Are Electromagnetic Waves Always Transverse?

[Delta2]

In this insight, we shall endeavor in the realm of classical electrodynamics and examine whether EM waves are always transverse. We shall make use of Jefimenko’s equations and Poynting’s Theorem and conclude that

EM waves are always transverse per the  weak definition of transverse where we only require the fields to be perpendicular to the propagation vector
EM waves are not always transverse per the strong definition of transverse where we also require that the E and B fields are perpendicular to each other

For what follows we’ll assume that the region of interest where we examine the behavior of the fields is in a vacuum. Similar conclusions should hold for regions filled with linear, isotropic nondispersive materials. This is needed so that the Poynting vector equals a nice simplified form.
We also will assume that there are no boundaries that...

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[vanhees71]

Great article, but of course this is for vacuum E&M only. In matter you can have" plasma waves"! A nice summary is here:

https://en.wikipedia.org/wiki/Waves_in_plasmas

 

[bobob]

Also, in waveguides you can have modes where only the electric or magnetic fields are transverse. For TE mode, there is no electric component in the direction of propagation. For a TM mode, there is no magnetic field in the direction of propagation and for a TEM mode both the E and H fields are transverse, TEM modes cannot be supported in a hollow waveguide. Those are what you get in coax cable.

 

[Delta2]

Also, in waveguides you can have modes where only the electric or magnetic fields are transverse. For TE mode, there is no electric component in the direction of propagation. For a TM mode, there is no magnetic field in the direction of propagation and for a TEM mode both the E and H fields are transverse, TEM modes cannot be supported in a hollow waveguide. Those are what you get in coax cable.

Yes in waveguides there are boundary conditions imposed on the E,B fields that make the direction of propagation different than the direction of the Poynting vector. In this article we assumed that there are no boundary conditions imposed on the fields and that the propagation direction coincides with the direction of energy flow.
I believe in the waveguide case, the Poynting vector has one major component along the direction of propagation, and one smaller component perpendicular to the propagation direction, which represents a small fraction of energy that is trapped between the walls of the waveguide.

 

[Adesh]

A very nice article and easy to read. I really liked when you concluded from the integrands that the fields will be perpendicular, that cross-product maneuver was very elegant.

 

[nasu]

Great article but I believe it should be made more explicit the fact that it refers to a restricted case.
Given the fact that there are many exceptions, the wording ("fields are always perpendicular to the direction of propagation") is misleading. Especially for such students who are too easily inclined to memorize a statement without a care about the conditions of valability of that statement. As the title does not specify any conditions, the answer should be definitely "NO". Source https://www.physicsforums.com/insights/are-electromagnetic-waves-always-transverse/

 

[jasonRF]

Great article but I believe it should be made more explicit the fact that it refers to a restricted case.
Given the fact that there are many exceptions, the wording ("fields are always perpendicular to the direction of propagation") is misleading. Especially for such students who are too easily inclined to memorize a statement without a care about the conditions of valability of that statement. As the title does not specify any conditions, the answer should be definitely "NO".

Yes - when I saw the title I was assuming the answer would be NO... The author lists some of the restrictions at the top of the article, but perhaps could add that they are also assuming there are no boundaries. Delta2 is of course dealing with the most important cast (in my opinion), if not the most general.

 

[Delta2]

Yes it is true that if we want to answer directly the question of the article then the answer is NO, electromagnetic waves are NOT always transverse(with either the weak or the strong notion).

However given that the medium of propagation is the vacuum (or any linear, isotropic and non dispersive medium where the Poynting vector gets the nice form $$\mathbf{S}=\mathbf{E}\times\mathbf{H}=\mathbf{E}\times\frac{1}{\mu}\mathbf{B}$$) and also given that there are no boundaries (I ll edit the insight and add this condition as @jasonRF notes) then the fields are perpendicular to the direction of propagation, and furthermore in the far region they are perpendicular to each other.

 

[vanhees71]

This is way more subtle! There is a century-old debate about Minkowski vs. Abraham and which is the right energy-current density or the momentum density of the em. field in polarizable media. The resolution is very salomonic: Both approaches are correct describing the canonical vs. the kinetic momentum of the field, and which one you have to consider depends on the situation you want to describe. See, e.g.,

https://doi.org/10.1098/rsta.2009.0207 (open access!)