Complex Refractive Method

Table III shows that the experimental and predicted evaporation rates are in good agreement at all beam intensities. There is some inconsistency at the highest power levels. It was difficult to maintain the droplet in the center of the laser beam at the highest power level, and the measured evaporation rate is somewhat low as a result of that problem. Additional computations demonstrate that the predicted evaporation rate is quite sensitive to the choice of the imaginary component of N, so the results suggest that this evaporation method is suitable for the determination of the complex refractive index of weakly absorbing liquids. For strong absorbers, the linearizations of the Clausius-Clapeyron equation and of the radiation energy loss term in the interfacial boundary condition may not be valid. In this event, a numerical solution of the governing equations is required. The structure of the source function, however, makes this a rather tedious task.

It should, however, be noted that there exist rather complex and nontransparent descriptions made [15] in terms of the absorption vibration spectroscopy of water. This approach takes into account a multitude of the vibration lines calculated for a few water molecules. However, within the frames of this method for the wavenumber1 v < 1000 cm-1, it is difficult to get information about the time/spatial scales of molecular motions and to calculate the spectra of complex-permittivity or of the complex refraction index—in particular, the low-frequency dielectric spectra of liquid water. 

The reflectivity spectra R(E) and the reflectivity-EXAFS Xr(E) = R(E) — Rq(E)]/R()(E) are similar, but not identical, to the absorption spectra and x(E) obtained in transmission mode. R(E) is related to the complex refraction index n(E) = 1 — 8(E) — ifl(E) and P(E) to the absorption coefficient /i(E) by ji fil/An. P and 8 are related to each other by a Kramers-Kronig transformation, p and 8 may be also separated in an oscillatory (A/ , AS) and non-oscillatory part (P0,80) and may be used to calculate Xr- This is, briefly, how the reflectivity EXAFS may be calculated from n(E). which itself can be obtained by experimental transmission EXAFS of standards, or by calculation with the help of commercial programs such as FEFF [109] with the parameters Rj, Nj and a, which characterize the near range order. The fit of the simulated to measured reflectivity yields then a set of appropriate structure parameters. This method of data evaluation has been developed and has been applied to a few oxide covered metal electrodes [110, 111], Fig. 48 depicts a condensed scheme of the necessary procedures for data evaluation. 

Birefringence and dichroism represent two optical methods which can be applied to materials under flow conditions, forming the basis of Optical Rheometry [3,4]. The aim of these two techniques is to measure the anisotropy of the complex refractive index tensor n = n - i n". Birefringence is related to the anisotropy of the real part, whereas dichroism deals with the imaginary part. Recent applications of birefringence measurements to polymer melts can be foimd in Chapter III.l of the present book. 

The method is based on the magnetorefractive effect (MRE). The MRE is the variation of the complex refractive index (dielectric function) of a material due to change in its conductivity at IR frequencies when a magnetic field is applied. A direct measure of the changes of dielectric properties of a material can be performed by determining its reflection and transmission coefficients. Hence, IR transmission or reflection spectroscopy can provide a direct tool for probing the spin-dependent conductivity in GMR and TMR [5,6]. 

Polarimetry is a powerful method for studying solar-system bodies. It has allowed the determination of such parameters as the complex refractive index of particles in planetary atmospheres, the size distribution functions of these particles, the methane concentrations, the atmospheric pressure values above the cloud layers, etc. Independent spectral analyses of linear P) and circular (V) polarization observational data also may facilitate the determination of physical characteristics of particles at different heights in a planetary atmosphere. Polarimetiy enables us to make qualitative conclusions about... 

The purpose of obtaining spectral data on the complex refractive Index of polycarbonate polymer was to permit detailed Interpretations to be made of the IR-RA spectra collected In situ on metal-backed films of this material. Several of the principal methods for obtaining the optical constants n and k of an Isotropic medium have been reviewed by Humphreys-Owen [18]. All of the methods outlined are Insensitive to k when k Is close to zero, which Is the case for frequencies between absorbance bands. For this study, a polarlmetrlc technique (method D In Ref. 18) was chosen to obtain the optical constants of BPA-PC. To apply this method, the ratio of surface reflectances Rp/Rg at two large, but well-separated, angles of Incidence (9 ) was obtained for BPA-PC In the IR. Rp Is defined as the reflectance measured for a sample using radiation polarized parallel to the Incidence plane and R... 

Ellipsometry is a useful method if a consistent set of optical parameters k, n) can be determined. Then a measurement of the complex refraction index allows the determination of d and k. 

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). 

In order to calculate the optical generation rates in the organic absorbers (see appendix 1), it is necessary to determine the complex refractive index n = n + ik of all layers. The most useful method to obtain this data is spectroscopic ellipsometry, which allows us to determine the real part n and imaginary part k of the refractive index. The general measurement principle of ellipsometry is to measure the polarization of an output beam after the polarized input beam has interacted with the sample. From the change in polarization we derive the optical properties of the layer by fitting the measured output polarization to a model of the optical response of the material [144]. 

There is a consensus that Maxwell s equations work fine for nanoparticles with size down to at least 1 nm. In other words, a good fit of experimental data can be obtained using a rigorous simulation method and proper data for the complex electric permittivity e or equivalently the complex refractive index h [36]. This makes choosing a particular value of e an important practical question, which can be divided into two parts ... 

As described in detail in Chapter 8, calculations based on the Kramers-Kronig relations give the real and imaginary parts of a complex refractive index (n(v) and k(v) see Section 1.2.4) from a reflection spectrum measured by the method of specular reflection from a... 

The multi-wavelength ellipsometiy (i.e., spectroscopic elhpsome-try) can characterize spectroscopic property of the passive oxide. Figure 24 indicates spectra of the complex refractive index, N2 = 2 - j 2, of the passive oxide formed on iron at 1.43 V vs. reversible hydrogen electrode at the same solution (RHE) in pH 8.4 borate solution and in pH 3.1 phosphate solution for 1 In Fig. 24, the thickness of the passive oxide was estimated at each wavelength of incident light. The measurement and estimation were made by the 3-parameter method. Similar results were also reported by Cahan et al. " ... 

Figure 8.36 shows a calculated plot with r a=5 ander,fi=80. Curve parameter is the exponent a. Data points for sandstone (Fig. 8.33) are plotted in the curve set. The experimental data correspond with calculated curves for an exponent a = 0.35-0.70. The Complex Refractive Index Method (CRIM) curve (see Section 8.7.4.3) with the exponent a = 0.5 gives a good approximation. 

The philosophy of Wyllie s time-average formula (see Section 6.6.2) leads to the CRIM or Complex Refractive Index Method formula (Calvert et al., 1977). The time-average equation is explained as a summation of the travel time of the signal passing the solid matrix and the pore fluid both rock components are condensed as a layer. 

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