Animation 5
Polarization is a characteristic of the time-harmonic electromagnetic wave.
When the orientation of the E-field vector of a plane wave does not change, we say that the wave is linearly polarized. For example,

is a linearly polarized wave along the x-axis. At a fixed observation point, this vector changes with time as in Animation 1 .

Animation 1
If two linearly polarized waves, whose phases differ by 0 or 180 deg., are superimposed, the result is again a linearly polarized wave. Usually, we consider two orthogonal linearly polarized waves, which compose a resultant wave, for example,

The angle between the resultant linearly polarized E-vector and the x-axis is simply

Observe in Animation 2 a linearly polarized E-vector at 45 deg. with respect to the x-axis. Its x- and y-linearly polarized components are of the same magnitude and are in phase.

Animation 2
If the two orthogonal linearly polarized components have the same magnitude and are in phase quadrature, then the resultant time-dependent E vector rotates in the x-y plane, and its tip follows a perfect circle. Mathematically,

Such a wave is called circularly polarized. It is illustrated in Animation 3.

Animation 3
The circularly polarized waves can be right or left circularly polarized. The wave has right circular polarization if the direction of the E-vector rotation and the direction of wave propagation are related through the right-hand rule. If they are related through the left-hand rule, the wave has left circular polarization.
In the most general case, neither the magnitudes of the x- and y-polarized linear components are the same, nor their phases differ by some multiple of 90 deg. Then, the resultant E vector rotates but also, in the course of the rotation, its magnitude changes: its tip follows an ellipse (see Animation 4 ). There, the two linearly polarized components are in phase, however, their magnitudes differ by a factor of two.

Animation 4
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