Fresnel difference between polarizations

P2(z) is the polarization in the transition layer and P3 is the polarization in the bulk of the transparent isotropic substrate. The y axis is chosen to be perpendicular to the plane of incidence. Since the polarization vector components P2j z) and P j are proportional to the same electric field components of the incident wave, the parameters jj do not depend on the amplitude of the external exciting field. Being calculated in the zeroth order in d / A, they do not depend on the wavelength of the light. These quantities therefore characterize the optical properties of the transient layer to first order in d / A. They are determined by the relative difference between the mean local field in the layer and the local field in the bulk medium. Therefore, Eqs (3.57) and (3.58) predict deviations from the two-phase Fresnel formulae even when there are no perturbations in the selvedge region, i.e., the surface is clean and the optical properties of atoms nearby the surface are identical with those in the bulk. 

The Fresnel coefficients are a function of the polarization and the angle of incidence of the incident beam. We commonly work with linearly polarized light, where the electric field vector is either perpendicular (5, J.) or parallel (a id to the plane of incidence. For 5-polarization, the electric field vector E is parallel to the surface at all angles of incidence, while for p-polarized light at oblique angles of incidence, the electric field vector has a component normal to the surface. At normal incidence, the physical difference between 5- and p-polarization vanishes. 

Ellipsometry. Determination of h(u>) by KK analysis and coupled measurements of 1Z and T are affected, respectively, by the problem of the tails added to the experimental R(u>) spectra and by the need to perform 7Z and T measurements separately These problems, which introduce some uncertainty, can be solved by spectroscopic ellipsometry. The technique involves analyzing the polarization of a light beam reflected by a surface. The incident beam must be linearly polarized and its polarization should be allowed to rotate. A second linear polarizer then analyzes the reflected beam. The roles of polarizer and analyzer can be exchanged. The amplitudes of the s and p components of the reflected radiation are affected in a different way by reflection at the surface. The important function describing the process is the ellipsometric ratio p, which is defined as the polarization of the reflected wave with respect to the incident wave, expressed as the ratio between the Fresnel coefficients for p and s polarizations ... 

The reflectivity / of a plane interface between two regions with complex refractive indices n n — iK and = 2 can be calculated from Fresnel s formulas [4.15]. It depends on the angle of incidence a and on the direction of polarization. Reflectivity R a) is illustrated in Fig. 4.51 for three different materials for incident light polarized parallel (/ p) and perpendicular (/ s) to the plane of incidence. 

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