Polarization of EM waves is preserved after reflection/refraction -- Why?

Click For Summary

Discussion Overview

The discussion centers around the preservation of the polarization state of electromagnetic (EM) waves during reflection and refraction, particularly in the context of Fresnel's equations. Participants explore the theoretical underpinnings, boundary conditions, and specific examples that challenge or support the notion of polarization conservation.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that the isotropic nature of boundary conditions leads to the conservation of transverse electric (TE) and transverse magnetic (TM) modes upon reflection and refraction.
  • Others question the ease of concluding TE/TM conservation from isotropic boundary conditions, suggesting that further algebraic proof is necessary.
  • A participant references Feynman's lectures, indicating that there is significant algebra involved in the derivation of these principles.
  • Another participant mentions the 1962 edition of Jackson Classical Electrodynamics as a source that details these concepts, emphasizing the importance of understanding Brewster's angle and the behavior of circularly polarized waves upon reflection.
  • One participant provides a counterexample, stating that a linearly polarized radio wave can change its polarization state when interacting with a dipole oriented away from the electric field plane.
  • Concerns are raised about the implications of non-perfect conductors, suggesting that a pseudo Brewster angle effect could lead to changes in polarization state due to differing reflection effects on resolved components of a wave.

Areas of Agreement / Disagreement

Participants express differing views on the preservation of polarization, with some supporting the notion of conservation under certain conditions while others provide counterexamples and challenge the assumptions involved. The discussion remains unresolved regarding the definitive proof of polarization conservation.

Contextual Notes

Participants note that the discussion relies on specific assumptions about boundary conditions and the nature of the reflecting surfaces, which may not hold in all scenarios. The complexity of the algebra involved in proving these concepts is also acknowledged.

xxxyyy
Messages
14
Reaction score
2
Hello,
here's my question:
during the usual derivation of Fresnel's equations, it is assumed that an incident EM wave (plane monochromatic) is transverse electric or magnatic and that it keeps this nature after reflection and transmission.
How can this be proven?
Thank you!
 
  • Like
Likes   Reactions: Delta2
Physics news on Phys.org
Because the boundary condition itself is isotropic in the plane. Notice it will change the sense of circular polarization upon reflection.
 
  • Like
Likes   Reactions: vanhees71
I'm sorry I have to bring up again this discussion but I don't get why from isotropic boundary conditions it's so easy to conclude TM/TE "conservation" upon reflection/refraction.
Apart from that, here, in Feynman's lectures
https://www.feynmanlectures.caltech.edu/II_33.html
below Fig. 33-6, he says there's a lot of algebra behind it...
Has anyone ever done this calculation? I don't seem to find it anywhere and I'd really like to see it.
Thanks everyone!
 
Its done in my 1962 edition of Jackson Classical Electrodynamics. The details are, well, detailed. So long as you understand Brewster's angle and why a circularly polarized wave changes helicity upon reflection you know what you need IMHO.
 
  • Like
Likes   Reactions: vanhees71
hutchphd said:
Its done in my 1962 edition of Jackson Classical Electrodynamics. The details are, well, detailed. So long as you understand Brewster's angle and why a circularly polarized wave changes helicity upon reflection you know what you need IMHO.
1962 edition of Jackson? I thought the first edition was 1973...
 
NVM my mistake its 1962. All this time i thought i had the first edition but i actually had the second edition (which is from 1975 not 1973) which i bought back at 1999 when I couldn't find the 3rd edition in Greek bookstores.
 
Last edited:
  • Like
Likes   Reactions: hutchphd
xxxyyy said:
it keeps this nature after reflection and transmission.
That's not always the case. I only need one example to show this: If a linearly polarised radio wave is intercepted by a dipole that's orientated away from the plane of the E field then there will be a wave, re-radiated from the dipole that's in the plane of the dipiole.
 
hutchphd said:
Its done in my 1962 edition of Jackson Classical Electrodynamics. The details are, well, detailed. So long as you understand Brewster's angle and why a circularly polarized wave changes helicity upon reflection you know what you need IMHO.
In chapter 7.5 Jackson assumes it (pag 218, "all the electric fields are shown directed away from the viewer"). He actually discards the first boudary condition, saying it gives nothing...
It is satisfied, and that's good, but, as Feynman said, we need to prove that this is the only solution (together with the other one, the transverse magnetic).
Is it proven somewhere else in the book?
 
Delta2 said:
1962 edition of Jackson? I thought the first edition was 1973...
I graduate school I used my 1962 ed from my undergraduate course rather than buy the second edition. The first test, do problems 11.2, 14.7 ...
 
  • Like
Likes   Reactions: Delta2 and hutchphd
  • #10
It's worth noting that isotropy of the boundary conditions in the plane means that the induced surface current will be in the same direction as the incident electric field component in the plane. To change linear polarization, the induced currents would need to have components normal to this direction. This would violate the stated isotropy.
 
  • Like
Likes   Reactions: vanhees71, DaveE and hutchphd
  • #11
If the surface is
Paul Colby said:
It's worth noting that isotropy of the boundary conditions in the plane means that the induced surface current will be in the same direction as the incident electric field component in the plane. To change linear polarization, the induced currents would need to have components normal to this direction. This would violate the stated isotropy.
If the reflecting surface is not a perfect conductor, we may find a pseudo Brewster Angle effect. Waves approaching at this angle, if in the plane of the paper, are weakly reflected. Waves normal to the paper are strongly reflected. But if we have a wave polarised at 45 degrees to the paper, it may be resolved into two waves in the principle planes. These two waves suffer different reflection effects, in amplitude and phase, so when they are re-combined to give the emergent ray we might find it to be elliptically polarised.
 
  • Like
  • Informative
Likes   Reactions: vanhees71, Paul Colby and Delta2

Similar threads

  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 21 ·
Replies
21
Views
2K
  • · Replies 15 ·
Replies
15
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 10 ·
Replies
10
Views
6K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 15 ·
Replies
15
Views
4K