Effective refractive index theories

Classic perturbation theory considerations [55] predicts that changes in the effective refractive index of a guided mode A eff are related to the changes in the... 

Porous silicon can be specified as an effective medium, whose optical properties depend on the relative volumes of silicon and pore-filling medium. Full theoretical solutions can be provided by different effective medium approximation methods such as Maxwell-Gamett s, Looyenga s, or Bruggeman s (Arrand 1997). Effective medium theory describes the effective refractive index, fieff, of porous silicon as a function of the complex refractive index of silicon, fisi, and that of the porefilling material, flair = 1, for air. The porosity P and the topology of the porous structure will also affect fleff (Theiss et al. 1995). 

The effective medium theory (EMT) or the homogenization method regards a structured diffractive medium as a homogeneous material with an effective refractive index equal to a weighted and spatially averaged value of the refractive index of both structural materials. This is a very old theory and it was considered even in the works of Lord Rayleigh near the end of the nineteenth century. 

A quantitative description does become possible, however, if the system under examination satisfies special conditions. These include diffuse, monochromatic illumination, homogeneous pigmentation, isotropic scattering in the coating, no difference in refractive index between vehicle and air, and a coating so thick that the substrate has no effect on the exiting radiation. This is the special case treated by the Kubelka-Munk theory. 

Usually, the most general nonspecific effects of dipole-orientational and electronic polarization of the medium are discussed, and the results of the theory of relaxational shifts developed under the approximation of a continuous dielectric medium may be used.(86 88) The shift of the frequency of the emitted light with time is a function of the dielectric constant e0, the refractive index n, and the relaxation time xR ... 

We should first correct the wavevector inside the crystal for the mean refractive index, by multiplying the wavevectors by the mean refractive index (1 + IT). This expression is derived from classical dispersion theory. Equation (4. 18) shows us that is negative, so the wavevector inside the crystal is shorter than that in vacuum (by a few parts in 10 ), in contrast to the behaviom of electrons or optical light. The locus of wavevectors that have this corrected value of k lie on spheres centred on the origin of the reciprocal lattice and at the end of the vector h, as shown in Figure 4.11 (only the circular sections of the spheres are seen in two dimensions). The spheres are in effect the kinematic dispersion surface, and indeed are perfectly correct when the wavevectors are far from the Bragg condition, since if D 0 then the deviation parameter y, 0 from... 

Very much more is known about the theory of concentration gradients at electrodes than has been mentioned in this brief account. Experimental methods for observing them have also been devised, based on the dependence of refractive index on concentration (the Schlieren method) by means of interferometry (O Brien, 1986). Nevertheless, the basic concept of an effective diffusion-layer thickness, treated here as varying in thickness with fi until the onset of natural convection and as constant with time after convection sets in (though decreasing in value with the degree of disturbance, Table 7.10), is a useful aid to the simple and approximate analysis of many transport-controlled electrodic situations. A few of the uses of the concept of 8 will now be outlined. 

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. 

The most evident reason is that dilute solution measurements can preferably be compared directly with the unmodified dilute solution theory as reviewed in Chapter 3. As has already been pointed out in Section 2.6.1, the form birefringence in dilute solution can effectively be suppressed by the choice of a solvent of practically the same refractive index as the polymer. In such a "matching solvent the contrast between the coil of the macromolecule and its surrounding practically disappears. This means that, at the same time, the influence of the shape (form) of the coil disappears. Also the comparison with measurements on con-... 

The a carbon shifts of haloalkanes depend on temperature and solvent. Strong solvent effects are observed for the iodinated carbon atoms in iodoalkanes, as shown in Table 4.18 [253]. As expected from theory [254], carbon-13 solvent shifts are linearly dependent on (e — l)/(2e + n2) (e dielectric constant n refractive index) [253]. 

The energy-dependent speed of light is associated with the effect of the medium on the propagation of photon. The fluctuating refractive index of the medium induces this kind of the energy dependence. This kind of the medium has been considered, such as quantum gravity and the Maxwell vacuum with nonzero conductivity. So, it to make distinction between the contributions from standard model predictions as well as from other theories is needed. 

It may appear very tempting to apply the Forster s formalism to the question of electrolyte effects onto the lifetime. However, some features of this effect render the use of the Forster s theory difficult experiments with Eu have shown that the observed variations cannot be reproduced solely on the basis of the refractive index changes, a term included in the Forster s... 

In contrast, EET has been historically modelled in terms of two main schemes the Forster transfer [15], a resonant dipole-dipole interaction, and the Dexter transfer [16], based on wavefunction overlap. The effects of the environment where early recognized by Forster in its unified theory of EET, where the Coulomb interaction between donor and acceptor transition dipoles is screened by the presence of the environment (represented as a dielectric) through a screening factor l/n2, where n is the solvent refractive index. This description is clearly an approximation of the global effects induced by a polarizable environment on EET. In fact, the presence of a dielectric environment not only screens the Coulomb interactions as formulated by Forster but also affects all the electronic properties of the interacting donor and acceptor [17],... 

---