How to Collimate a Laser Beam: Lens Choice, Waist Placement and Checking

Scope

This article gives the procedure for collimating a diverging laser beam, from the end of a single-mode fiber or from a laser diode, with a single lens: what collimation means for a Gaussian beam, how to choose the focal length, where the lens must sit and how sensitive that position is, and how to check the result. Measuring the resulting beam's divergence is covered in How to Measure Laser Beam Divergence, and the reverse task, focusing a collimated beam into a fiber, in Coupling a Free-Space Beam into Single-Mode Fiber.

What collimation means for a Gaussian beam

No beam of finite width stays parallel indefinitely. A Gaussian beam leaving the lens with waist radius $w'$ stays within $\sqrt{2}$ of that radius over a length $2z_R'$ centered on the waist, where

$$z_R' \;=\; \frac{\pi w'^2}{\lambda}$$

is the Rayleigh range of the collimated beam. Collimating a beam means choosing $w'$ large enough that $2z_R'$ covers the distance over which the beam must stay nearly constant in size, and placing the waist near the middle of that distance. A larger beam stays collimated for longer, in proportion to the square of its size.

Choosing the focal length

A source whose own waist has radius $w_0$ (the mode field radius of a fiber, for example) placed at the front focal point of a lens of focal length $f$ produces an output waist of radius

$$w' \;=\; \frac{\lambda f}{\pi w_0}$$

at the back focal point. For the end of a single-mode fiber at 1550 nm with a 10.4 μm mode field diameter ($w_0$ = 5.2 μm) and a lens of $f$ = 11 mm:

The focal length is therefore chosen from the beam size wanted, and the beam size from the distance over which it must stay collimated; the collimation entry gives the waist that keeps a beam narrowest over a given distance. The lens's clear aperture must be at least about 1.5 times the output $1/e^2$ diameter so that it does not clip the beam; equivalently, its numerical aperture must exceed the source's, since the beam fills the lens to a radius of about $f$ times the source's divergence half angle.

How far away the waist can be

Moving the source slightly away from the focal point moves the output waist away from the lens. By the Gaussian lens formula (Self, 1983), the distance $s''$ of the output waist from the lens, for a source at distance $s$ in front of it, is

$$\frac{1}{s + z_R^2/(s - f)} + \frac{1}{s''} \;=\; \frac{1}{f}.$$

Unlike the ray-optics lens formula, $s''$ does not grow without limit. It reaches its maximum,

$$s''_\text{max} \;=\; f + \frac{f^2}{2z_R},$$

when the source is one source Rayleigh range beyond the focal point. For the fiber example, $s''_\text{max}$ = 1.11 m: the waist of this beam cannot be placed further than that from the lens, whatever the lens position. The sensitivity to the source position is high:

A few microns of lens travel therefore sweep the waist across the bench, and the lens mount needs a fine axial adjustment.

Equipment

Procedure

1. Mount the source and lens on a common axis. Center the lens on the source laterally, using the beam's position on a card at a distance: the beam should leave along the lens axis, not at an angle, which happens when the source is off-axis.
2. Set the lens roughly at the focal distance. For a fiber in a connector-matched collimation mount, this is set by the mount; otherwise, start with the lens at its specified back focal length from the source.
3. Choose where the waist should be. For a beam that must stay collimated over a path of length $L$ shorter than $2s''_\text{max}$, place the waist near $L/2$. For a short path, place it at the back focal plane.
4. Adjust the lens axially while measuring the width at the far end of the path and near the lens. Move the lens in small steps until the two widths are as expected for a waist at the chosen place: equal widths at equal distances either side of the waist.
5. Check with a shear plate if the beam is large enough. A shear plate produces fringes whose orientation relative to the reference line indicates the wavefront curvature: fringes parallel to the line mean a plane wavefront at the plate. The check tells whether the waist is at the plate, which is useful for placing the waist at a specific location; it does not by itself say how far the beam will stay collimated, which is set by $z_R'$.
6. Lock the lens and re-check, since tightening a mount often shifts the lens by more than the few microns that matter.

Laser diodes

An edge-emitting laser diode differs from a fiber in two ways. Its emission is elliptical, diverging much faster perpendicular to the junction than parallel to it (see far-field divergence), so a single rotationally symmetric lens produces an elliptical collimated beam. The two axes may also appear to originate from slightly different points, an astigmatism that no position of a single spherical or aspheric lens corrects in both axes at once. The fast axis has the larger numerical aperture, and it sets the lens's minimum NA. Circularizing the beam needs an anamorphic prism pair or a pair of cylindrical lenses after the collimator. Because diode beams are usually not Gaussian in the slow axis, the Gaussian formulas above give only a guide there, and the beam quality factor should be measured as in M² Beam Quality Measurement.

Common failure modes

Lens too short in focal length. The beam is small and its Rayleigh range short, so it diverges visibly within the working distance, however carefully the lens is positioned.

Waist placed too far. Trying to push the waist beyond $s''_\text{max}$ by moving the lens further only brings it back closer; the lens should instead be replaced with a longer focal length.

Clipping. A lens whose NA is smaller than the source's cuts off the beam's wings, reducing power and adding diffraction rings to the collimated beam.

Off-axis source. The collimated beam leaves at an angle equal to the lateral offset divided by the focal length, and aberrations grow away from the axis.

Lens reversed. Plano-convex and aspheric lenses have a correct orientation for collimation; reversed, spherical aberration increases and the collimated beam carries rings.

References: S. A. Self, "Focusing of spherical Gaussian beams," Applied Optics 22, 658 (1983); A. E. Siegman, Lasers (University Science Books, 1986), chapters on Gaussian beams; H. Kogelnik and T. Li, "Laser beams and resonators," Applied Optics 5, 1550 (1966).