Circular Polarization

circular polarization - elliptical polarization - quarter-wave retardation plate - birefringence

What it shows:
A linear polarizing filter followed by a quarter-wave plate, whose slow and fast axes are at 45° to the axis of the polarizer, becomes a circular polarizing filter and incident unpolarized light emerges as circularly polarized light. This will not work if the order of the polarizer and wave plate is reversed. A quarter-wave plate converts circularly polarized light into linearly polarized light.

How it works:
The quarter-wave retardation plate is a sheet of birefringent (double refracting) material 1   of thickness such that horizontally and vertically polarized light entering in phase will emerge from the retardation plate 1/4 of a wavelength out of phase. Unpolarized light is not affected by this retardation plate (or by any thickness of birefringent material) because the retardation plate only changes the phase of each component of polarization -- incident light polarized in all directions (which is unpolarized light) will emerge as light polarized in all directions. The situation dramatically changes when the incident light is polarized.



A polarizing filter is placed in front of the quarter-wave plate at an angle of 45° w.r.t. it (so that the incident horizontal and vertical components are of equal intensity). Because of the phase shift between the two components as they pass through the retardation plate, the direction of polarization of the light that emerges from the wave plate will rotate in time. Thus incident unpolarized light emerges as circularly polarized light. More generally, if the angle between the wave plate and polarizing filter is not 45°, the two components will differ in intensity and the emerging light will be elliptically polarized.

The circular polarization produced by the linear polarizer/quarter-wave plate sandwich is made evident by placing a mirror behind it and looking through the circular polarizer at the mirror reflection. The mirror reverses the direction of circular polarization, and the reflected reversed circularly polarized light is converted back into linearly polarized light by the wave plate. However, it is now polarized perpendicular to the linear polarizing filter's orientation, so it is absorbed and the mirror appears dark 2 . The effect is undone by rotating the linear polarizer w.r.t. the wave plate. The effect is also undone by reversing the order of the polarizer and wave plate. Finally, one can substitute a non-reversing mirror (two mirrors mounted together at right angles) to see what happens!

Setting it up:
The mirror should be propped up and clamped on the lecture bench while the linear polarizer and quarter-wave plate are hand-held in place. The simplest way to perform the experiment is to look through the circular polarizer and view your own reflection in the mirror as the angle between the polarizer and wave plate is changed. Unhappily, the audience cannot appreciate the effect you are seeing so we substitute a TV camera for you. On the TV monitor, the audience will see the reflection of the camera in the mirror fade in and out as you rotate the polarizer (or wave plate). If the class is small, you may wish to invite students to come up after the lecture and experience the anti-reflection effect first-hand.

Comments:
Circular polarizers are used for just this very purpose -- to reduce annoying reflections, eliminate glare, and enhance contrast for a variety of commercial applications. 3

Note that retardation plates do not influence the state of polarization of incident linearly polarized light, if the light's polarization direction lies along either the slow or the fast axis of the retardation plate. Also, a retardation plate can't convert unpolarized light into polarized light. We also have a half-wave and a full-wave plate available. A half-wave plate converts right-handed circularly polarized light into left-handed circularly polarized light and vice versa. Rating **

1 Polaroid 140 nm 1/4-wave retarder -- the retardation is 1/4 wavelength if the wavelength is 4 x 140 nm = 560 nm (which is green); the wave plate is backed onto 0.030" thick plastic and comes in 12" square sheets. Ours have been cut down to 6" squares and mounted in a wooden frame. ($65/sheet from Polaroid in 1985, product no. 605206))
2 An excellent explanation is given by Frank S. Crawford, Jr. in Waves, Berkeley Physics Course - Vol 3, (McGraw-Hill, NY, 1968), p 434. Indeed, the entire chapter 8 (on polarization) is one of the best found in any undergraduate textbook.
3 Polaroid non-glare circular polarizer HNCP 10% 0.030 (product no. 606953) is available in 19"x50"x0.030" sheets ($113/sheet from Polaroid in 1985).