Laser Beam Expander Calculator
Enter your laser beam parameters and expander design to instantly find the output beam diameter, reduced divergence, lens separation, and how large the beam will be at any target distance. Choose between solving by magnification or by focal lengths, and switch between Galilean and Keplerian configurations.
What is a laser beam expander?
A laser beam expander is a two-lens telescope that increases a laser beam's diameter by a fixed factor while proportionally reducing its divergence. A larger, more parallel beam spreads out more slowly over distance, making beam expanders essential wherever a laser must travel far or be focused to the smallest possible spot by a downstream lens. Applications range from laser cutting and marking to LIDAR, interferometry, holography, and free-space optical communications.
Galilean vs Keplerian designs
A Galilean expander uses a short-focal-length negative (concave) input lens and a longer-focal-length positive (convex) output lens. Because the lenses share a common focal point that lies outside the physical hardware, there is no internal focus, which prevents dielectric breakdown in the air gap at high peak powers. This makes Galilean expanders the default choice for pulsed and high-power lasers. The resulting instrument is shorter than the equivalent Keplerian design for the same magnification. A Keplerian expander uses two positive lenses positioned so their back and front focal points coincide inside the expander. The intermediate focal point lets you insert a spatial filter pinhole at that location, which strips higher-order spatial modes and can substantially improve beam quality (lower M squared). This is the preferred approach in research optics and fiber coupling setups where beam quality matters more than compactness.
How magnification, divergence, and beam diameter are related
The governing relationship is simple: if the magnification is M, then the output diameter D_out = M x D_in and the output divergence theta_out = theta_in / M. Doubling the beam diameter halves the divergence. Because the divergence shrinks, the beam at any downrange distance will be correspondingly narrower than the unexpanded beam. The diameter at a target distance L is D(L) = D_out + 2 x L x tan(theta_out / 2), which for small angles simplifies to D_out + L x theta_out (with theta in radians and L in the same length unit as D_out).
Lens separation and system sizing
For a Galilean expander the two lenses are separated by f2 - f1 (both in absolute magnitude), which is always shorter than the equivalent Keplerian system. For a Keplerian expander the separation is f1 + f2. Once you know the magnification you want, you can choose a convenient input focal length f1 and then compute f2 = M x f1. Practical constraints include the tube length available, the size of commercial off-the-shelf lenses, and the required clear aperture: the output lens must have a clear aperture at least as large as the output beam diameter, plus a 20% margin to avoid diffraction from the lens edge.
Common beam expander magnifications and applications
| Magnification | Output / Input diameter | Divergence reduction | Typical use |
|---|---|---|---|
| 2x | 2:1 | 50% | Minor collimation improvement, compact systems |
| 3x | 3:1 | 67% | Interferometry, short-range LIDAR |
| 5x | 5:1 | 80% | Laser machining, long-range pointing |
| 10x | 10:1 | 90% | Long-range LIDAR, free-space communications |
| 20x | 20:1 | 95% | Astronomical range-finding, directed energy |
Typical expansion ratios used in photonics and laser applications. Higher magnification gives a larger, more collimated beam that travels farther before diverging significantly.
Frequently asked questions
How does a beam expander reduce divergence?
Divergence is the angular rate at which a laser beam spreads. When you expand the beam by factor M, you increase the wavefront curvature radius by M at the exit, which means the beam appears to come from a source M times farther away. The result is that the far-field half-angle shrinks by exactly 1/M. A 5x expander on a 1.5 mrad beam yields 0.3 mrad at the output.
What is the difference between Galilean and Keplerian beam expanders?
Both designs expand the beam by the ratio of their lens focal lengths. The Galilean type uses a negative first lens and has no internal focal point, keeping peak intensity inside the instrument low and preventing air breakdown at high powers. The Keplerian type uses two positive lenses, creating an intermediate focus where a spatial filter pinhole can be placed to clean up the beam profile and reduce the M squared parameter.
Can I use a beam expander in reverse to reduce a beam?
Yes. Physically reversing a beam expander turns it into a beam reducer (compressor). The same magnification formula applies: a 5x expander used backwards compresses a 10 mm beam to 2 mm. Keep in mind that the compressed beam will have correspondingly higher divergence (5x more than before), so verify this is acceptable for your downstream optics.
What magnification should I choose?
That depends on the beam size your application needs and how far the light travels. For laser cutting where the beam must be focused tightly, a higher magnification improves the diffraction-limited spot size of the final focusing lens. For long-range applications like LIDAR or free-space links, choose the magnification that keeps the beam small enough at the target distance. This calculator shows how the beam grows with distance for both the expanded and original beams, making it easy to compare options.
How do I choose the focal lengths?
Pick an input focal length f1 that suits your mount and available lenses (25 mm and 50 mm are common), then set f2 = M x f1. For a Galilean system, f2 - f1 is the physical lens separation; for a Keplerian system it is f1 + f2. Verify that the output lens clear aperture exceeds the output beam diameter by at least 20%, and that the input lens clear aperture is larger than the input beam diameter.
Does a beam expander affect laser power?
An ideal beam expander is lossless; it does not change total power, only how that power is distributed. In practice, anti-reflection coatings reduce surface losses to around 0.2% per surface, so a two-lens expander typically transmits 99% or more of the incident power. The peak intensity (power per unit area) at the output is reduced by M squared, which is important for protecting downstream optics and samples from damage.