# Beam Expanders

Beam expanders (also known as collimators or up-collimators) typically are used in systems with a long beam path to keep the beam collimated, or to vary the focus spot size for a given focusing lens. Various magnifications are available, but it is important to ensure that the input and output beams clear the apertures.

Beam expanders are useful in a variety of applications including interferometry, laser scanning and remote sensing.

The CO_{2}mpact beam expander has a slide and lock focus setting. The normal setting is infinity. It can be changed to fit certain beam parameters. To keep the beam path enclosed the output should be coupled to an adjustable beam tube to maintain an overall fixed length.

- Focus adjustable beam expanders
- Zoom beam expanders
- Available for 10.6 µm and 9.3 µm

**CO2mpact Beam Expander (C-BE) power handling**

Assuming clean and uncooled ZnSe coated lenses here are some guidelines:

For CO2 continuous wave lasers, we would expect thermal lensing to become noticeable at around **250watts per mm of laser beam diameter.**

At 500 watts, for which our CO2mpact beam delivery systems are rated, we recommend a minimum beam diameter of 2.5mm.

Part Number | Diameter | Length | Magnification |

C-BE1.3 | 44 mm | 70 +5/-4 mm | 1.3 |

C-BE1.6 | 44 mm | 70 +5/-4 mm | 1.6 |

C-BE2.0 | 44 mm | 70 +5/-4 mm | 2.0 |

C-BE2.5 | 44 mm | 70 +5/-4 mm | 2.5 |

C-BE3.0 | 44 mm | 70 +5/-4 mm | 3.0 |

C-BE3.5 | 44 mm | 70 +5/-4 mm | 3.5 |

C-BE3.75 | 44 mm | 70 +5/-4 mm | 3.75 |

C-BE4.0 | 44 mm | 70 +5/-4 mm | 4.0 |

C-BE5.0 | 44 mm | 70 +5/-4 mm | 5.0 |

C-BE6.0 | 44 mm | 70 +5/-4 mm | 6.0 |

C-BE7.0 | 44 mm | 70 +5/-4 mm | 7.0 |

C-ZBExx | 96 mm | 242 mm | 1 to 8 zoom |

## Beam Expander Theory

The first known optical telescopes were invented in the Netherlands in the early 17th century and used glass lenses. A few decades later mirrors were used, dividing telescopes into two types : refracting and reflecting.

Refracting telescopes are again divided into two types: Keplerian and Galilaen

A Keplerian telescope’s lenses are of a positive focal length and are separated at a distance equal to the sum of their focal lengths. The lens nearest to the object or image is known as the objective lens and the lens that creates the image is called an image lens.

A Galilean telescope’s lenses are of also separated by the sum of their focal lengths, however in a Galilean design one of the lenses is negative. The use of a negative lens allows the distance between the two lenses to be much shorter than in a Keplerian telescope.

The magnifying power can be calculated using the focal lengths of the objective and image lens using the formula:

If the magnifying power is more than 1, the image the telescope produces is of increased size; if the magnifying power is less than 1 the images size is reduced.

**Laser Beam Expanders**

In the design of a laser beam expander, the objective and image lenses are reversed. In a Keplerian beam expander the input beam is focussed to a point between the two lenses. This creates a spot of concentrated energy within the beam expander which heats the air within the system and deflects light from it’s optical path. This has the potential to lead to wavefront errors, therefore the majority of laser beam expanders are of galilean design.

The output beam divergence determines the deviation from perfect collimation. Beam divergence can be calculated using the following equation:

We can now express the magnifying power in terms of the beams divergences or beam diameters

Considering these two equations, we can see that there is a negative correlation between beam diameter and beam divergence. Due to this negative correlation, when a beam expander is used as a beam minimiser, the beam diameter will decrease but the beam divergence will increase.

It is often useful to be able to calculate the beam diameter at a specific distance (L). This can be done using the formula:

Beam divergence is expressed as a full angle in terms of θ_{I} and not θ_{I}/2 .

Because a beam expander will increase the beam diameter and decrease the beam divergence by it’s magnifying power, we can combine these equations to give us:

ULO Optics beam expanders are an example of applying the Galilean telescope design to laser beams. Our extensive range of focus adjustable collimators are available to purchase directly. Contact us today for an enquiry.