Is polarised light a result of destructive interference?

[Jilang]

This question is prompted by a recent discussion I have been following regarding the insertion of a 45 degree angle polariser between two polarisers at 90 degrees to each other. The insertion of the filter seems to restore missing components which would suggest that those components were present all along, but just not apparent. It was reminiscent of Huygens principle as applied to the direction of light propagation where destructive interference keeps things moving in the right direction, until say the light passes through a slit and some of the components that were responsible for destructive interference are removed (and after which the light spreads out). Is there a Huygens type principle that applies to polarisation?

 

[Matternot]

First of all, this question really got me thinking. It's a really good question.

The intermediate polariser does reveal a component of the wave, but that component isn't necessarily missing. This effect is a quantum mechanical effect where the measurement of the polarisation of the photons in a particular direction sets it into that direction (thus revealing it having a probability of being measured in that direction). Until then the photons are in a quantum superposition.

Polarisers themselves work by having polymer chains that react strongly with waves polarised in a particular direction (often along their length) and therefore only absorb photons polarised in that direction. They aren't actually waves passing small slits as suggested in high school.

No more waffle. About the actual question:

Slits can be explained using Huygen's principle because this is a phenomena deriving from the concept of interference. I'm not entirely familiar with "destructive interference keeps things moving in the right direction, until say the light passes through a slit and some of the components that were responsible for destructive interference are removed (and after which the light spreads out)" phenomena, so I will look that up soon. My immediate thought that Huygen's principle would be difficult to apply to a polariser because polarisers aren't immediately related to interference. It is also a quantum mechanical effect, meaning that there is no certainty that Huygen's principle wouldn even explain it fully. (e.g. it doesn't explain diffraction when photons are fired one at a time).

My later thought is that with diffraction and polarisation both being quantum mechanical effects, could it be possible to reduce this polarisation problem to a similar one involving slits (to which I could try to use huygen's). I can't yet think of a way to reduce the problem. It is difficult since they are, to me, they seem to be about different quantum mechanical phenomena.

These are just my thoughts.

I hope someone comes up with a solution!

 

[tech99]

First of all, this question really got me thinking. It's a really good question.

The intermediate polariser does reveal a component of the wave, but that component isn't necessarily missing. This effect is a quantum mechanical effect where the measurement of the polarisation of the photons in a particular direction sets it into that direction (thus revealing it having a probability of being measured in that direction). Until then the photons are in a quantum superposition.

Polarisers themselves work by having polymer chains that react strongly with waves polarised in a particular direction (often along their length) and therefore only absorb photons polarised in that direction. They aren't actually waves passing small slits as suggested in high school.

No more waffle. About the actual question:

Slits can be explained using Huygen's principle because this is a phenomena deriving from the concept of interference. I'm not entirely familiar with "destructive interference keeps things moving in the right direction, until say the light passes through a slit and some of the components that were responsible for destructive interference are removed (and after which the light spreads out)" phenomena, so I will look that up soon. My immediate thought that Huygen's principle would be difficult to apply to a polariser because polarisers aren't immediately related to interference. It is also a quantum mechanical effect, meaning that there is no certainty that Huygen's principle wouldn even explain it fully. (e.g. it doesn't explain diffraction when photons are fired one at a time).

My later thought is that with diffraction and polarisation both being quantum mechanical effects, could it be possible to reduce this polarisation problem to a similar one involving slits (to which I could try to use huygen's). I can't yet think of a way to reduce the problem. It is difficult since they are, to me, they seem to be about different quantum mechanical phenomena.

These are just my thoughts.

I hope someone comes up with a solution!

May I suggest an experiment with microwaves which I have done and which might be helpful. Consider a horizontal transmitting antenna and a vertical receiving antenna. No reception occurs, but the energy is present in the path. Now place a metal rod between the two antennas, tilted at 45 degrees and in a plane normal to the path . Now a signal is received. The horizontally polarised wave excites a current on the rod, which then re-radiates energy with 45 degree polarisation. The 45 degree polarisation can be considered as comprising H and V components, and the V component is received by the antenna. The experiment also works using three polarising grids.

 

[Jilang]

Thanks Stephen and tech99. The antenna experiment is very interesting. The photons approaching the 45 degree antenna presumably then could be safely declared to be different photons to the ones leaving it? How far would this be applicable to the way polarising filters work?

 

[sophiecentaur]

The photons approaching the 45 degree antenna

When dealing with a classical wave problem, it is not helpful to introduce photons. It doesn't add to any 'understanding' of the situation; rather, I would say, it detracts. Photons cannot be described as 'individuals' or 'different' in this context. They are merely the dollops of energy that are emitted and then detected or not, by the final receiver. Talking in terms of single, identifiable photons takes you into the realm of Fock States, which is definitely not related to classical wave theory.

 

[tech99]

Thanks Stephen and tech99. The antenna experiment is very interesting. The photons approaching the 45 degree antenna presumably then could be safely declared to be different photons to the ones leaving it? How far would this be applicable to the way polarising filters work?

I think you are correct about the photon explanation. In the case of Polaroid film, it seems to have needle-like crystals which all point in the same direction, so I presume the mechanism is similar to the microwave case.

 

[sophiecentaur]

The formation of polarised light by the 'addition' of two beams (coherent, of course) is the result of how vectors work. You could. I suppose, say that one polarisation can be canceled and the other enhanced in the same way that power in one direction can be canceled and enhanced in another in an interference pattern. I would really think that the term 'interference' is not necessarily appropriate but it's a pretty open point - it can still be the effect of the addition of vectors.
I think the way tech99 thinks, in this matter. My background in RF work makes me reach for models using antennas, for many wave problems, rather than using optical arguments. A whole range of polarisations can be produced with suitably phased and spaced linear polarised antennae. The great thing about RF thought experiments is that you can feed multiple sources with same signal (down wires) so they tend to work ideally when you actually build them.

 

[sophiecentaur]

I think you are correct about the photon explanation. In the case of Polaroid film, it seems to have needle-like crystals which all point in the same direction, so I presume the mechanism is similar to the microwave case.

Photons have lead you into an impasse, here, I think. What happens to a 'single' photon which arrived at one of these crystals? It corresponds to the minimum possible energy of the wave so what happens to it (in your model) when you only let through 1/2 of that energy through your polariser? Best to steer clear of Quantum when you can.

 

[Jilang]

I am thinking that trying to pin a definite polarisation on a single photon seems futile. One you determine it's in one direction it is then simultaneously in a quantum superposition of states in any other direction! For the single photon, it will have some probability of making it through the second polariser. If the polarisation was definite it would have zero chance, unless it could somehow "borrow or steal" the extra field required.