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I’m a radio amateur (ham). Let us consider a half wavelength horizontal dipole antenna in free space – say at 10MHz and look at its far field.

Conventional high school physics says that because the antenna is horizontal, the electrons are accelerated horizontally and the resulting electromagnetic (radio) wave is horizontally polarised.

(Incidentally, this appears only to be true when broadside on. Due to simple 3D geometry, a vertical component creeps in when off-axis (see the plots from an antenna modelling program eg MMANA-GAL).)

However we know that linear polarisation (eg horizontal) can also be described by the combination of a right hand circular polarised wave with a left hand one. Obviously the amplitudes must be equal and for horizontal the two circularly polarised waves need to be in-phase.

We also know that circular polarisation of a wave is the manifestation of photon spin. Two photon spin states are permitted, and so its angular momentum can be either right hand, or left hand. Hence RHCP and LHCP waves.

Question:

So how can the above antenna be described to explain the production of right hand and left hand spin photons which when combined produce linear polarisations?

There appear to be two obvious possibilities. Either:

A) Production of opposite spin photons happens as a concerted process throughout the antenna such that all parts of the antenna produce equal numbers of RH and LH photons?

Possibly this might be due to the photon’s spin resulting from spin of the electron which has been accelerated. Because electron spins are evenly distributed throughout the antenna wire, so the resulting photons are evenly spread out in the resulting wave.

B) Opposite photon spins are produced simultaneously, but from opposite ends of the dipole antenna.

This might be due to the direction of current flow (ie electron flow). It flows into one arm of the dipole producing one spin, but at the same time electrons flow out of the other limb, so producing the opposite spin at the same time ie from positive and negative accelerations in the direction of electron flow.

Any comments please? The Internet is remarkably quiet about this!

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  • $\begingroup$ As an FYI, there is a Ham site here on Stackexchange. You might want to stop by. $\endgroup$ – Jon Custer Mar 21 '18 at 13:38
  • $\begingroup$ Many thanks for the pointer! I wasn't aware of ham.stackexchange.com. Have just taken a look and sadly it is lacking the rigour that I'm enjoying here on physics.stackexchange. Its not only knowledgeable, but also a supportive community. My apologies for lower the tone of its debate with lowly ham radio! Many thanks! $\endgroup$ – G4FLQ Mar 23 '18 at 9:13
  • $\begingroup$ Oh, I wasn’t worried about lowering the tone, just making sure a newish user found it! $\endgroup$ – Jon Custer Mar 23 '18 at 14:34
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If you want to describe this process in terms of photons, then you must understand the notion of quantum superposition, so you're going to need to learn about this notion if you haven't already done so to understand what's happenning here.

Each photon produced by a linear polarizing antenna is a quantum superposition of a one photon left handed circular polarized Fock state and a one photon right handed circular polarized Fock state.

And it's more accurate to say that the quantum field is in a pure coherent state where all the Fock states are quantum superpositions of corresponding number left and right handed circular polarized states.

A classical current is well known to produce photons in pure states. There's nothing stochastic about the photon state that most antennas produce.

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  • $\begingroup$ To put it another way: the photons from an antenna are LH and RH, in the same sense that Schrödinger's cat is alive and dead before one opens the box. $\endgroup$ – Michael Seifert Mar 21 '18 at 13:02
  • $\begingroup$ @MichaelSeifert Actually that's a great way to put it to this particular poster, who probably would have to do a bit of reading otherwise to decode my answer. Thanks. $\endgroup$ – WetSavannaAnimal Mar 21 '18 at 13:03
  • $\begingroup$ @WetSavannaAnimal aka Rod Vance Yes I’m still re-reading^n your reply! Just to clarify 100%: if superposition makes it a pointless question to ask of a single photon, presumably it also makes it equally pointless to ask where on an antenna and when in the ac cycle a given CP wave originates? However in the antenna’s far field, is it still OK to talk of say RHCP wave being formed of just photons with a single spin, or have I got more reading to do? $\endgroup$ – G4FLQ Mar 23 '18 at 9:34
  • $\begingroup$ @G4FLQ Try reading my answer here or here for more info. The first chapter of the book "Quantum Optics" by Scully and Zubairy gives a great deal of insight. There was also an issue of "Optics and Photonic News" (a magazine put out by the Optical Society of America) wholly devoted to the question "What is a Photon?" in 2006 or 2007 and this is a good read too. $\endgroup$ – WetSavannaAnimal Mar 23 '18 at 9:42

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