## Illustration 39.1: Polarization

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The animation shows the result of adding two perpendicular electric fields together. Each field is part of an electromagnetic wave traveling along the z axis. Each electric field is shown separately on the two graphs on the left. The graphs show the electric field at one point on the z axis for various times. On the right the animation shows both electric fields and their sum at the same point on the z axis and at the same times as the graphs on the left. It is as if you are looking down the z axis at the electric field. You can change the electric fields and the phase difference between the two fields and see the resulting waves. Restart.

The direction of polarization for an electromagnetic wave is described by the direction in which the electric field points. In Chapter 32 (Electromagnetic Waves) the electric field was always along either the x or the y axis (usually the x axis). An electromagnetic wave with this kind of electric field is called linearly polarized light. Light is linearly polarized when its electric field lies on a plane (linearly polarized light is often called plane-polarized light for this reason) defined by a line perpendicular to the propagation direction. To see this wave for numerous points along the z axis, revisit Illustration 32.3.

However, the electric field need not be on an axis. For a wave traveling in the z direction, the electric field pointing in the x or the y directions is not the only possibility. For example, the electric field could lie on a plane defined by a line off the x axis by 45° (or π/4 radians). If you are looking at just one point on the z axis, as we are for this animation, you see the electric field pointing along the 45° line. Such an electric field is shown when E_{x} = 8 N/C, E_{y} = 8 N/C, and there is a phase difference of 0 radians. Notice that the angle off of the x axis depends on the amount of the x and the y electric fields you have. So, for example, an electric field of E_{x} = 8 N/C, E_{y} = 4 N/C, and with a phase difference of 0 radians yields an electric field that is linearly polarized off of the x axis by 26.56° (or 0.464 radians).

Circular and elliptical polarization occurs when two or more linearly polarized waves add together such that the electric field rotates in a plane perpendicular to the direction of propagation. For circularly polarized light, in which the direction the electric field points rotates in a plane, but its magnitude stays the same. For elliptically polarized light both the magnitude and the direction of the electric field varies. If you enter the following values, E_{x} = 8 N/C, E_{y} = 8 N/C, and a phase difference of 0.5* π radians, a wave that is right-circularly polarized will result. If you change E_{y} to 4 N/C, a wave that is right-elliptically polarized will result.

Illustration authored by Melissa Dancy.