An interface exists between two semi-infinite media at the plane defined by $z = 0$. Region 1 is defined by $z < 0$ and Region 2 is defined by $z > 0$. The material in Region 1 is defined by $Re[\epsilon_1] = 100 \text{ pF/m}$, $Im[\epsilon_1] = 0$, $Re[\mu_1] = 5 \text{ µH/m}$, and $Im[\mu_1] = 0$. The material in Region 2 is defined by $Re[\epsilon_2] = 200 \text{ pF/m}$, $\tan \delta_2 = 0.5$, $Re[\mu_2] = 50 \text{ µH/m}$, and $Im[\mu_2] = 0$. If a wave is incident on this interface from Region with following form:
$\vec{E_1^+} = 600e^{-\alpha_1 z} \cos(5 \times 10^{10}t - \beta_1 z)\hat{a}_x \text{ V/m}$,
determine the following:
a) Attenuation coefficient in Region 1, $\alpha_1$
b) Phase constant in Region 1, $\beta_1$
c) Phasor form of the forward propagation wave in Region 1
d) Phasor form of the backward travelling wave in Region 1
e) Phasor form of the forward travelling wave in Region 2
f) Phasor form of the backward travelling wave in Region 2
