INDEX electrodynamics

Phase functions can also be used to measure the size and refractive index of a microsphere, and they have been used by colloid scientists for many years to determine particle size. Ray et al. (1991a) showed that careful measurements of the phase function for an electrodynamically levitated microdroplet yield a fine structure that is nearly as sensitive to the optical parameters as are resonances. This is demonstrated in Fig. 21, which presents experimental and theoretical phase functions obtained by Ray and his coworkers for a droplet of dioctylphthalate. The experimental phase function is compared with two... 

The difference this derivation has in comparison to the previous derivation of the nonlinear Schrodinger equation is that the nonlinearity is more fundamentally due to the non-Abelian wavefunction rather than from material coefficients. In effect these material coefficients and phenomenology behave as they do because the variable index of refraction is associated with non-Abelian electrodynamics. Ultimately these two views will merge, for the mechanisms on how photons interact with atoms and molecules will give a more complete picture on how non-Abelian electrodynamics participates in these processes. However, at this stage we can see that we obtain nonlinear terms from a non-Abelian electrodynamics that is fundamentally nonlinear. This is in contrast to the phenomenological approach that imposes these nonlinearities onto a fundamentally linear theory of electrodynamics. 

In contrast to the present treatment there are two types of earlier theories of refraction of light. Yvon32 has developed a statistical-mechanical theory of the refractive index. This theory is set up in such a way that an explicit expression is obtained for the index of refraction. It does not, however, contain an analysis of the optical phenomena (such as the extinction of the incident field) which are involved. These last aspects are considered very carefully in the other, electrodynamic, type of theory, which Hoek,8 following work done by a number of authors, has presented with great rigor. The disadvantage of this second method is that macroscopic quantities are not obtained by statistical-mechanical methods, but by averaging the microscopic quantities oVer physically infinitesimal volume elements. The result is that almost all the effect of density fluctuations is lost. Both of the theories mentioned assume furthermore thp molecular polarizability to be a constant independent of intermolecular distances. 

If irradiation passes the interface from an optically denser medium to one of smaller refractive index, at angles larger than a certain limiting one (with respect to the perpendicular optical axis) the radiation will no longer leave the medium. It is totally reflected at the interface. Electrodynamics explain the fact that the reflected radiation couples to an evanescent field, which exponentially decreases into the medium of lower optical density. Thus the reflected beam gathers information about the optical properties of this medium across the interface. 

Figure 1 Experimental and calculated 1-dimensional Franhofer diffraction patterns from electrodynamically levitated polyethylene oxide (PEO) particles produced in situ with an on-demand droplet generator. ThePEO weight fractionsinwaterwere3,2.5 and 1% fora, b, and c respectively. The refractive index (1.461 0.001) determined from the data analysis is in good agreement with the refractive index ofbulk (1 OK molecular weight) PEO.

On the other hand, Forster showed a lot of insight by including the factor n in the denominator. This factor is not included in our derivation. It depends on the polarizability of the medium, since n is the refractive index. In our derivation, we have not accounted for the fact that there are a number of other electrous present that are not excited. In electrodynamics theory, these electrons are approximately taken into account by the factor of n 2 in the denominator. 

Dyson-type equations have been used extensively in quantum electrodynamics, quantum field theory, statistical mechanics, hydrodynamic instability and turbulent diffusion studies, and in investigations of electromagnetic wave propagation in a medium having a random refractive index (Tatarski, 1961). Also, this technique has recently been employed to study laser light scattering from a macromolecular solution in an electric field. 

Classical electrodynamics is the theoretical treatment used to describe the LSPR effect. The shape and size of the nanoparticles define the resonant response, as well as the theoretical treatment. Mie theory solves the sphere case, while almost no analytic calculations have been established for other nonspher-ical particles. When particles are small enough with respect to incident wavelength (X) (j = (InanmlX) 1, where a is the size of the particle and m is the surrounding media refractive index), same approximations can be achieved and Rayleigh extinction (Cext) cross section expression is obtained ... 

It is possible to understand many phenomena in optics and spectroscopy in terms of classical models based on concepts of classical electrodynamics. For example, the absorption and dispersion of electromagnetic waves in matter can be described using the model of damped oscillators for the atomic electrons. This model leads to a complex refractive index and to dispersion relations which give the link between absorption and dispersion. It is not too difficult to give a quantum mechanical formulation of the classical results in most cases. The semiclassical approach will be outlined briefly. 

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