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Optics

Laser Beam Expander Calculator

Calculate expansion ratio, output diameter, divergence reduction, and design Galilean or Keplerian beam expanders.

Interactive calculator

Laser Beam Expander Calculator

Calculate expansion ratio, output diameter, divergence reduction, and design Galilean or Keplerian beam expanders.

Try an example

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose: expansion ratio, output diameter, divergence reduction, Galilean design, Keplerian design, or telescope magnification.
  • Use presets for common 3×, 5×, and 10× expanders.
  • Click Calculate for complete design parameters.

Table of Contents

Key Takeaways

  • A beam expander increases beam diameter while reducing divergence by the same factor.
  • Galilean expander (concave + convex): compact, no internal focus, safe for high power.
  • Keplerian expander (convex + convex): longer, internal focus enables spatial filtering.
  • Magnification M = f₂/|f₁| (Galilean) or M = f₂/f₁ (Keplerian).
  • Expanding the beam before focusing yields a smaller spot size at the target.

Beam Expanders

A beam expander is an afocal optical system that changes the diameter of a laser beam. By increasing beam diameter, the divergence decreases proportionally — a direct consequence of the beam parameter product being conserved. This is essential for long-distance laser propagation and achieving tight focus.

Galilean vs Keplerian

Galilean: Uses a negative (diverging) lens followed by a positive (converging) lens. Compact design with no internal focus point, making it safe for high-power lasers. Length = f₂ − |f₁|.

Keplerian: Uses two positive lenses. Longer (length = f₁ + f₂) but creates an internal focus point where a spatial filter (pinhole) can clean the beam profile.

Key Formulas

M=f2∣f1∣,θout=θinMM = \frac{f_2}{|f_1|}, \quad \theta_{\text{out}} = \frac{\theta_{\text{in}}}{M}

Where M is the magnification, f₁ and f₂ are the lens focal lengths, and θ is the beam divergence.

How to Use

  1. Select a design or calculation mode.
  2. Enter focal lengths or beam parameters.
  3. Click Calculate for magnification, separation, and divergence.

Examples

3× Galilean (f₁ = −25 mm, f₂ = 75 mm)

M = 75/25 = 3×; L = 75 − 25 = 50 mm; divergence reduced 3×

5× Keplerian (f₁ = 20 mm, f₂ = 100 mm)

M = 100/20 = 5×; L = 20 + 100 = 120 mm; has internal focus

FAQ

What is a beam expander?›

A beam expander is a two-lens telescope that increases the diameter of a laser beam while proportionally reducing its divergence. It's used to improve beam collimation, reduce focused spot size, or fill a larger optical aperture.

Galilean vs Keplerian — which is better?›

Galilean expanders are shorter and have no internal focus (safe for high-power lasers). Keplerian expanders are longer but allow spatial filtering at the internal focus to clean up the beam. Choice depends on power level and beam quality needs.

Does expanding the beam change its power?›

No — total power is conserved (ignoring lens losses). Expanding the beam reduces power density (W/cm²) proportionally to the area increase (M²).

How do I choose the right magnification?›

Match the expanded beam to your application: fill the focusing lens aperture for smallest spot, match detector size, or reduce divergence for long-range propagation. Higher M means lower divergence but larger optics.

Sources

  1. Edmund Optics – Beam Expanders
  2. RP Photonics – Beam Expanders
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

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