Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 223

Equation (5.2.8c,d) for the reflection and transmission coefficients of the obliquely incident TE‐polarized wave, using an equation (5.3.5a) are reduced to the following expression:

(5.3.6)

The interface surface acts as a PMC surface for the TE‐polarized incident wave under the case θ₁ ≥ θ_c because . Over a certain frequency band, it is realized as the artificial magnetic conductor (AMC) surface. At the critical angle, θ₂ = π/2, the transmitted wave propagates along the y‐direction at the interface x = 0⁺, as shown in Fig (5.5b). For the case θ₁ > θ_c, shown in Fig (5.5c), the interface supports the slow‐wave type surface wave propagation. It is demonstrated below.

For the case θ₁ > θ_c, the electric and magnetic field component and power flow of the TE‐polarized wave in the medium #2 is obtained from using equation (5.3.5) with equation (5.2.10a):

(5.3.7)

In equation (5.3.7a,b,c), the y‐directed wavevector k_2y and attenuation factor α are given by equation (5.3.5). Equation (5.3.7a,b,c) shows that along the direction normal to the interface, i.e. + x‐direction, the field is exponentially decaying in medium #2; showing the confinement of field near the interface. However, the wave propagates in the y‐direction. It is also evident from the complex Poynting vector giving real power transportation in the y‐direction, while imaginary power shows storages of energy in the x‐directed evanescent field. So the interface supports a surface wave, excited at the interface of two media by the obliquely TE‐polarized incident plane wave at the angle of incidence θ₁ ≥ θ_c. The surface wave, in more detail, is discussed in chapter 7. Its phase velocity along the y‐axis is

(5.3.8)

In equation (5.3.8), as ε_r1 > ε_r2; so , i.e. the phase velocity of the surface wave is less than that of in the medium #2. Therefore, the surface wave is a slow‐wave.