Intensity of elliptically polarized light

In summary, the time averaged norm of the Poynting vector of an electromagnetic field with elliptically polarized light is given by I(\bar{x})=\frac{c\epsilon_{0}}{2}(\bar{E}_{0x}^{2}+2\bar{E}_{0x}\cdot\bar{E}_{0y}\cos\delta+\bar{E}_{0y}^{2}) in SI-units J/(m^{2}s). This can be verified by setting \delta=0 for a linear polarized beam and finding I(\bar{x})=\frac{c\epsilon_{0}(\bar{E}_{0x}+\bar{E}_{0y})^{2
  • #1
Wox
70
0
The time averaged norm of the Poynting vector of this electromagnetic field (elliptically polarized light):
[tex]
\begin{split}
\bar{E}(t,\bar{x})=&(\bar{E}_{0x}+\bar{E}_{0y}e^{i \delta})e^{\bar{k}\cdot\bar{x}-\omega t}\\
\bar{B}(t,\bar{x})=&\frac{1}{\omega}(\bar{k}\times\bar{E}(t,\bar{x}))
\end{split}
[/tex]
with [itex]\bar{E}\perp\bar{B}\perp\bar{k}[/itex], becomes (as I calculated in SI-units [itex]J/(m^{2}s)[/itex])
[tex]
I(\bar{x})=\left<\left\|\bar{P}(t,\bar{x})\right\|\right>=\frac{c\epsilon_{0}}{2}(\bar{E}_{0x}^{2}+2\bar{E}_{0x}\cdot\bar{E}_{0y}\cos\delta+\bar{E}_{0y}^{2})
[/tex]
I have been trying to verify this, but I can't find a source that explicitly discusses this. For a linear polarized beam, [itex]\delta=0[/itex] so that [itex]I(\bar{x})=\frac{c\epsilon_{0}(\bar{E}_{0x}+\bar{E}_{0y})^{2}}{2}[/itex], which is correct. For general elliptical polarization I found this link which basically says that
[tex]
I(\bar{x})=E_{x}E_{x}^{\ast}+E_{y}E_{y}^{\ast}= \bar{E}_{0x}^{2}+\bar{E}_{0y}^{2}
[/tex]
which can't be right (as it doesn't work for linear polarized light). Does anyone know of a proper reference for this? Or even better, can someone verify my solution?
 
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  • #2
Ok, this is embarassing. I didn't see that [itex]\bar{E}_{0x}\cdot\bar{E}_{0y}=0[/itex] which fixes the problem.
 

What is elliptically polarized light?

Elliptically polarized light is a type of electromagnetic radiation in which the electric field vector traces an elliptical path as the light propagates through space.

What is the difference between elliptically polarized light and linearly polarized light?

Elliptically polarized light is a combination of two perpendicular linearly polarized waves with different amplitudes and phases, whereas linearly polarized light consists of only one linearly polarized wave.

How is the intensity of elliptically polarized light measured?

The intensity of elliptically polarized light is measured by taking the square of the electric field amplitude at each point in space and averaging it over one period of the wave.

What factors affect the intensity of elliptically polarized light?

The intensity of elliptically polarized light is affected by the amplitudes and phases of the two linearly polarized waves that make up the elliptical polarization, as well as the angle between their electric field vectors.

Can the intensity of elliptically polarized light be changed?

Yes, the intensity of elliptically polarized light can be changed by altering the amplitudes and phases of the two linearly polarized waves that make up the elliptical polarization. This can be done using optical devices such as polarizers, wave plates, and quarter-wave plates.

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