# Collimated Beams

Definition: laser beams with weak divergence

German: kollimierte Strahlen

Author: Dr. Rüdiger Paschotta

A collimated beam of light is a beam (typically a laser beam) propagating in a homogeneous medium (e.g. in air) with a low beam divergence, so that the beam radius does not undergo significant changes within moderate propagation distances. In the simple (and frequently encountered) case of Gaussian beams, this means that the Rayleigh length must be long compared with the envisaged propagation distance. For example, a 1064-nm beam with a 1-mm beam radius at its beam waist has a Rayleigh length of ≈ 3 m in air, so that it can be considered as being collimated within a normal laboratory setup. Note that the Rayleigh length scales with the square of the beam waist radius, so that large beam radii are essential for long propagation distances.

For beams with non-ideal beam quality, the Rayleigh length is effectively reduced by the so-called *M*^{2} factor, so that the beam waist radius needs to be larger for a beam to be collimated.

When describing a collimated beam with light rays, it consists of essentially parallel rays only. However, the ray picture cannot account for the phenomenon of beam divergence and is therefore of limited value.

## How to Collimate a Beam

A divergent beam can be collimated with a beam collimator device, which in simple case is essentially a lens or a curved mirror, where the focal length or curvature radius is chosen such that the originally curved wavefronts become flat. (Of course, the beam radius at the position of the lens or mirror should be large enough to obtain a low divergence.) Any residual divergence can be fine adjusted via the position of the lens or mirror along the beam direction. The collimation can be checked, for example, by measuring the evolution of beam radius over some distance in free space, via a Shack–Hartmann wavefront sensor, or with certain kinds of interferometers.

In principle, one can use lenses with very different focal lengths to collimate a diverging beam. The longer the focal length, the larger will be the resulting diameter of the collimated beam. Assuming a tight focus to start with (and subsequent beam expansion over a distance far beyond the Rayleigh length, the required distance between focus and collimation lens will equal the focal length. From that, one can obtain the collimated beam radius as the product of beam divergence half-angle (or precisely speaking its tangent) and the distance. And for a Gaussian beam, the beam divergence half-angle is <$\lambda / (\pi w_0)$>. In total, we obtain (within the paraxial approximation):

$${w_{{\rm{col}}}} = \theta \;d = \frac{\lambda }{{\pi {w_0}}}f$$In fiber optics, one often uses fiber collimators. These are available both for bare optical fibers and for connectorized fibers, i.e., for mating with fiber connectors.

Collimated beams are very useful in laboratory setups because the beam radius stays approximately constant, so that the distances between optical components may be easily varied without applying extra optics, and excessive beam radii are avoided. Most solid-state lasers naturally emit collimated beams; a flat output coupler enforces flat wavefronts (i.e., a beam waist) at the output, and the beam waist is usually large enough to avoid excessive divergence. Edge-emitting laser diodes, however, emit strongly diverging beams, and are therefore often equipped with collimation optics – at least with a fast axis collimator, largely reducing the strong divergence in the “fast” direction. For fibers, a simple optical lens may often suffice for collimation, although the beam quality can be better preserved with an aspheric lens, particularly for single-mode fibers with a large numerical aperture.

See also: beam collimators, laser beams, Gaussian beams, beam divergence, beam radius, Rayleigh length, lenses, fiber collimators

## Questions and Comments from Users

2020-05-22

What is the smallest possible collimated laser beam diameter?

The author's answer:

That depends on the optical wavelength and on the propagation distance over which it needs to be collimated. For example, if you need a 1064-nm beam to be collimated over a length of 1 m, you want its Rayleigh length to be of the order of 1 m (or longer), which implies a Gaussian beam diameter of 1.2 mm (or larger).

2021-02-24

How do you measure the Gaussian waist of a collimated beam without fancy equipment?

The author's answer:

I suppose you mean the beam radius at the waist (focus). See the encyclopedia article on beam radius.

2021-03-11

Some people talk about a laser's smile – what's that?

The author's answer:

This is and unwanted slight curvature of the emission pattern of a diode bar. Ideally, the emitters of such an array would be exactly in a straight line. If they deviate from that, it is more difficult to collimate the output such that one obtains a high beam quality.

2021-04-26

To achieve the smallest possible divergence for a laser diode beam, is it better to directly use a suitable lens (e.g. an aspheric doublet) in front of the laser first couple the beam into a single-mode fiber and then collimate what emerges from that?

The author's answer:

That depends basically on whether the near-field profile from the laser diode or the fiber mode is closer to a Gaussian. That is hard to predict without specific information on the two.

2021-07-05

Some people talk about a 'collimation distance' of a laser output -– what's that? Is that referring to distance where the beam waist located from the laser output?

The author's answer:

Probably not – I would think it is the distance over which a laser beam stays collimated, i.e., maintains an approximately constant beam radius. That would be something like the (effective) Rayleigh length. But I think the term is not generally defined.

2021-08-31

I am trying to estimate the divergence of a multi-color laser source that is fiber-coupled. How do you calculate results approximation (mainly collimated beam size and divergence) given fiber size, NA, wavelength, and focal length of collimator?

The author's answer:

That is a bit tricky, partly because you need sufficient data concerning chromatic aberrations, i.e., essentially the wavelength dependence of the focal length. The output beam can be perfectly collimated only for one of the involved wavelengths, but you can minimize chromatic effect by choosing a correspondingly optimized achromatic collimation lens.

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2020-03-14

What restrictions apply to how long the light from an extended, non-laser source like a tungsten lamp can stay collimated?

The author's answer:

You can estimate that with the beam parameter product, using the source size (like a beam waist) and the divergence of outgoing light (light a beam divergence). You can reduce that product e.g. with one or more optical apertures, but at the expense of losing part of the optical power.

The length over which the diameter of the formed beam stays roughly constant can be estimated as the effective Rayleigh length, which can be calculated using the beam parameter product.