Effective optical constants

Another kind of effective or average optical constants involves mixtures of different particles such as atmospheric aerosols or soils. Effective optical constants for compacted samples of these mixtures might be inferred from reflectance and transmittance measurements as if the samples were homogeneous. But scattering or extinction calculations based on these optical constants would not necessarily be correct. 

An example of practical importance in atmospheric physics is the inference of effective optical constants for atmospheric aerosols composed of various kinds of particles and the subsequent use of these optical constants in other ways. One might infer effective n and k from measurements—made either in the laboratory or remotely by, for example, using bistatic lidar—of angular scattering fitting the experimental data with Mie theory would give effective optical constants. But how effectual would they be Would they have more than a limited applicability Would they be more than merely consistent with an experiment of limited scope It is by no means certain that they would lead to correct calculations of extinction or backscattering or absorption. We shall return to these questions in Section 14.2. 

Quantitative simulation of spectra as outlined above is complicated for particle films. The material within the volume probed by the evanescent field is heterogeneous, composed of solvent entrapped in the void space, support material, and active catalyst, for example a metal. If the particles involved are considerably smaller than the penetration depth of the IR radiation, the radiation probes an effective medium. Still, in such a situation the formalism outlined above can be applied. The challenge is associated with the determination of the effective optical constants of the composite layer. Effective medium theories have been developed, such as Maxwell-Garnett 61, Bruggeman 62, and other effective medium theories 63, which predict the optical constants of a composite layer. Such theories were applied to metal-particle thin films on IREs to predict enhanced IR absorption within such films. The results were in qualitative agreement with experiment 30. However, quantitative results of these theories depend not only on the bulk optical constants of the materials (which in most cases are known precisely), but also critically on the size and shape (aspect ratio) of the metal particles and the distance between them. Accurate information of this kind is seldom available for powder catalysts. 

According to the EMT, the effective optical constants of an islandlike film depend on the packing density of the particles, the optical constants of the surroundings, and the polarizability of the mutually interacting metal islands... 

This free path value is not an estimate of the average particle size, as in addition to size there are other unmanageable factors contamination, crystalline structure defects etc. But it is quantity 1 that determines the effective optical constants of a medium, which are used in further calculations to estimate the pwameters of AgPG holograms. Comparison of effective optical parameters of "ideal" (with pjarticles 1 = 8 nm) and real (with particles 1 = 2 nm) media with identical structure piarameters, whose calculated values are given on Fig. 5a, shows the attenuation sp>ectrum of real medium to be essentially wider than that of the "ideal" one, whereas the change of refractive index due to the presence of silver particles (AnAg) is practically the same and is determined by their concentration, CAg, (the quoted calculations used the volume silver concentration in the medium equal to ICH). 

Having obtained values of A and p for the electrode/solution interface of interest, or more commonly detected changes as the electrode potential is varied, the next step is to relate these values to the properties of the interface. As with all reflection techniques, this is usually done in terms of a three layer model consisting of bulk substrate/interfacial region/bulk solution as shown in Fig. 10.10. Assuming the optical constants of the substrate and solution and the film thickness are known, it is possible to obtain unique values of the effective optical constants of the interphase from A and p [15]. The optical characteristics of any phase are simply defined by p, the magnetic permeability (usually equal to unity) and either the wavelength dependent complex dielectric constant defined by Equation (10.11)... 

The expressions for scattered light intensity (and Rayleigh ratio) must be corrected by dividing by the appropriate Cabannes factor. Effectively this is equivalent to replacing the optical constant K as defined in Eq. (24) by Kf and by 2 Kfj for unpolarised and vertically polarised incident light respectively. 

From a practical point of view the consequences of TOF dispersion are important only for short intrinsic fluorescence decay times of to < 1 nsec. Figure 8.15 shows an example with to = 50 psec and realistic optical constants of the substrate. The intensity maximum in Fb(t) is formed at At 30 psec after (5-excitation. After this maximum, the fluorescence decays with an effective lifetime of r ff = 100 psec that increases after long times to t > > 500 psec. The long-lived tail disappears as soon as there is some fluorescence reabsorption, and for Ke = K there is practically no difference to the intrinsic decay curve (curve 3 in Figure 8.15). 

In 10 there a great variety of materials is used, and their optical constants may be affected e.g. by film deposition technologies. What is thus required is the access to data for material dispersion with relation to technological parameter as well, either as Sellmeier or related formula, or as tabulated values. Additionally, refractive indices respond to temperature, which may be intended for device operation in case of a TO-switch, or unintended in field use. The temperature dependence of the refractive index can be attributed to the individual material, simply, but the influence of heater electrodes needs special consideration. If an 10 design-tool comes with inherent TO or EO capabilities, those effects are taken into account in the optical design directly. 

C urves of extinction as a function of size parameter show a wealth of features, even when calculated with uninteresting constant optical constants, as has often been done. When realistic optical constants are used in calculations the different types of extinction effects become even more numerous. In this section we incorporate optical constants of the three illustrative materials of... 

Mie theory does an admirable job of predicting extinction by spherical particles with known optical constants even the finest details it predicts—ripple structure—have been observed in extinction by single spheres. Several different causes—a distribution of sizes or shapes, and absorption—have the same effect of effacing the ripple structure or even the broader interference structure. 

The curves of Fig. 12.17 nicely illustrate the varied optical effects exhibited by small metallic particles in the surface mode region, both those explained by Mie theory with bulk optical constants and those requiring modification of the electron mean free path (see Section 12.1). Absorption by particles with radii between about 26 and 100 A peaks near the Frohlich frequency (XF — 5200 A), which is independent of size. Absorption decreases markedly at longer... 

Fig. 88. Theoretical spectra of gold-coated silver colloids. The optical constants were taken from Johnston and Christy [536], The dielectric constants were corrected for the effect of the mean free path using the method proposed [537] by Kreibig [534]...

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