# Some questions about polarization and intensity

1. Sep 10, 2011

### a b

Hello everybody,
I have some questions:

I'm talking only about travelling waves, not standing waves.
If a linear polarized electromagnetic wave has electric field amplitude E_0, i know that its intensity is given by

I=(1/2) (E_0^2 ) /c

that is the Poynting vector averaged over a period.

But if I have the same E_0 amplitude in a circularly polarized wave, the Poynting vector remains constant so i'd expect to have an intensity

I= (E_0^2)/c

this difference sounds strange to me: am I right or am I making some mistake?

and also, if I send a circularly polarized wave through a linear polarizer, what will it be the intensity of the wave exiting from the polarizer?
And if I send a linearly polarized wave through a circular polarizer (circular dichroic filter), am I right if I say that the exiting wave will have the same intensity but with a linear polarization rotated in respect to the ingoing wave?

Thank you in advance and sorry if my english is not very good.

2. Sep 10, 2011

### BruceW

Actually, the time-average of the Poynting vector of a linearly polarised plane wave is equal to:
$$\frac{\varepsilon_0 c}{2} E_0^2$$

3. Sep 10, 2011

### a b

to BruceW:
I was certainly wrong , but maybe you too, or maybe you were just using a notation that I don't know:
if you define Poynting vector as
$$\vec S= \frac{1}{\mu } \vec E \times \vec B$$

then you have, for linear polarization,

$$<S>= \frac{1}{2} \sqrt{\frac{\varepsilon }{\mu}} E_0^{2}$$