(5.2b) shows the equivalent transmission line model of the obliquely incident TE‐polarized wave. The wave impedances Similarly, the wave impedances viewed by the interface with the obliquely incident TM‐polarized wave are obtained with reference to Fig (5.3a):
The superscripts k1 and k2, used in equations (5.2.22) and (5.2.23) are dropped in further discussion.
Refection/Transmission Coefficients at Media Interface and Lines Junction
The reflection and transmission coefficients of both the TE and TM‐polarized obliquely incident waves at the interface (x = 0) of physical media as taken as follow:
(5.2.24)
The reflection and transmission coefficients of TE‐polarized at the junction of two equivalent lines, shown in Fig (5.2b), are obtained from Ez‐field components of the incident, reflected, and transmitted waves using equations (5.2.2)–(5.2.4):
(5.2.25)
Thus, for the TE‐polarized obliquely incident EM‐wave, the line reflection, and transmission coefficients correspond to the reflection and transmission coefficients at the interface of two physical media. However, for the TM‐polarized case, shown in Fig (5.3b), change occurs for the transmission coefficient. The Ey‐field components of the incident, reflected, and transmitted waves using equations (5.2.12)–(5.2.14) are considered to define line junction reflection and transmission coefficients of the TM‐polarized case:
Computation of Reflection and Transmission Coefficients
At this stage, the reflection and transmission coefficients of the TE/TM‐polarized waves at the interface of two physical media could be computed. Using the above discussion, the reflection coefficient
Equation (5.2.27a,b) are identical to equation (5.2.8c,d), The reflection coefficient
Equations (5.2.23) and (5.2.26) are used to get the above expressions. Equation (5.2.28a, b) are identical to equation (5.2.16c,d). The transmission line models are also used to obtain the reflection and transmission coefficients of both normal and oblique incident plane waves on a multilayered slab medium [B.1, B.3, B.4]
5.3 Special Cases of Angle of Incidence
There are two special cases of the angle of incidence: one for the complete transmission of waves at the interface, and another for the total reflection of the wave at the interface of two media. These are known as Brewster angle and critical angle. Brewster angle is the angle of incidence at which the reflection coefficient is zero and the incident wave is fully transmitted from one medium to another with refraction. So the Brewster angle corresponds to the impedance matching condition under which reflection at the interface, in the medium #1, is zero, and the incident power is completely transmitted to the medium #2. At the critical angle of incidence or the incidence angle greater than the critical angle, the incident wave is completely reflected by the interface of two dielectric media. This kind of total reflection is superior to that of the total reflection from any metallic surface that always introduces loss. We consider these two special cases of the angle of incidence for both the TE and TM polarizations.
5.3.1 Brewster Angle
The Brewster angle of incidence could be obtained for both the TE and TM polarizations.
TE‐Polarization
In the case of the TE‐polarization, at an incident angle θ1 = θB, i.e. at Brewster angle the reflection coefficient
(5.3.1)
