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I have often seen people informally (and sometimes formally) refer to TE and TM modes interchangeably with polarization. I don't see how these modes are related to polarization.

Here is what I think is right:

If one has a TE mode in a simple rectangular metal waveguide, the component of the electric field in the direction of propagation is zero. This is not true for the TM mode, which can have a non-zero component along the direction of propagation. Let us consider that the electric field is horizontally polarized. That is, the mode has a non-zero electric field along the x-axis and a zero field along the y-axis and z-axis.

Now, if we rotate the polarization of this mode by 90 degrees, the electric field is non-zero along the y-axis but zero along the x-axis and z-axis. The magnetic field can now have non-zero components along the x-axis and z-axis but zero along the y-axis.

In this case, the mode is still TE, but just polarized vertically instead of horizontally.

However, this is not what is found in multiple answers on this Researchgate page.

One of the answers from that page is:

TE and TM are used to describe polarization relative to a device (modes in a waveguide, waves incident onto a surface, etc.), while vertical and horizontal describe polarization relative to the ground.

That answer doesn't make much sense to me because it doesn't appear to be referring to which field (electric or magnetic) has a non-zero component along the direction of propagation.

Tl;Dr: how and why are TE and TM modes related to the polarization of light in a waveguide?

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  • $\begingroup$ Simply put, not everybody who answers questions on Researchgate knows what they are talking about. The same is true here, but at least we have the voting mechanism to help you work out which answers are and aren't sensible. $\endgroup$
    – The Photon
    Oct 20, 2022 at 4:10

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I would not say that TE and TM describe polarizations, although the mode is closely related to the polarization.

If we're talking about a rectangular waveguide, then a TE mode will in fact have a definite linear polarization of the electric field. The magnetic field, on the other hand will have a polarization with a component along the longitudinal axis of the waveguide, and the polarization may vary along the waveguide at any instant in time.

The TM mode will not have a definite polarization of the electric field. The electric field will have a longitudinal component, and as with the magnetic field of the TE mode its polarization will be varying along the waveguide.

As to the answer you found on Researchgate, I believe it is simply somewhat confused, although it is not completely wrong (linear polarizations due specify the polarization relative to some Cartesian coordinate system, which might often be oriented with a specific relationship to the physical ground).

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  • $\begingroup$ Thanks! Could you also confirm that rotating the polarization of a TE mode yields simply another TE mode (assuming it is a solution for that system) and does not become a TM mode? $\endgroup$
    – Paddy
    Oct 21, 2022 at 2:55

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