The generation of nondiffracting beams using inexpensive computer- generated holograms

Because laser applications are found in a wide variety of scientific and engineering disciplines, the dynamics of wavefields associated with laser beams are of special interest in the undergraduate physics curricula. One problem arises when a laser beam is to be shaped to a particular profile. For most applications, it is desirable that most of the laser energy be confined to a small spot. Many laser resonators readily yield a beam with this characteristic, namely a Gaussian beam. The spot size of a laser beam is affected by diffraction as the beam propagates, which results in a limited useful range of propagation. The more tightly a laser beam is focused, the faster it will diverge. Diffractive spreading limits the useful range of lasers in areas such as metrology, freespace communications, and optical lithography. Alternate beam shapes are more convenient for certain applications. For instance, in laser surgery for vision correction, an annular beam is sometimes required to ablate annular sections of tissue from the cornea. Application-specific beam shaping can be achieved in several ways. For instance, when a Gaussian beam is incident on a specifically tailored hologram, the shape of the beam is modified according to the information encoded in the hologram. This phenomenon can be exploited to generate a beam with an arbitrary profile. In this paper we present a simple step-by-step technique for this purpose. Recipes for making holograms have been the subject of several popular articles see, for instance, Ref. 3 . Many papers explaining the operating principles of holography at the undergraduate level are available, some of which stress the experimental techniques and their implementation. In particular, Ref. 4 is a useful starting point for the newcomer to holography. It pinpoints many practical aspects to be taken into consideration for the successful generation of holograms. There are also several articles that describe detailed procedures to make computer-generated holograms. For example, Marsh and Smith took advantage of an early programmable calculator with graphical capabilities to compute and plot Fourier computer-generated holograms of simple objects. This technique can now be used with desktop computers to make holograms of objects of much greater complexity. Similarly, Chen and colleagues took a picture of a computer-generated hologram in a computer display with only a few samples and used their negatives as downscaled holograms with very good results. Leming and Hastings devised a particularly ingenious experiment that demonstrates how the calculation of a hologram is done and how the hologram is constructed. In their procedures for the microwave regime, they utilize aluminum foil and construction paper