Laser Beam Expander Calculator

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Choose whether to specify the magnification directly or derive it from the two lens focal lengths.
Galilean expanders use a negative input lens and are shorter with no internal focal point. Keplerian expanders use two positive lenses and produce an intermediate focus, which enables spatial filtering.
The expansion ratio M = output diameter / input diameter. A value of 5 means the beam is expanded 5x in diameter.
x
Diameter of the laser beam entering the expander, measured at the 1/e² intensity level for Gaussian beams.
mm
Full-angle divergence of the input beam. A beam expander reduces this by the magnification factor.
mrad
Propagation distance from the expander exit to a target or work surface. Used to estimate the beam diameter at that point.
m
Output beam diameterHigh expansion
10mm

Beam diameter at the expander exit (1/e² width)

Magnification5x
Output divergence0.3mrad
Beam diameter at target13mm
Lens separation100mm
System length100mm
Output diameter (mm)10
Diameter at target (mm)13
Lens separation (mm)100

5.0x Galilean expander: 10.00 mm output, 0.300 mrad divergence.

  • The beam is expanded 5.00x in diameter, from 2.00 mm to 10.000 mm.
  • Divergence drops from 1.500 mrad to 0.3000 mrad - a 5.0x reduction, improving far-field collimation.
  • At 10 m from the expander, the beam diameter is approximately 13.00 mm.
  • Galilean design: compact and no internal focal point, reducing risk of air breakdown at high peak powers.

Next stepCheck the clear aperture of your output lens is at least the output beam diameter plus some margin (typically 20%) to avoid clipping losses.

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