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Conflicting Definitions of S and P Polarization

Posted on 2012-03-03 as part of the Photonics Spotlight (available as e-mail newsletter!)

Permanent link: https://www.rp-photonics.com/spotlight_2012_03_03.html

Author: Dr. Rüdiger Paschotta, RP Photonics AG, RP Photonics AG

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.

Dr. Rüdiger Paschotta

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:

  • Usually, p-polarized light is understood to have an electric field direction parallel to the plane of incidence on a device, and s-polarized light has the electric field oriented perpendicular to that plane. (Actually, the letters have a German origin: s = senkrecht = perpendicular, p = parallel.) According to that definition, we can obtain vanishing reflectivity of a surface at Brewster's angle for p polarization. That's easy to remember: “p” is closer to “B” (like “Brewster”), so Brewster's trick works with p polarization.
  • In the context of diffraction gratings, the opposite definition can be found. Here, “s” still means perpendicular, but in that case perpendicular not to the plane of incidence, but to the lines of the grating. So for s polarization, the electric field vector is perpendicular to the lines, i.e., it lies in the plane of incidence.

So there is another trap to fall into! When reading some paper, we have to find out which definition has been used.

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.

This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the RP Photonics Encyclopedia.

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Questions and Comments from Users


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.

The author's answer:

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.


When there is normal incidence, how can I define the plane of incidence and s and p polarizations?

The author's answer:

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

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