if we take an very small point source of EM wave, we will find that the EM wave is polarized. How does the polarization vary depending on which point of the sphere ? Polarization is always shown along one axis, but in a real 3D spherical wave it's impossible to keep a transversal EM field vector without changing its direction EDIT: My question comes from optics, if the image of a point is formed from constructive interference, then for such interference to occur, the polarization must have a specific configuration in 3D
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The E and B vectors of a spherical EM wave lie in a plane normal to the direction of the propagation of the wave and their magnitude and direction (within that plane), at any point in space, are randomly changing with time.
The source of such wave could be considered a point source only in a sense that it is small relative to the distances at which the wave is evaluated. The source has to contain a large number of incoherent radiators to ensure a uniform distribution of radiation in all directions.
We can also loosely say that the EM spherical wave is unpolarized, such as EM radiation from a light bulb or a star, keeping in mind that it is in fact always polarized, but the polarization is randomly changing.
You can find more details on this topic in this post.
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$\begingroup$ Thanks, let's assume it's not perfectly spherical, say, just half a sphere. Let's freeze time, how does polarization change around that half sphere ? see my EDIT on the question $\endgroup$ Commented May 13, 2018 at 16:31
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$\begingroup$ Yes, the image of a point, is indeed is formed by interference of multiple wavelets and, since the interference could be constructive or destructive, the image will look like a series of rings (Airy pattern). All the wavelets forming such image will be coming from the same point of the source, i.e., the point will radiate light in all directions, some segment of that light will pass through a lens and converge on the image plane. In other words, all these wavelets will be coherent and have the same polarization. But the wavelets forming other points could have different polarization. $\endgroup$– V.F.Commented May 13, 2018 at 20:25
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$\begingroup$ how could they all be polarized the same, when, as you said, the E field is normal to the direction of the propagation and the direction of the propagation is different for every single ray; You can do this if all the rays are in a plane but not in 3d $\endgroup$ Commented May 14, 2018 at 6:33
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$\begingroup$ For small apertures, like the pupil in a human eye, that difference in polarization won't be significant and won't cause any significant image distortion. $\endgroup$– V.F.Commented May 14, 2018 at 12:22
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1$\begingroup$ A single point won't produce a spherical or hemospherical wave. It could possibly be modeled as a dipole with its doughnut-shaped radiation pattern. E-vector of a dipole will be in the same plane as the dipole, will be getting smaller in magnitude as the altitude angle increases and will be normal to the direction of the wave propagation or to the line connecting the mid-point of the dipole with the point of interest. $\endgroup$– V.F.Commented May 14, 2018 at 22:25