Martin Čermák

Thin Static Charged Dust Majumdar–Papapetrou Shells with High Symmetry in D≥4

We present a systematical study of static D≥4 space-times of high symmetry with the matter source being a thin charged dust hypersurface shell. The shell manifold is assumed to have the following structure

Universal Dispersion Model for Characterization of Thin Films Over Wide Spectral Range

\mathbb{S}_{\beta}\times\mathbb{R}^{D-2-\beta}

Ellipsometry of Layered Systems

, β∈{0,…,D−2} is dimension of a sphere

Optical Characterization of Thin Films Exhibiting Defects

\mathbb{S}_{\beta}

Optical quantities of multi-layer systems with randomly rough boundaries calculated using the exact approach of the Rayleigh–Rice theory

. In case of β=0, we assume that there are two parallel hyper–plane shells instead of only one.The space-time has Majumdar–Papapetrou form and it inherits the symmetries of the shell manifold—it is invariant under both rotations of the

Determination of thicknesses and temperatures of crystalline silicon wafers from optical measurements in the far infrared region

\mathbb {S}_{\beta}

Cosmologically inspired Kastor-Traschen solution

and translations along ℝD−2−β.We find a general solution to the Einstein–Maxwell equations with a given shell. Then, we examine some flat interior solutions with special attention paid to D=4. A connection to D=4 non-relativistic theory is pointed out. We also comment on a straightforward generalisation to the case of Kastor–Traschen space-time, i.e. adding a non-negative cosmological constant to the charged dust matter source.

Dispersion models describing interband electronic transitions combining Tauc's law and Lorentz model

The universal dispersion model is a collection of dispersion models (contributions to the dielectric response) describing individual elementary excitation in solids. All contributions presented in this chapter satisfy the basic conditions that follow from the theory of dispersion (time reversal symmetry, Kramers–Kronig consistency and finite sum rule integral). The individual contributions are presented in an unified formalism. In this formalism the spectral distributions of the contributions are parameterized using dispersion functions normalized with respect to the sum rule. These normalized dispersion functions must be multiplied by the transition strengths parameters which can be related to the density of charged particles. The separation of contributions into the transitions strengths and normalized spectral distributions is beneficial since it allows us to elegantly introduce the temperature dependencies into these models.

Optical characterization of randomly microrough surfaces covered with very thin overlayers using effective medium approximation and Rayleigh-Rice theory

In this chapter the theoretical aspects of ellipsometry and their applications in optics of layered systems are presented. The basic formulae of the theory of ellipsometric measurements are introduced. For this purpose the Jones and Stokes–Mueller matrix formalisms are used. By using these formalisms the individual types of ellipsometry and the most utilized ellipsometric techniques are briefly described. Furthermore, the matrix formalisms enabling us to derive the formulae for the optical quantities of optically isotropic and anisotropic layered systems are described as well. Applications of the matrix formalisms in practice are illustrated by means of three examples.

Use of the Richardson extrapolation in optics of inhomogeneous layers: Application to optical characterization: Use of the Richardson extrapolation in optics of inhomogeneous layers

In this chapter the influence of the main defects on the optical characterization of thin films is described. These defects are random roughness of boundaries, thickness non-uniformity, optical inhomogeneity corresponding to refractive index profiles, overlayers and transition layers. The theoretical approaches and the formulae for the corresponding optical quantities of the thin films exhibiting these defects are presented. The attention is concentrated on the ellipsometric parameters and reflectance of these thin films belonging to the specular reflection. The selected numerical examples illustrating the influence of the defects are introduced. Several experimental examples of the optical characterization of the thin films with the defects are also shown. The discussion of both the numerical and experimental results is carried out too.