S-polarized waves

By convention, in a p-polarized wave the electric vector oscillates in the plane parallel to the plane of incidence. The wave in which the electric vector oscillates in the plane perpendicular to the plane of incidence is referred to as the s-polarized wave. See e.g. [17]... 

Let us first consider an oblique reflection of a light wave at a planar interface between two optically isotropic media. For a given amplitude and polarization of the incident wave, the reflected amplitude and polarization are determined from the continuity relation for the E and H fields at the interface. This leads to the complex Fresnel s equations [1] for the complex reflectivities of the p-polarized rp = Er pjEi p, and s-polarized waves, = Er,s/Ei s- The same applies to the transmitted waves. Here, i and r denote incident and reflected light respectively. 

From the viewpoint of quantum mechanics, the polarization process cannot be continuous, but must involve a quantized transition from one state to another. Also, the transition must involve a change in the shape of the initial spherical charge distribution to an elongated shape (ellipsoidal). Thus an s-type wave function must become a p-type (or higher order) function. This requires an excitation energy call it A. Straightforward perturbation theory, applied to the Schroedinger aquation, then yields a simple expression for the polarizability (Atkins and Friedman, 1997) ... 

H.W. Schurmarm, V.S. Serov and Yu.V. Shestopalov, TE-polarized waves guided by a lossless nonlinear three-layer stmctms ,Phys.Rev.E 58, 1040 - 1050 (1998). 

Figure 5. Photorefractive two-beam coupling gain coefficient of undoped and doped BaTi03 crystals. Curves are theoretical fits to the data. Experimental conditions X = 515 nm, I = 3-5 W/cm2, beam ratio > 200, s-polarization, grating wave vector parallel to c-axis Concentrations refer to dopant atoms per BaTi03 formula unit in the melt.

The dipole moment of a compound is a function of the distribution of charge within the molecule, and appears to be a sensitive test for the accuracy of the compound s molecular wave functions. The dipole moment of a molecule can be approximated for a given direction as the sum of two components, /iq, the contribution from net charge densities on the atoms, and for each atom A, ftsp (A), an atomic polarization moment produced by the distortion of the electronic cloud around the atom. The atomic polarization moment results essentially from the mixture of s and p orbitals and, for a heteroatom, includes mv, the lone pair moment. 

In an anisotropic dielectric the phase velocity of an electromagnetic wave generally depends on both its polarization and its direction of propagation. The solutions to Maxwell s electromagnetic wave equations for a plane wave show that it is the vectors D and H which are perpendicular to the wave propagation direction and that, in general, the direction of energy flow does not coincide with this. 

In the general case, when s-polarized light is converted into p-polarized light and/or vice versa, the standard SE approach is not adequate, because the off-diagonal elements of the reflection matrix r in the Jones matrix formalism are nonzero [114]. Generalized SE must be applied, for instance, to wurtzite-structure ZnO thin films, for which the c-axis is not parallel to the sample normal, i.e., (1120) ZnO thin films on (1102) sapphire [43,71]. Choosing a Cartesian coordinate system relative to the incident (Aj) and reflected plane waves ( > ), as shown in Fig. 3.4, the change of polarization upon reflection can be described by [117,120]... 

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 individual corrections and appearing on the r.h.s. of Eqs. (1-25) are referred, after Hirschfelder75, to as the nth-order polarization energy and polarization wave function, respectively. The nth-order energy correction is given by... 

R is I l, v4 + 1 s,. Obviously, < >, = 1. v, is not a good approximation to The component lsB due to the perturbation V is as large as the unperturbed function itself. Hence, the operator V cannot be considered as a small perturbation. Since the polarization wave functions for this system are all localized at the nucleus A, i.e. they decay exponentially with the distance from the nucleus A, the polarization expansion can possibly recover the component of P, localized on the nucleus B, only in very high orders. 

Fluctuations in the dielectric properties near the interface lead to scattering of the EW as well as changes in the intensity of the internally reflected wave. Changes in optical absorption can be detected in the internally reflected beam and lead to the well-known technique of attenuated total reflectance spectroscopy (ATR). Changes in the real part of the dielectric function lead to scattering, which is the main topic of this review. Polarization of the incident beam is important. For s polarization (electric field vector perpendicular to the plane defined by the incident and reflected beams or parallel to the interface), there is no electric held component normal to the interface, and the electric field is continuous across the interface. For p polarization (electric field vector parallel to the plane defined by the incident and reflected beams), there is a finite electric field component normal to the interface. In macroscopic electrodynamics this normal component is discontinuous across the interface, and the discontinuity is related to the induced surface charge at the interface. Such discontinuity is unphysical on the molecular scale [4], and the macroscopic formalism may have to be re-examined if it is applied to molecules within a few A of the interface. 

Within the polarization scheme used here where p-polarized light is polarized in the plane of incidence, and s-polarized light is polarized perpendicular to the plane, the Cartesian components of , (a>, ) are given by the projection of the s and p components of the incident wave... 

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