Question on wave equation of plane wave.

[yungman]

For plane wave travel in +ve z direction in a charge free medium, the wave equation is:

$$\frac{\partial^2 \widetilde{E}}{\partial z^2} -\gamma^2 \widetilde E = 0$$

Where $\gamma^2 = - k_c^2 ,\;\; k_c= \omega \sqrt {\mu \epsilon_c} \hbox { and } \epsilon_c = \epsilon_0 \epsilon_r -j\frac{\sigma}{\omega}$ .


$$\widetilde E = E_0^+ e^{-\gamma z} \;+\; E_0^- e^{\gamma z} \;=\; E_0^+ e^{-\alpha z}e^{-j \beta z} \;+\; E_0^- e^{\alpha z}e^{j \beta z}$$

Notice the second term is the reflected wave AND is growing in magnitude as it move in -ve z direction! That cannot be true. It should still decay at rate of $e^{-\alpha z }$.

What am I missing?

 

[Delta2]

erm as we move towards -ve z direction z gets smaller and smaller hence $$e^{az}$$ gets smaller too for a>0.

 

[yungman]

Why didn't I think of that!

Thanks

 

[Delta2]

Happens to me too, when i focus my mind on something i miss some relatively simple things.