Laser Beam Expander Calculator

A laser beam expander is an optical system that increases the diameter of a collimated laser beam while simultaneously reducing its divergence angle by the same factor. It typically consists of two lenses and is used to improve beam quality, extend working distance, and reduce power density on optical surfaces.

Magnification (MP) is calculated as the ratio of the output lens focal length to the input lens focal length: MP = f₂ / f₁. For example, if f₁ = 25 mm and f₂ = 100 mm, the magnification is 4×, meaning the output beam diameter is four times larger and the divergence is four times smaller.

The two primary designs are Galilean and Keplerian beam expanders. A Galilean expander uses one diverging (negative focal length) and one converging (positive focal length) lens — it is compact and has no internal focus point. A Keplerian expander uses two converging lenses with a real focal point between them, allowing spatial filtering but making it longer and susceptible to air breakdown at high powers.

This is a consequence of the optical invariant (étendue conservation). When a beam expander increases the beam diameter by a factor M, the full-angle divergence must decrease by the same factor M to conserve the beam's phase-space volume. A larger beam wavefront has a smaller angular spread, which means reduced divergence and a longer collimated propagation distance.

For a Keplerian expander, the lens separation equals the sum of both focal lengths: d = f₁ + f₂. For a Galilean expander, the separation equals the difference: d = f₂ − |f₁| (where f₁ is negative). This makes Galilean designs more compact for the same magnification.

No. A beam expander cannot improve the intrinsic beam quality factor M² of a laser. M² is a property of the laser source itself. However, a Keplerian expander can incorporate a spatial filter (pinhole) at its internal focus point, which can significantly reduce M² by removing higher-order modes and wavefront distortions.

The magnification is MP = f₂ / f₁ = 100 mm / 25 mm = 4×. This means the output beam diameter will be 4 times larger than the input diameter, and the output divergence will be 4 times smaller than the input divergence.

Temperature changes cause thermal expansion of the lens mounts and refractive index shifts in the glass elements, altering effective focal lengths and lens separation. This can introduce wavefront errors, shift the output collimation, and slightly change the effective magnification. Athermalized mounts or temperature-compensated glass types are used in precision field deployments to minimize these effects.