User:Dave3457/Sandbox/Circular polarization First Section

Toward the right is an illustration of a right-handed, clockwise circularly polarized wave. Observe that the helix forms a right-handed screw in space. The helix is traced out by a series of electric field vectors which have a constant magnitude but a direction which changes in a rotary type manner. Given that this is a plane wave, each vector represents the magnitude and direction of the electric field for an entire plane that is perpendicular to the axis. These particular vectors indicate that the electric field, from plane to plane, has a constant strength while its direction steadily rotates. Refer to the plane wave article for an illustration and discussion of a circularly polarized plane wave. It should be noted that this is an electromagnetic wave and therefore for each electric field vector there is corresponding, but not illustrated, magnetic field vector that is at a right angle to the electric field vector and proportional in magnitude to it. As a result, the magnetic field vector would trace out a second helix if displayed. Circular polarization is often encountered in the field of optics and in this section, the electromagnetic wave will be simply referred to as light.  The nature of circular polarization and its relationship to other polarizations is often understood by breaking the electric field into two components which are at right angles to each other, (orthogonal). Refer to the second illustration. The horizontal component and its corresponding plane are illustrated in green while the vertical component and its corresponding plane are illustrated in blue. Notice that the rightward (relative to the direction of travel) horizontal component leads the vertical component by one quarter of a wavelength. It is this quadrature phase relationship which creates the helix and causes the points of maximum magnitude of the vertical component to correspond with the points of zero magnitude of the horizontal component, and visa versa. The result of this alignment is that there are select vectors, corresponding to the helix, which exactly match the maximums of the vertical and horizontal components. To minimize visual clutter these are the only helix vectors displayed.

To appreciate how this phase shift corresponds to an electric field that rotates while maintaining a constant magnitude, imagine a dot traveling clockwise in a circle. Consider how the vertical and horizontal displacements of the dot, relative to the center of the circle, vary sinusoidally in time and are out of phase by one quarter of a cycle. The displacements are said to be out of phase by one quarter of a cycle because the horizontal maximum displacement (toward the left) is reached one quarter of a cycle before the vertical maximum displacement is reached. Now referring again to the illustration, imagine the center of the circle just described, traveling along the axis from the front to the back. The circling dot will trace out a helix with the displacement toward our viewing left, leading the vertical displacement. Just as the horizontal and vertical displacements of the rotating dot are out of phase by one quarter of a cycle in time, the magnitude of the horizontal and vertical components of the electric field are out of phase by one quarter of a wavelength. 

The next pair of illustrations is that of left-handed, counter-clockwise circularly polarized light. Because it is left-handed, the rightward (relative to the direction of travel) horizontal component is now lagging the vertical component by one quarter of a wavelength rather than leading it. One should appreciate that our choice to focus on the horizontal and vertical components was arbitrary. Given the symmetry of circularly polarized light, we could have in fact selected any other two orthogonal components and found the same phase relationship between them.

To convert a given handedness of polarized light to the other handedness one can use a half-wave plate. A half-wave plate shifts a given component of light one half of a wavelength relative to the component that it is orthogonal to. The handedness of polarized light is also reversed when it is reflected off of a mirror. Initially, as a result of the interaction of the electromagnetic field with the conducting surface of the mirror, both orthogonal components are effectively shifted by one half of a wavelength. However as a result of the change in direction, a mirror image of the wave is created and the two component’s phase relationship is reversed.

For a better appreciation of the nature of circularly polarized light one may find it useful to read how circularly polarized light is converted to and from linearly polarized light in the circular polarizer article.