Light pipephysics

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Indeed I found such a statement on the page https://en.wikipedia.org/wiki/Polarization_(waves) (under “s and p designations”), and some others sources show similar things. However, I don't agree with that. In my opinion, one should not use the terms transverse-electric and transverse-magnetic (https://en.wikipedia.org/wiki/Transverse_mode) in the context of electromagnetic waves propagating in a simple homogeneous medium, where both electric and magnetic fields are perpendicular to the propagation direction. These terms are appropriate in the context of waveguide modes and the like, where we do have guided light. TE then means that the electric field is perpendicular to the propagation direction, while the magnetic field is not; a plane of incidence does not occur there.

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By the way, some people call a laser beam s-polarized, when its polarization is vertical, i.e., perpendicular to the lab's floor. It is better, though, to restrict the terms s polarization and p polarization to cases where the polarization direction with respect to a plane of incidence is relevant. For example, if you have a Brewster-angled prism in the common orientation where the reflected beam stays horizontal in direction, s polarization according to the first definition above is vertical. However, if you turn the prism such that the reflected beam goes upwards, that will change, of course.

Wikipedia says that TE = s, TM = p. Are these notations completely replaceable? I don't think so, but I couldn't find clear explanation of it.

Abstract: There are conflicting definitions of s and p polarization in the scientific literature. What some people call p polarization, is s polarization for others. Obviously, that can cause confusion.

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It is quite common to talk about s-polarized and p-polarized laser beams, incident on optical surfaces or diffraction gratings. Therefore, it is quite disturbing that there are conflicting definitions in the scientific literature:

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These explain quite comprehensively a wide range of aspects, not only physical principles of operation, but also various practical issues.

These are then no longer relevant: the optical effects will not depend on the polarization direction, assuming non-birefringent materials.