This article reviews the need for optical beam expanders and basic elements of their design.

The output of most lasers is on the order of one millimeter or so. Many laser applications require larger beam diameters, and it is common practice to combine a laser with a beam expander. Because a beam expander is a telescope, the beam divergence is reduced by the same factor as the beam expansion ratio which is the telescopic magnification.

Lower power beam expanders (two to twenty power) are almost always designed as forms of the conventional Galilean telescope with a negative input lens and a positive output lens. Some manufacturers offer the Kepler telescope form consisting of two positive lenses with an intermediate focus. The two forms are illustrated in Figure 1. In order to be useful, it is often required that the performance level of the beam expanders be quite high. This is usually expressed in terms of the wavefront distortion which should be less than about one tenth of a wave for diffraction limited performance.

In order to achieve this kind of performance level, it may be necessary to use multiple components in the telescope. The Kepler telescope requires multiple elements for good performance unless very high f-number singlets are used to minimize the optical aberrations. The resulting telescope is usually very long. If it is required, the Kepler telescope permits the use of spatial filtering which is accomplished by placing a pinhole at the intermediate focus.

Some of the advantages of the Galilean telescope are a smaller package, minimum risk of gas breakdown at the focus with high power lasers, and very good performance with simple lenses. For example, diffraction limited performance can be achieved if plano forms are used for both positive and negative lenses, provided that certain conditions are met. These involve proper selection of radii, separation between lenses and the index of refraction of each element. Referring to Figure 2, the following rules are applied:

where M is the magnification, N₁ and N₂ are the index of refraction of the negative and positive lenses respectively, and d₂ is the thickness of the positive element.

The choice of index of refraction for each element is not arbitrary. In order to achieve the best performance, reference should be made to Figure 3. It can be seen that there is an optimum combination of glasses for a given beam expansion. For example, if a magnification of 5x were required, a good combination would be N₁=1.5 for the negative lens and N₂=1.6 for the positive lens. After the glasses to be used have been selected from the catalogues, the final step is to optimize the system by adjusting the air space and radii for best performance. By following this procedure, wavefront distortion approaching one twentieth of a wave can be achieved with a very economical lens system.

It is not suggested that this is the only or even the best approach to the design of a beam expander. Other factors, such as the necessity for chromatic correction, manufacturing tolerances, immunity to misalignment and many others must be considered. In the final analysis, the truly economical approach requires an experienced optical engineer to assess the requirements and determine how to meet them.