Light can be circularly polarized, plane polarized or unpolarized. A plane-polarized wave has an electric field whose direction is fixed in a plane like the previous animation. A circularly polarized wave is a superposition of two an x-polarized and a y polarized wave, where the relative phase is 90 degrees. For a circularly polarized wave moving along the z axis, the x component of the electric field wanes the y component builds which results in the electric field's direction rotating about the z axis. By having the relative phase as +90 degress or -90 degrees, the rotation is either right-handed or left-handed. Unpolarized light would be a random mixture of x- and y-polarized waves with random relative phases.
Certain materials polarize light along a certain axis do to their crystal structure. Once light passes through a polarizer, the direction light's polarization is known. If the incident wave had a polarization angle finc relative to a fixed axis and the polarizer is set at an angle fpol, the resultant electric field is reduced in magnitude by a factor of the cosine of the relative angle. The intensity is therefore reduced by the square of the relative angle's cosine.
For unpolarized light, the final intensity will be half the original.
Materials whose molecules are helical, can produce circularly polarized light. Examples are sugar syrups. In fact, the sugar molecules used by biological organisms are all left-handed helixes, never right-handed.