Table of Contents
What Is a Beam Expander?
A beam expander is an optical system that increases the diameter of a laser beam while proportionally reducing its divergence. It works on the same principle as an inverted telescope: the beam enters through a short-focal-length lens (or small end of the telescope) and exits through a long-focal-length lens (large end), emerging with a larger diameter and lower divergence.
Beam expanders are essential components in laser systems where a larger beam is needed to reduce divergence for long-distance propagation, to fill a larger optic for focusing to a smaller spot, or to reduce power density on optical surfaces to prevent damage. They are used extensively in laser machining, lidar, free-space optical communications, and scientific instruments.
Design Formulas
Galilean vs. Keplerian
| Feature | Galilean | Keplerian |
|---|---|---|
| Eyepiece lens | Negative (diverging) | Positive (converging) |
| Internal focus | No | Yes (at common focal point) |
| System length | Shorter (f2 - |f1|) | Longer (f1 + f2) |
| Image orientation | Erect | Inverted |
| Spatial filter | Not possible | Possible at internal focus |
| High power | Better (no focus) | Risk of air breakdown at focus |
Selection Guide
- 2x-5x expansion: Galilean designs are compact and cost-effective for moderate magnification.
- 5x-20x expansion: Keplerian designs offer better beam quality with spatial filtering capability.
- High-power lasers: Use Galilean type to avoid the internal focus point that can cause air ionization.
- Beam cleanup: Keplerian with a pinhole at the internal focus removes higher-order modes and improves beam quality.
- Achromatic designs: For broadband or tunable lasers, use achromatic lens pairs to minimize chromatic aberration.
Frequently Asked Questions
Does a beam expander increase laser power?
No, a beam expander does not increase the total optical power. It redistributes the same power over a larger cross-sectional area, actually reducing the power density (irradiance) by the square of the magnification. A 5x expander reduces power density by 25x. The benefit is reduced divergence, which means the beam stays smaller over long distances.
How does magnification affect divergence?
Divergence is reduced by exactly the magnification factor. A 10x beam expander reduces the beam divergence by 10 times. This is a direct consequence of the conservation of beam parameter product (BPP = w0 x theta), which is constant through any perfect optical system. Increasing beam size necessarily decreases divergence by the same factor.
What determines the minimum achievable spot size?
The minimum spot size when focusing a laser beam is determined by the ratio of wavelength to beam diameter at the focusing lens: d_spot is proportional to lambda x f / D. A beam expander increases D, which proportionally decreases the achievable spot size. This is why beam expanders are used before focusing optics in laser machining and microscopy.