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I know that the magnetic and electric field vectors are perpendicular to each other and the direction of propagation of the wave. I believe that the direction of those field vectors can rotate around the axis of forward propagation. This is more of a practical question than a mathematical one. I'm wanting to physically generate EM waves and find the orientation of the electric field vector. How do I set up this experiment? How can I physically test for that orientation at a specific location?

For clarity, I'm specifically interested in 4-10MHz waves.

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    $\begingroup$ The antenna you use to generate the waves will determine the polarization. $\endgroup$
    – The Photon
    Aug 30, 2022 at 18:26
  • $\begingroup$ I understand that, but how do I figure out what the polarization actually is? I don't know how to look at an antenna and figure out what the electric field is going to do. $\endgroup$
    – Tsaru
    Aug 31, 2022 at 22:31
  • $\begingroup$ use a polarization selective receiver antenna, or place a polarizing filter (as proposed in Shaktyai's answer) in front of your receiver, and rotate it to determine the polarization. If you need to distinguish between RCP and LCP polarizations, you may need an antenna specifically sensitive to circularly polarized signals. $\endgroup$
    – The Photon
    Sep 1, 2022 at 2:23

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You must use a "polarizing filter" made of five copper rods supported by a 1-meter square wooden frame. enter image description here

The spacing between the rods is about (0.4)λ. This "filter" is placed between the transmitting and receiving antennas. When the rods are parallel to the transmitting antenna (i.e., E-field), the field does work in moving electrons along the length of the rods and reduces the energy in the field. This is depicted in the figure below. enter image description here

Consequently, if the receiving antenna is also parallel to the rods, very little energy reaches it and the bulb does not light. When the rods are perpendicular to the transmitting antenna, the light bulb on the receiving antenna shows no appreciable diminution in power received.

The filter can be rotated so that it is 45˚ w.r.t. the transmitting antenna. The receiving antenna light bulb will dim, but stay lit. If the receiving antenna is now also rotated 45˚, so that it is perpendicular to the rods, the intensity of the light increases again, notwithstanding that the receiving antenna is now tilted 45˚ w.r.t. the transmitting antenna. This is a nice analog of rotating the plane of polarization of light with polarizing filters.

Source:

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  • $\begingroup$ Can this method distinguish between left and right circularly polarized waves? $\endgroup$
    – The Photon
    Sep 1, 2022 at 2:24
  • $\begingroup$ @ThePhoton Circular polarization is a specific linear combination of perpendicular plane polarizations. A single absorbing filter will just eat one polarization and transmit the other. With two perpendicular absorbing filters, it might be possible to measure the phase shift between the orthogonal transmitted waves. (I’m not a radio guy so there’s probably a better way.) $\endgroup$
    – rob
    Sep 1, 2022 at 3:47
  • $\begingroup$ @ the photon Obviously the method is quite crude and you the electrons will flow in the wire with the two types of polarization. From what I remember from lab courses, we were using a reflection on a mirror (metal sheet) physics.bu.edu/~duffy/sc545_notes08/brewster.html $\endgroup$
    – Shaktyai
    Sep 1, 2022 at 9:44
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If you add two linearly-polarized electromagnetic waves traveling in the same direction but with different polarization vectors and different temporal phases, you will get what is called an elliptically-polarized plane wave. Suppose one plane wave is polarized along the $\hat x$ axis, while another is polarized along the unit vector $\hat \epsilon$ within the $x$-$y$ plane and given temporal phase $\delta_{\epsilon}$, both propagating along the $\hat z$ axis. This could be described by

$$\vec{E}(x,y,z,t)=E_{0,x}\cos (kz-\omega t)\hat x+E_{0,\epsilon}\cos (kz-\omega t -\delta_{\epsilon} ) \hat \epsilon$$

If $\hat \epsilon = \hat y$ and $\delta_{\epsilon}=0$, the resulting $\vec E$ vector at any point will trace out a circle, and thus is called circular polarization.

As for generating circularly polarized radiation, it would depend on which frequency you're trying to generate. As an example, to produce circularly polarized visible light, you could simply buy a circular polarizer, which you can find in most modern 3D glasses at movie theaters. Simply shine unpolarized light through the filter, and voila - unpolarized light. Likewise, to detect circularly polarized light, simply place your detector (e.g. your eye) behind one of these filters.

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  • $\begingroup$ Can you make it more clear how this addresses OP's questions: "How do I set up this experiment? How can I physically test for that orientation at a specific location?" $\endgroup$
    – The Photon
    Aug 30, 2022 at 18:31
  • $\begingroup$ @ThePhoton Good point, I'll amend my answer to address this. $\endgroup$ Aug 30, 2022 at 18:32
  • $\begingroup$ Thanks for taking the time to answer! To be honest, your answer is a bit over my head, but I understand a lot of the pieces so I'll spend some time with it to try and understand the whole. I should have been specific, but I'm more focused on radio frequency electromagnetic waves, and determining the orientation of the electric field at a given point away from the generator. $\endgroup$
    – Tsaru
    Aug 31, 2022 at 22:28
  • $\begingroup$ @Tsaru Oh sorry, I wrote it assuming you were taking an undergraduate course on electricity and magnetism. I believe Shakytai's answer may have been worded better. The basic idea is that, if you measure the voltage/current across a straight conducting wire/rod as a function of time, you can measure electromagnetic waves that pass by it. The electric field component of an EM wave will push the free charges within the conducting wire back and forth. $\endgroup$ Sep 1, 2022 at 21:53

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