow angle to the droplet refractive index and size, and the other describes the dependence of the refractive index on temperature of the liquid of interest. The former can be calculated on the basis of the Lorenz-Mie theory, whereas the latter may be either found in reference handbooks/literature or calibrated in laboratory. 

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). 

Mie s Theory. Mie applied the Maxwell equations to a model in which a plane wave front meets an optically isotropic sphere with refractive index n and absorption index k [1.26]. Integration gives the values of the absorption cross section QA and the scattering cross section Qs these dimensionless numbers relate the proportion of absorption and scattering to the geometric diameter of the particle. The theory has provided useful insights into the effect of particle size on the color properties of pigments. 

When a monochromatic, coherent light is incident into a dilute macromolecule solution, if solvent molecules and macromolecules have different refractive index, the incident light is scattered by each illuminated macromolecule to all directions [9, 10]. The scattered light waves from different macromolecules mutually interfere, or combine, at a distant, fast photomultiplier tube detector and produce a net scattering intensity I(t) or photon counts n(t) which is not uniform on the detection plane. If all macromolecules are stationary, the scattered light intensity at each direction would be a constant, i.e. independent of time. 

Figure 9A (a) The incoming pump beam kp is scattered at the scattering center S. (b) The scattered wave ks interferes with the propagating pump beam. A sinusoidal light interference pattern /(r) occurs, which is transferred into a refractive-index modulation An(r) via the pho-torefractive effect, (c) The pump beam is diffracted at the recorded refractive index modulation. Initially scattered light in direction of the polar axis is depleted and amplified in the opposite direction. 

For isotropic spherical particles of given refractive index in a medium of known refractive index, the exact form of C can be found by matching the incident, internal and scattered electromagnetic waves at the particle surface, subject to certain boundary conditions7. The solution comes in the form of an infii te series ... 

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