User's Guide for Simulation of Wave Reflection and Transmission - Parallel Polarization

A parallel-polarized uniform plane wave in medium 1 is incident on medium 2. The incident, reflected, and transmitted electric fields respectively are given as follows

where

The incident, reflected, and transmitted angles have the following relationships

The reflection and transmission coefficients are given as

The total electric fields in media 1 and 2 are given as

The applet shows the magnitudes of the electric fields given as

The parameters include the incident angle q_i , the relative permittivities and permeabililites of the two media, and the frequency. A standing wave pattern appears medium 1 if R_h is not zero.

The critical angle q_c is defined as the incident angle for which k_ix = k₂ or

If the incident angle is less than the critical angle, then the component k_tz is real and the magnitude of the electric field in medium 2 would be a constant, i.e.,

If the incident angle is greater than the critical then k_tz is imaginary and the wave becomes a surface wave propagating in the x direction with a exponentially decaying amplitude, i.e.,

The table below lists the notations used in the applet and their definitions

Ex 1: Let f = 100 MHz, m₁ = m₀ , e₁ = 3e₀, m₂ = m₀ , e₂ = 4e₀ , q_i = 60^o

then, applying the equations above,

k₁ = 3.63,  k₂ = 4.19

q_t = 48.6^o  

k_x = 3.14,  k_z = 1.82,  k_tz = 2.77

R_h = -0.07, T_h = 0.93

At z = -1 we have

|H₁| = 1.06  , |H₂| = 0.93