0
$\begingroup$

If I have a linearly polarised plane wave given by \begin{equation} \textbf{E}_i (\textbf{r})=E_i e^{-ik_0 z}\hat{\textbf{x }} \end{equation} Then is the counter-propagating wave (the wave coming in the other direction) just written as \begin{equation} \textbf{E}_c (\textbf{r})=E_c e^{ik_0 z}\hat{\textbf{x }}~? \end{equation}

I am confused because of the sign of $\hat{x}$. I am given only the electric field, but if you do the cross product of $-\hat{x}$ with the same direction of magnetic field then you get the opposite direction. Which is the right answer?

$\endgroup$
4
$\begingroup$

First, you need to specify the time-component in order to establish the direction of propagation, which depends on the relative sign in $kz\pm\omega t$.

Next, as written, the wave propagates either along $\pm \hat z$, so it must be that, while you cannot establish if $e^{ikz}$ propagates to the left or the right, $e^{-ikz}$ will propagate in the reverse direction. The $\hat x$ direction does not enter in the direction of propagation beyond being orthogonal to the direction $\pm\hat z$ of propagation.

$\endgroup$
  • $\begingroup$ Yeah I forgot to say $\textbf{E}_i (r,t) = E_i (r) e^{-i \omega t}$. So the conclusion is that $e^{ikz}$ moves in the opposite direction? $\endgroup$ – math4everyone Jan 22 '17 at 1:12
0
$\begingroup$

In the equation of the electric field that you have given, the information about direction of the propagation is contained in the exponential. When the exponential is negative, the wave is called right polarized and it prpagates in the clockwise direction. Otherwise, it propagates in the counter clockwise direction.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.