Fresnel transmission

For the case of non-normal illumination incidence at some angle 0, the Fresnel transmission and reflection coefficients are now functions of the angle of incidence as well as the polarization of the incident light they are given hy ... 

The transmission coefficient T is found by using the local plane-wave description of a ray. We regard the local plane wave as part of an infinite plane-wave incident on a planar interface between unbounded media, whose refractive indices coincide with the core and cladding indices and of the waveguide, as shown in Fig. l-3(b). For the step interface, Tis identical to the Fresnel transmission coefficient for plane-wave reflection at a planar dielectric interface [6]. In the weak-guidance approximation, when s n, the transmission coefficient is independent of polarization, and is derived in Section 35-6. From Eq. (35-20) we have [7]... 

O. S. Heavens. Optical Properties of Thin Solid Films. Buttcrworths, 1955. Chapter 4 presents a detailed mathematical description of the Fresnel fringing phenomenon for the transmission of light through thin films. 

Parameters e, ( = h2) are the dielectric constants of the respective media (which may be complex for light-absorbing materials). Parameters Tp s are the Fresnel coefficients for transmission through a stratified three-medium system with the beam incident from the medium 3 side and an intermediate medium 2 of thickness (5(l0) ... 

Equations (2.67)-(2.70) are the Fresnel formulas for reflection and transmission of light obliquely incident on a plane boundary. 

Ie is the true scattered intensity I e is the measured scattered intensity at angle 6, and Z i8o-e is at the supplementary angle. fa and fi are the Fresnel s coefficients for the fractions of light reflected at perpendicular incidence at the glass-air and glass-liquid interfaces, respectively ta and tx are the corresponding transmission coefficients. They are defined by the following equations ... 

Optical Absorption. Figure 3 compares the optical absorption spectra of undoped, Co-, Mn-, and Fe-doped BaTi03 crystals grown in air. Transmission spectra were obtained on a Perkin-Elmer Lambda 9 spectrophotometer modified for use with polarized light and were reduced to absorption coefficients by correction for Fresnel... 

The natural extension of this model is to consider a free-standing film, i.e., a thin transmitting sample not deposited on a substrate. In this case we have two interfaces (assumed to be flat) and transmission and reflection Fresnel coefficients at both interfaces (air/material and material/air). Even though it is not easy to produce such films, some examples are reported in the CP literature [13,14,26,27,32], Assuming that the medium is in vacuum (no = 2 = 1) with thickness d, it is easy to calculate the total reflectance R, and transmittance T of the sample as [21-23]... 

A nice qualitative derivation of the Gladstone-Dale equation was given by Schoorl (1920). The Huygens-Fresnel wave optics leads to the conclusion that the refractive index is equal to the ratio of the light velocities in the two media of transmission and also to the ratio of the respective wave-lengths so Snellius law can be extended to... 

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]. 

To describe transmission and refraction we have Introduced the transmission and reflection coefficients called t and r, respectively. Generally these are complex quantities, i.e. they eure written as ( and r, but for non-adsorbing media and Fresnel surfaces they become real, and we recall from (1.7.10.6 and 7) that... 

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