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Using Laser Beam Expanders

Laser Beam expanders are designed to decrease the laser's beam spot size at large distances. There are two main types of beam expanders: Keplerian and Galilean. In its simplest form, the Galilean type consists of a positive and a negative focal length lens whereas the Keplerian type consists of two positive focal length lenses. Both designs provide a certain angular magnification, called the Expander Power. The beam diameter is first increased in size by this power and then the beam divergence is reduced by the same power. This combination yields a beam that is not only larger, but one that is also highly collimated. The result is a smaller beam at a large distance when compared to the laser alone (Equation 1.0).

Equation 1.0: BL = ß + ØL (0.3048)
where: BL = Beam Diameter (mm) at distance L
  ß = Increase in Beam Diameter
    = Beam Diameter (mm) x Expander Power
  Ø = Decrease in Beam Divergence
    = Beam Divergence (mrad) Expander Power
  L = distance (ft.)

This equation is an approximation for the collimated output beam size at a given distance.

Note that the beam divergence specifications in our catalogs are for the full angular spread of the beam.

In addition, an expanded beam can yield smaller spot sizes when used in combination with additional focusing optics. This is very useful in focusing optimization. however, many applications simply require a larger continuous beam.

The beam expander power (MP) is equal to the ratio of the effective focal length (EFL) of the objective lens to the effective focal length of the entrance optic. The physical separation between the objective lens and entrance optic is equal to the sum of their back focal lengths (BFL).

The relation between beam expander power, input and output beam divergences as well as lens spacing for both Keplerian and Galilean type expanders is:

All designed beam expanders are of the Galilean type. The advantages of the Galilean design over the Keplerian are twofold.

In addition to improving beam collimation, all Optics beam expanders can be used to focus laser beams. The simulated focusing performance for the 5x, 10 and 20x beam expanders is listed below for comparison. The spot sizes are given in units of microns and were calculated for a 0.63mm diameter laser beam at 632.8nm assuming M2=1 and a perfectly collimated input beam.

Beam Expander Power
Distance 5x 10x 20x
1.2m 439.19µm 219.63µm 111.04µm
1.5m 559.62µm 279.84µm 141.47µm
2.5m 961.07µm 480.54µm 242.89µm
5m 1964.86µm 982.26µm 496.36µm
10m 3973.17µm 1985.49µm 1002.87µm
The 1/e2 spot diameters listed were calculated from the equation:
2 * f/# * wavelength, where f/# is the working f/#.