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If polariser a and polariser b were kept exactly facing each other, then would the result be as shown?

Diagram 1

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Diagram 2 Side View

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In this case, how would the electromagnetic wave (diagram 3) look like when they collide? Would theories like superposition (addition of displacements), repulsion, standing waves still apply? Would the electric field and magnetic field collide? What exactly will happen?

Diagram 3

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Edit: Let's assume that the polariser A produces an electromagnetic wave. Then, the electric field will be on the x-plane and the magnetic field will be on the y-plane. Polariser B will produce electromagnetic wave as well. But, the electric field will be in the y-plane and the magnetic field will be in the x-plane. What happens when these two electromagnetic waves meet.

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  • $\begingroup$ Could you describe the setup with the polarizers a little more? I'm confused about what you mean. Do you mean you shine two beams of linearly polarized light at each other with their polarizations orthogonal to each other? $\endgroup$ May 19, 2018 at 20:58
  • $\begingroup$ Done. See the side view in the question of the entire setup. Assume that they are perfectly aligned. And yes, they are linearly polarised. $\endgroup$ May 20, 2018 at 5:10
  • $\begingroup$ I think you need some mirrors so that the 2 pols at least have the same direction. As, is, it's H pol moving right an V pol moving left, which doesn't really differ from the blue sky: directionally dependent linear polarization. $\endgroup$
    – JEB
    May 20, 2018 at 5:25
  • $\begingroup$ I'm not sure what you're referring to when you say "repulsion" here. But as long as classical electromagnetism is valid (i.e. with photon energies of less than 511 keV and for macroscopic cavity dimensions) superposition will be the principle of interest here. $\endgroup$ May 20, 2018 at 5:32

2 Answers 2

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Two light beams cannot "collide" in the way billiard balls collide. They are superposed, i.e. added. When going to the quantum mechanical level of the photons which build up the classical electromagnetic wave, what are superposed are the wavefunctions. In both the classical and quantum mechanical frames, the superposition allows for interference patterns , but not of scattering.

This is because at the quantum mechanical level, the underlying level from which the classical emerges, photon photon scattering is very very small, particularly at visible and below frequencies. The beams will pass through each other, showing interference in the overlap regions.

There is this very interesting MIT demonstration of what happens when two laser light beams are superposed.

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If two waves "collide" with each other, they form interference pattern, meaning that at any given point in space and time, the resulting electric and magnetic fields will be a sum of the fields produced by the interfering individual waves, if acting alone, which is the principle of superposition.

In a more specific case of two waves linearly polarized at 90 degrees relative to each other, assuming that they have the same wavelength, the interference pattern will depend on their relative phase.

If the phase difference is a multiple 180 degrees, the resulting wave will be linearly polarized, meaning that the direction of the electrical and magnetic field will be the same everywhere, but it will be different from the direction of the fields of the two original linearly polarized waves.

If the phase shift is not a multiple of 180 degrees, the resulting wave will be elliptically polarized, meaning that the direction of the resulting field will be constantly changing and the vector of the field, at any point in space, will be describing an ellipse.

In a specific case, when the two original waves have the same amplitude and are phase shifted by $90\times (2n+1)$ degrees, the resulting wave will be circularly polarized.

You can read more about it and visualize the resulting wave here.

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