Focussing Light With Diffraction

Danielle Bourguet, Paul D. Schreiber High School; John Noé, Harold Metcalf, Laser Teaching Center, Department of Physics and Astronomy, Stony Brook University.

The diffraction and interference of light are closely related phenomena resulting from the wave nature of light that are familiar to anyone who has studied optics. (Sometimes one term or the other is used but both effects always occur together.) Diffraction is basically the bending of light around an obstruction, while interference is the interaction between light waves from different sources to produce cancellation or enhancement of intensity. Both effects work together to produce patterns of light called "diffraction patterns." Less well known is that diffraction and interference can be used to create images or to focus light, or even x-rays. Creation of "self images" of an object through diffraction is called the Talbot effect after Henry Fox Talbot (an inventor of photography) who first noticed noticed the effect in 1836. Focussing light with a zone plate - a bull's eye like pattern of clear and opaque rings of varying width - is named after Fresnel, who developed the theory of zone plates in the early 1800's. Fresnel zone plates have the fascinating property that they increase light (at the focal point) by removing light (from the blocked zones). They are of considerable practical importance in x-ray optics. The Fresnel zone plate phenomenon and Talbot effect are similar in that the "lens" created by diffraction has multiple focal lengths, unlike an ordinary lens, which has just one.

The Talbot effect and Fresnel zone plates were explored with the same setup. By using mirrors I directed the light beam from a red (632.8 nm) helium-neon (HeNe) laser into a single-mode fiber optic cable. The light emerges from the fiber as a ideal spherical wave-front. This is then transformed into an ideal plane-wave of light with the help of a large lens (3.9 cm diameter ) that has a relatively short focal length (4.1 cm). The fiber-optic cable and lens are attached to sleds which can slide along a precise carriage. The carriage has two more sleds on it: the one closest to the lens is used to hold either a Ronchi diffraction grating or a Fresnel zone plate, and the second holds a viewing screen. So far with my setup I have successfully collimated the light beam so that the most intense part of the beam covers the entirety of the zone plate. It was discovered that the type of lens, as well as its diameter and focal length, is an important factor for getting good collimation. To view the foci the sled carrying the screen was slid a millimeter at a time along the carriage, watching for places where the light came to a bright spot.

In the immediate future I plan to compare my observed focal point data with predictions calculated using the known or measured properites of the zone plate and Ronchi grating. I also plan to measure the varying intensity of the light at the multiple foci. After this I plan to learn the Mathematica computer program and use it to simulate diffraction effects and possibly create novel diffractive optics of my own design.

This research was supported by the Simons Foundation and the Laser Teaching Center.

Danielle Bourguet
Tennisailax (at) AOL.com
July 2004
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