Optical constants index, complex

The real and imaginary parts of the complex refractive index satisfy Kramers-Kronig relations sometimes this can be used to assess the reliability of measured optical constants. N(oj) satisfies the same crossing condition as X(w) N (u) = N( — u). However, it does not vanish in the limit of indefinitely large frequency lim JV(co) = 1. But this is a small hurdle, which can be surmounted readily enough by minor fiddling with JV(co) the quantity jV(co) — 1 has the desired asymptotic behavior. If we now assume that 7V( ) is analytic in the top half of the complex [Pg.28]

Mass of a molecule Mass of proton Mass of ion Concentration Avogadro constant Complex refraction index Optical refraction index Polarization... 

In this chapter we have reviewed a number of techniques used for optical characterization of organic samples, in particular those concerning the determination of complex optical constants and the dynamics of elementary photoexcitations. It has been stressed that very good optical quality samples are needed in order to obtain reliable estimates of the refractive index. In general, samples with controlled morphology, low defect and impurity concentration, and good optical quality allow more reliable photophysical studies and hence better determination of the intrinsic properties of the material. 

Thus, in principle, one can obtain the complex index of refraction from the upper left-hand quarter of the optical tensor M= [My, (i,j = 1,..., 3)]. We now explain how these optical constants can be derived from ellipsometry. 

Usually, the absorption coefficient of the conducting crystals is so high that producing a crystal sufficiently thin and suitable for absorption measurements presents a great difficulty. If this is so, the bulk optical constants of a solid may be computed from the normal-incidence reflectivity of that material over an extended range of frequencies, followed by a Kramers-Kronig analysis of the measurements [12,14]. In this method the real, n, and imaginary, k, parts of the complex index of refraction... 

The above relationships (Figure 1.10) show that the optical pigment properties depend on the particle size D and the complex refractive index n = n (1 - i/c), which incorporates the real refractive index n and the absorption index k. As a result, the reflectance spectrum, and hence the color properties, of a pigment can be calculated if its complex refractive index, concentration, and particle size distribution are known [1.40]. Unfortunately, reliable values for the necessary optical constants (refractive index n and absorption index k) are often lacking. These two parameters generally... 

In practice, the sharp cut-off predicted above never occurs, because absorption processes are not totally negligible. A sizable absorption means that the refractive index cannot be regarded as a real number and its complex nature (compare Eq. (11)) leads to a dispersion in the optical constants which results in a broadening of the sharp cut-off. 

In view of the experimental difficulties a theory for radiation properties is desirable. The classical theory of electromagnetic waves from J.C. Maxwell (1864), links the emissivity e x with the so-called optical constants of the material, the refractive index n and the extinction coefficient k, that can be combined into a complex refractive index n = n — ik. The optical constants depend on the temperature, the wavelength and electrical properties, in particular the electrical resistivity re of the material. In addition, the theory delivers, in the form of Fresnel s equations, an explicit dependence of the emissivity on the polar angle / , whilst no dependence on the circumferential angle ip appears, as isotropy has been assumed. 

Materials are characterized optically by their optical constants, i.e. the extinction coefficient and refractive index. The extinction coefficient k is the imaginary part of the complex refractive index N = n - ik It assumes the role of an index of attenuation. If this attenuation is caused by true absorption alone, it is termed the absorption coefficient k. The absorption (or extinction) constant is defined as a( = 4 n (J X, 1. Finally, 1 dB cm"1 = 4.34 a ... 

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... 

In order to interpret the reflectance spectrum, modeling of the interface is the key issue. For example, in the simulation above, we tacitly made some assumptions. One is that the change of the optical properties of the substrate and refractive index of the solution immediately adjacent to the film surface are independent of potential and the presence of the film. The use of the Fresnel model with optical constants is based on the assumption that the phases in the three-strata model are two-dimen-sionally homogeneous continua. However, if the adsorbed molecule is a globular polymer which possesses a chromophore at its core, a better model of the adsorption layer would be a homogeneously distributed point dipole incorporated in a colorless medium. To gain closer access to the interpretation of the spectrum, a more precise and detailed model would be necessary. But this may increase the number of adjustable parameters and may demand a too complex optical treatment to calculate mathematically. Moreover, one has to pile up approximations, the validity of which cannot easily be confirmed experimentally. 

Definition (optical constants) The refractive index, w, and the extinction coefficient, A , which together determine the complex refractive index N = n - ik of an absorbing medium. [41]... 

In this section, only the optical constants of isotropic films determined by the multiwavelength approach in IRRAS will be discussed. The optical constants are assumed to be independent of the film thickness, and any gradient in the optical properties of the substrate (Section 3.5) is ignored. This undoubtedly lowers accuracy of the results. Anisotropic optical constants of a film are more closely related to real-world ultrathin films. At this point, it is worth noting that approaches to measuring isotropic and anisotropic optical constants are conceptually identical An anisotropic material shows a completely identical metallic IRRAS spectrum to the isotropic one if the complex refractive index along the z-direction for the anisotropic material is equal to that for the isotropic one [44]. However, to... 

Tables 57.2-57.4 list the optical constants of some polymers at 157 nm. In these tables, and Jg are weight average molecular weight and glass transition temperature, respectively. Both the real (n) and imaginary k) parts of the complex refractive indices (n- -i ) are listed. The absorption coefficient (a) is correlated to the imaginary k) part of the refractive index via the following equation ...

Kramers-Kronig integrals can also be used to evaluate the optical constants from the experimentally measured reflectance or transmission. Let us consider the complex reflectance index r = exp , where is the reflectivity of the solid and 0(m) is the phase change between incident and reflected waves. KK integrals provide the connection between 0(m) and R o))-. 

Such a technique has been shown [26] to work well, for example, for the computation of the refractive index of CH3CN in the microwave and far-infrared. Crawford and co-workers [22-24] have also advocated using a correlation function based on the complex part of the local susceptibility, (introduced to correct for dielectric effects on the optical constants). In that case. 

Reflection occurs at any interface where the complex refractive index changes. We can define the medium with the lower refractive index as the optically rare medium and material with the higher refractive index as the optically dense medium. The optically dense medium will be designated by the subscript 2 and the optically rare medium will be designated by the subscript 1. We will just consider the case where the optically rare medium is a gas or a vacuum, so that the refractive index n 1 and the absorption index k 0. In this case, the reflectance at the interface depends on the optical constants of the optically dense medium, 2 and the angle... 

For a light-absorbing medium, such as metals and semiconductors, the refractive index is complex, n = n — ik. For a (dielectric) medium which does not absorb light, the imaginary part of the refractive index is zero, A = 0. Therefore, the refractive index for a transparent medium is real. The magnitude of k is an index of light attenuation in the medium and is related to the absorption coefficient a by the relation a = Ank/X. Often, n and k are called the optical constants of a material. ... 

Many of the far-infrared spectral studies for chemical information have emphasized the gas phase. This emphasis should not be interpreted as meaning that far-infrared spectral studies of solids are not important. Physicists have put interferometers to use in the study of the solid state to determine optical constants such as the index of refraction, complex indices, phase angle transmission coefficients and the electronic processes in insulation crystals, as well as the intermolecular vibrations of molecular crystals. These studies have been very important in the development of interpretative theories of solids. 

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