Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 222

Figure (5.5c) shows the case for θ₁ > θ_c. Equation (5.3.3c) of Snell's refraction law shows that sinθ₂ > 1. Therefore, there is no real solution to the angle θ₂. However, the wave propagation in medium #2 requires sinθ₂ and cosθ₂, not the value of the angle of refraction θ₂. The sinθ₂ and cosθ₂ could be obtained from Snell's Law given by equation (5.2.7c), also from the wavevector k₂ and its x and y‐directed components k_2x and k_2y using equation (5.2.1):

Figure 5.5 Oblique incidence of plane wave at three different angles of incidence.

(5.3.5)

The negative (−) value is selected in further computation as it provides exponentially decaying fields with distance from the interface in the medium #2. The choice of positive (+) value results in the exponentially growing field with the distance that is physically not possible in a usual passive medium. The expressions (5.3.5b,d,e) are used for both the TE and TM polarization to compute the reflection and transmission coefficients, and also the refracted fields in medium #2 for the case θ₁ > θ_c