Optical constants n and

The optical constants n and k are not independent if k varies strongly, so must n. Either n must be measured by some other method or a theory of optical constants that couples them together properly must be used, such as the oscillator model (9.25) or the Kramers-Kronig relations [(2.49), (2.50)]. 

With a four-phase model, the results are shown in Table 7.1 where the mean square error (MSE) represents the goodness-of-fit parameter. The uncertainties of the film thickness listed in Table 7.1 were obtained with a 90% confidence limit. To verify that the dispersion in the experimental spectral range (1.55-6.53 eV) is correct, we used the data inversion to obtain its pseudo-optical constants (< n ) and ). Theseconstants are calculated from the measured 4 and A using the film thickness obtained from the fitting. 

Embrey, P. G., and A. J. Criddle (1978). Error problems in the two media method of deriving the optical constants n and k from measured reflectances. Amer. Mineral. 63, 853-62. 

These equations are used to subtract the contribution of reflections on the interfaces of such a strongly absorbing medium as liquid water, when one wishes to calculate the optical constant k and at the same time n. It is also used (37) in the calculation of these optical constants n and k when the measured value log(/o(i )//(f )) is that obtained using another set-up,... 

Figure 5. (A2) Various spectral quantities related to liquid water in the mid-IR region. Experimental values of log(/Q(i )//(i )) are shown in the case of an absorption set-np with a 1 p,m thick sample and of an ATR cell with an immersed portion of the crystal about 3 cm long (41). The optical constants n and k are also displayed together with the imaginary dielectric constants e".

But the amplitude or as5unmetric Fourier spectroscopy has not been applied only to solids but also to liquid samples and gases. Here too, it has been proved an important help to obtain the two optical constants n and x simultaneously 62a,b) In gases, for example, the anomalous dispersion of the refractive index in the neighbourhood of rotational absorption lines was determined experimentally by this method. 

Finally for certain 2, coatings with anatase structure deposited on fused silica, the optical constants n and were determined [28] from intensity measurements. The values are shown in Fig. 7. As can be seen in the figure, there is again a slight dependence of n on thickness d. 

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... 

The change of state of polarization caused by the reflection is described by two quantities, which are both angles A, a phase change term, and f, the tangent of which describes the amplitude change. For a clean, bare surface, these quantities are related to the optical constants n and k of the substrate in a one-to-one mapping. Ellipsometry is therefore one of the principal ways of evaluating the optical constants of materials. 

On the other hand, the maximum absorption index of bands in the spectra of most organic molecules (including polymers) rarely exceeds 0.3 above 1000cm In these cases, ( 2 — 1) > and the reflection spectrum looks more like the n spectrum (see Figure Ab) than the k spectrum. The specular reflection spectrum of a polycarbonate polymer is shown in Figure 13.2. Few experienced spectroscopists would immediately recognize this spectrum as a polycarbonate. To convert this spectrum to the optical constant (n and k) spectra, the Kramers-Kronig... 

The usual first step in practice is to determine the optical constants n and k of the substrate—the electrode material—by measuring A and ij/ on the bare surface before the substrate is covered by a film. Measurements of A and are taken again after a film is formed on the substrate if the film is to be studied. The A and if/ of the bare substrate will be denoted by A and ij/. By substituting Eqs. (2a) and (2b) into Eq. (4) and then equating the real and imaginary parts on both sides of the equation, the following relations can be obtained ... 

FIGURE 59. Optical constants, n and of a Zn deposit on ZnO as a function of mean film thickness D, formed at two different deposition potentials. The optical constants of bulk Zn are indicated by the shaded areas. After Ref. 163. 

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