Fresnell reflection coefficients

The Fresnel reflection coefficients r for the overall system can be obtained from the elements m of the characteristic matrix M associated with the overall system ... 

The overall reflectance R for parallel- and perpendicular-polarized light can be calculated from the Fresnel reflection coefficient ... 

Ellipsometry grants the independent determination of two results per resolution element without changing the experimental geometry this technique is described in Sec. 6.4.4.2. More often however, the information on the phase shift is abandoned and just the reflectance is determined. Usually it is measured by comparing the signal caused by the reflected intensity with the one obtained when the sample is replaced by a mirror. Even without correcting for its reflectance such results can often be used for further mathematical evaluation. The Fresnel reflection coefficient r in the form given by Eq. 

Figure 4.14. The four-layer model used for the calculations of the interfacial thickness, nj designates the refractive index, 0j the incidence angle, r. the Fresnel reflection coefficient, Rj the reflection coefficient in the incident plane and dj the thickness of the layer.

In Eqs (112) and (II3),r(jyy and rj2j 0 P- denote the Fresnel reflections coefficients at the O-1,1-2 interfaces of the ambient medium (0), layer (1), and substrate medium (2) in the reflecting system P is the phase change of the electromagnetic wave caused by the presence of the interfacial layer. 

The samples were freestanding films with thickness 40-100 p,m. This thickness is greater than the electromagnetic penetration depth [5 = c/ 2tt xwo-(w), where c is the speed of light and 10 S/cm. Samples with or cTdc < 10 S/cm were first checked to determine whether they had transmitted far-IR radiation. Therefore, the reflectance can be analyzed using the Fresnel reflection coefficients for semi-infinite media [103]. 

Antennas over ground can be modeled by several methods. The simplest is to assume a perfectly conducting Earth. This would be an excellent approximation for some situations, such as an antenna above sea water. For this case the method of images can be used. If Earth parameters do not warrant the perfectly conducting approximation, then the Fresnel reflection coefficients can be used to compute the ground reflected wave, which is superimposed with the direct wave. For antennas very close to Earth the Sommerfeld/Norton solution is used. This method uses the exact solution for fields in the presence of Earth. The NEC code discussed earher uses this method as an option, although computations require more time to complete. 

The reflectivity is calculated using the Fresnel reflection coefficient r, which is defined as 7 rp/ ip, where rp and Eip are the complex amplitudes of the electric vectors of the reflected and incident p-polarized light respectively. Values may also be calculated for = Ers/Eis, the reflection... 

Optics. The interfaces between air-layer and layer-substrate are characterized by the Fresnel reflectance coefficients roi and ri2,... 

Here rip and ris are the Fresnel reflection coefficients of the film surface, and r2p and rzs the Fresnel coefficients at the film-substrate interface. These in turn can be calculated from the material properties and wave directions, so that ... 

The diffuse reflection coefficient of the crystal side surface was taken equal to = 0.18 for radiation coming from the gas and = 0.823 for radiation coming from the crystal. The first value was obtained by averaging of the Fresnel reflection coefficient over an incident angle, while the second follows from relation between and p, Eq. (8.8). The specular reflection coefficient was calculated by the Fresnel formulae. The reflection coefficient of a free surface of a melt is unknown at present and was taken equal to p both for diffuse and specular reflection that can be justified by a small difference between refraction index of solid and hquid phases. The latter, along with opacity of the melt, permits consideration of the... 

For the three-phase system (123) shown in Fig. 3.2, the equivalent Fresnel reflection coefficient is defined by analogy to the two-phase system as the ratio of the amplitudes of the reflected and incident waves in the initial ambient phase (1). It can be written for both s- and p-polarizations as... 

The relationships between E, H, and the incident beam fields Ej and H are provided by the Fresnel reflection coefficients for plane-wave reflection at a dielectric interface, discussed in Section 35-6. In general, these coefficients depend on the polarization of the beam, but, if 0j is small, they are independent of polarization and are given by Eq. (35-18) with d replaced by Ujand... 

The reflectivity of an interface is calculated from Fresnel s equations, which are derived from the boundary conditions that the tangential (t) component of the electric field vector, and the normal (n) component of the electric displacement vector, D = e - E , are continuous across the inter-face. We define the so-called Fresnel reflection coefficient r as the ratio of the complex amplitudes of the electric field vectors of the reflected and the incident waves ... 

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