Reflection and Refraction Coefficients

Define the refracted wave as e2f and the reflected wave as e and also the characteristic (surge) impedance of the lines 1 and 2 as Zj and Z2, respectively. Then, current I on the line 1 is given from Equation 1.56 as 

Voltage V at the node P on the line 1 is given from Equation 1.91 by 

Substituting the earlier equation into Equation 1.204, Cy, is obtained as 

It should be clear from Equations 1.208 and 1.210 that the reflected and refracted waves are determined from the original wave by the reflection and refraction coefficients, which represent the boundary condition at the node P between the lines 1 and 2 with the surge impedances Z and Z2. The coefficients 0 and X give a ratio of the original wave (voltage) and the reflected and refracted voltages. For example, 

The earlier results show that the reflected voltage Cy, at the node P is the same as the incoming (original) voltage Cif and the current I becomes zero when the line 1 is open-circuited. On the contrary, under the short-circuited condition, e-y, = and the current becomes maximum. Under the matching termination of the line 1, there is no reflected voltage at the node P. 

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Equations (3.9), (3.12), and (3.16) are sufficient to calculate the reflection and refraction coefficients for a stratified structure of thin films. In writing the phase factors, 8(,... 

This problem was treated in section 1.6 of Chapter 1, where the Fresnel coefficients for reflected and refracted light were calculated and presented in equations (1.74) to (1.77). The problem being treated is pictured in Figure 1.4, and it is convenient to represent the electric vector as a Jones vector having orthogonal components that are either parallel... 

In addition to the tensor element dependence of the sum-frequency intensity, there is also a dependence on the geometry of the experiment that manifests itself in the linear and non-linear Fresnel factors that describe the behaviour of the three light beams at the interface. Fresnel factors are the reflection and transmission coefficients for electromagnetic radiation at a boundary and depend on the frequency, polarization and incident angle of the electromagnetic waves and the indices of refraction for the media at the boundary [16,21]. 

The method is based on the magnetorefractive effect (MRE). The MRE is the variation of the complex refractive index (dielectric function) of a material due to change in its conductivity at IR frequencies when a magnetic field is applied. A direct measure of the changes of dielectric properties of a material can be performed by determining its reflection and transmission coefficients. Hence, IR transmission or reflection spectroscopy can provide a direct tool for probing the spin-dependent conductivity in GMR and TMR [5,6]. 

The reflection and refraction of electromagnetic radiation at an interface can be discussed with relation to Fig. 2. The incident, reflected, and refracted rays are shown in this figure as I, R, and T and reflection and transmission coefficients can be derived straightforwardly from standard electromagnetic theory. In order to focus our ideas and to define the convention used in this section, we may write down the expression for the electric field, E, of the radiation, assuming that the light is propagating in the z direction (with unit vector ) and the electric field is oriented in the x direction (with unit vector... 

Under oblique incidence ( j=incidence angle, 2=refraction angle, with nisin i = n2 sin 2), the reflection and transmission coefficients depend on the polarization of the incident wave with respect to the incidence plane (see Fig. 6.1). If the polarization (direction of the electric field Eq) is perpendicular to the incidence plane (so-caUed s-polarization), the electric field is everywhere parallel to the interface, and using the same rules as above for the boundary conditions, its amplitude at the interface is now E()X2niCosi+n2Cosg>2), stiU much smaller than Eg [15]. However, if the polarization lies in the incidence plane (so-caUed p-polarization), the electric field has a component parallel to the interface and a component perpendicular to the interface. The parallel... 

The Fresnel equations describe the reflection and transmission coefficients at the interface of two optical media. The polarisation of the incident Hght affects the magnitude of these coefficients. It is possible to derive expressions for the intensities of the reflected and refracted rays. These differ for the TE and TM polarisations as follows ... 

This equation is the so-called basic ellipsometric equation. It contains R and R which depend on the optical properties of the reflecting system, the wavelength of the light X the angle of incidence cp and the experimentally measurable parameters Pand A. For the reflection at a clean interface, the Rp and R are the Fresnel coefficients (246) of the single uncovered interface. They depend only on the refractive indices of the two adjacent phases and the angle of incidence. For systems that do not absorb light the optical constants of the two bulk phases (ambient and substrate media) are usually obtained from the experimental values of P and A for the clean interface (denoted by subscript 0 via Eq. (111). For a layer-covered interface, multiple reflections and refractions take place within the layer (Fig. 24). 

Iq is the incident laser intensity R and a are sample reflectivity and absorption coefficient, respectively n is the refractive index, and pj is the angle between the incident beam and the sample surface i and s refer to the incident and scattered beam, respectively. We used the proper values of n and obtained by KK analysis the values of oq and ag were deduced from the values of k n and kj, applying the well-known relation a = 47ckA. The values of Rj and Rg were inserted as obtained above. All the previous optical parameters were evaluated at the wavelength of the exciting laser. 

If an isotropic layer with a thickness d.2 is located at the planar interface of two semi-infinite media (Fig. 1.12), the incident wave gives rise to reflected and refracted waves in all the media except for the ontput halfspace, where only the refracted wave exists. For such an optical configuration, the Fresnel coefficients (1.4.5°) can be rewritten in the Drude (exact) form [9] as... 

A method to solve the problem is to determine in the Fourier space the connection between the logarithm of refractive index values and the amplitude reflection and transmission coefficients, represented as complex wavelength-dependent functions. The global minimum of thus obtained dependence is then determined. The solution is an inhomogeneous layer, further transformed into a two-material system and subsequently subjected to a new procedure of fine optimization. 

Internal radiation through the crystal depends largely on the absorption coefficient and the refraction index. The first parameter determines the radiative heat absorption and emission inside the crystal, while the second determines reflection and refraction of radiation at the crystal side surface. The absorption coefficient of a melt is generally much greater than that of a crystal. Therefore, radiation is crucial in heat removal from the melt through the crystal/melt interface RTH within the crystal can even lead to instability of the crystallization front [5]. The refraction... 

The exact solution for the unperturbed system can be obtained by the Parratt formalism.For a thin film sample consisting of three layers (layers j= 1 vacuum, 2 thin film, and 3 substrate), as shown in Figure 3(a), the refractive index rij of layer j isnj=l-Sj + ifSj with a dispersion Sj and an absorption pj. The Fresnel reflection and transmission coefficients for each sharp interface arer j+j = + and... 

Optical Properties. The index of refraction and extinction coefficient of vacuum-deposited aluminum films have been reported (8,9) as have the total reflectance at various wavelengths and emissivity at various temperatures (10). Emissivity increases significantly as the thickness of the oxide film on aluminum increases and can be 70—80% for oxide films of 100 nm. 

Physically, this formula describes the power dissipated by a harmonic oscillator (the emission dipole with moment t) as it is driven by the force felt at its own location from its own emitted and reflected electric field. PT is calculable given all the refractive indices and Fresnel coefficients of the layered model(12 33)... 

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