Optical constants anisotropic

Infrared ellipsometry is typically performed in the mid-infrared range of 400 to 5000 cm , but also in the near- and far-infrared. The resonances of molecular vibrations or phonons in the solid state generate typical features in the tanT and A spectra in the form of relative minima or maxima and dispersion-like structures. For the isotropic bulk calculation of optical constants - refractive index n and extinction coefficient k - is straightforward. For all other applications (thin films and anisotropic materials) iteration procedures are used. In ellipsometry only angles are measured. The results are also absolute values, obtained without the use of a standard. 

Turner (1973) and McKellar (1976) applied RG theory to ensembles of randomly oriented particles of arbitrary shape the former author included spheres with anisotropic optical constants. Optically active particles have been treated within the framework of the RG approximation by Bohren (1977). 

We have discussed intrinsically anisotropic particles—ones with anisotropy originating in their optical constants rather than their shape—in previous chapters. In Section 5.6 we gave the solution to the problem of scattering by an anisotropic sphere in the Rayleigh approximation. From the results of that section and Section 5.5 it follows that the average cross section (C) (scattering or absorption) of a collection of randomly oriented, sufficiently small, anisotropic spheres is... 

The reason for the intractability of the anisotropic sphere scattering problem is the fundamental mismatch between the symmetry of the optical constants and the shape of the particle. For example, the vector wave equation for a uniaxial material is separable in cylindrical coordinates that is, the solutions to the field equations are cylindrical waves. But the bounding surface of the... 

Common liquids are optically isotropic, and the solids that physicists seem to like most are cubic and therefore isotropic. As a consequence, treatments of optical properties, particularly from a microscopic point of view, usually favor isotropic matter. Among the host of naturally occurring sohds, however, most are not isotropic. This somewhat complicates both theory and experiment for example, measurements of optical constants must be made with oriented crystals and polarized light. But because of the prevalence of optically anisotropic solids, we are compelled to extend the classical models to embrace this added complexity. 

More problems must be faced when trying to extract optical constants from measurements on particles of anisotropic solids. Random orientation of the particles averages somehow the two or three sets of optical constants. We... 

From the data reported in Fig. 2.2 and from spectroscopic ellipsometry measurements, the anisotropic complex optical constants of oriented PPV have been determined [32,69]. Several different data analyses, described previously, were carried out on the 7Z and T spectra in order to extract n, both below and above the HOMO-LUMO transition (transparent free-standing film and bulk material, respectively). In order to evaluate n below 1.6 eV, where the sum of 1Z and T is equal to 1 within experimental error, a numerical inversion of the 7Z and T spectra was performed by assuming k = 0... 

Next, we consider the absorbance due to a dichroic adlayer adsorbed onto the waveguide surface with the optical constants as indicated in Fig. 4. The optical properties of the dichroic layer are described by the different extinction coefficients k, ky, and k in each Cartesian direction. The reflectance of the waveguide-adlayer-cover system follows the analysis found in Macleod [9] with the anisotropic coefficients taken from Horowitz and Mendes [10]. By assuming a thin and weakly absorbing adlayer, the following expressions are obtained for the absorbance as measured through a guided mode at each polarization [8] ... 

M. Pope and C. E. Swenberg. Electronic Processes in Organic Crystals and Polymers. Oxford University Press, 2nd edition, 1999. C. M. Ramsdale and N. C. Greenham. Ellipsometric determination of anisotropic optical constants in electroluminescent conjugated polymers. Adv. Mater., 14(3) 212, 2002. 

Ellipsometry at noble metal electrode/solution interfaces has been used to test theoretically predicted microscopic parameters of the interface [937]. Investigated systems include numerous oxide layer systems [934-943], metal deposition processes [934], adsorption processes [934, 944] and polymer films on electrodes [945-947]. Submonolayer sensitivity has been claimed. Expansion and contraction of polyaniline films was monitored with ellipsometry by Kim et al. [948]. Film thickness as a function of the state of oxidation of redox active polyelectrolyte layers has been measured with ellipsometry [949]. The deposition and electroreduction of Mn02 films has been studied [950] below a thickness of 150 nm, the anodically formed film behaved like an isotropic single layer with optical constants independent of thickness. Beyond this limit, anisotropic film properties had to be assumed. Reduction was accompanied by an increase in thickness, which started at the ox-ide/solution interface. 

Fig. 2.6 The stratified three-phase layered optical model with optically anisotropic phases 2 and 3. where phase 1 is the electrolyte solution, phase 2 is the thin organic film of thickness d, and phase 3 is the electrode. For the optical constants, see text.

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... 

DETERMINATION OF MOLECULAR PACKING AND ORIENTATION IN ULTRATHIN FILMS ANISOTROPIC OPTICAL CONSTANTS OF ULTRATHIN FILMS... 

The MO measurements provide information about the angular distribution of molecules in the x, y, and z film coordinates. To extract MO data from IR spectra, the general selection rule equation (1.27) is invoked, which states that the absorption of linearly polarized radiation depends upon the orientation of the TDM of the given mode relative to the local electric field vector. If the TDM vector is distributed anisotropically in the sample, the macroscopic result is selective absorption of linearly polarized radiation propagating in different directions, as described by an anisotropic permittivity tensor e. Thus, it is the anisotropic optical constants of the ultrathin film (or their ratios) that are measured and then correlated with the MO parameters. Unlike for thick samples, this problem is complicated by optical effects in the IR spectra of ultrathin films, so that optical theory (Sections 1.5-1.7) must be considered, in addition to the statistical formulas that establish the connection between the principal values of the permittivity tensor s and the MO parameters. In fact, a thorough study of the MO in ultrathin films requires judicious selection not only of the theoretical model for extracting MO data from the IR spectra (this section) but also of the optimum experimental technique and conditions [angle(s) of incidence] for these measurements (Section 3.11.5). 

Since the substrate may influence the anisotropic optical properties of the overlying film [595], the method of Buffeteau et al. [247, 566-568, 593] is conceptually more reliable when the MO is studied on solid transparent substrates, whereas the initial anisotropic optical constants are extracted from normal- and oblique-incidence transmission or polarized reflection of the same film on the same substrate. In the case when different substrates participate into the measurements (e.g., when MO in monolayers at the AW interface is studied), the comparison of the simulated and experimental spectra can be used for distinguishing chemical effects generated by specific film-substrate interactions [568b]. In particular, the kmm values derived from spectra of monolayers at the AW interface obtained by IRRAS are usually larger than those obtained by eUipsometric measurements of thin films on solid supports [247]. This difference has been attributed to a gradient in the optical properties of the interfacial water [71]. 

The hexagonal rare-earth metals are highjy anisotropic, so for a single crystal surface the optical constants are functions of the directions of incidence and polarization. In most experiments the metal surface is polycrystalline, and the measured optical constants are average properties of the crystal. 

Kirov, K.R. and Assender, H.E. (2004) Quantitative ATR-IR analysis of anisotropic polymer films extraction of optical constants. Macromolecules, 37, 894-904. 

An extension of optical treatments to include anisotropy in the optical constants provides a means to estimate chain orientation and surface concentration from reflection-absorption intensities. Models of this kind are based on a definition of optical constants as in Figure 1. The ambient superphase and liquid sublease are isotropic, and the monolayer has the indicated anisotropic optical constants. Fina and Tung (26) originally used such a model to predict the dependence of the reflection-absorption of a monolayer on the chain orientation. The reflected amplitudes for a three phase system are found from the well known relationship ... 

Ellipsometry is a powerful tool to gain the optical properties of materials though measuring the change of polarization state of the probe light after interaction with the sample. It offers a sensitive, nondestructive and comprehensive way to accurately determine film thickness and optical constants of extensive materials, such as metals, ceramics, glasses, semiconductors, and its compounds and composites. These materials can be liquid phase or even gaseous phase, can be isotropic or anisotropic, and can be bulk materials or multi-layer thin films. 

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