Laser Beam Expander Calculator

X
Example: 5X expander means output is 5 times larger.
Units: Diameter in mm, Divergence in mrad.
meters
Calculate beam size at this distance after expansion.
Output Diameter
--- mm
Output Divergence
--- mrad
Magnification
--- Calculated Power

How it works?

A Laser Beam Expander is essentially a reverse telescope. Its primary function is to increase the diameter of a collimated input beam to a larger collimated output beam.

The fundamental rule of Gaussian optics is that diameter and divergence are inversely related. By expanding the beam, you significantly reduce its divergence, allowing the beam to travel longer distances without spreading.

$$ D_{out} = M \cdot D_{in} $$ $$ \theta_{out} = \frac{\theta_{in}}{M} $$

Where:

  • Magnification (M): The expansion ratio. Calculated as the ratio of focal lengths ($f_2 / f_1$).
  • D (Diameter): The beam width (typically 1/e²).
  • θ (Divergence): The full-angle spread of the beam (in milliradians).

Keplerian vs. Galilean

**Galilean:** Uses one negative (concave) lens and one positive (convex) lens. It does not have an internal focal point, making it shorter and suitable for high-power lasers (no air breakdown).

**Keplerian:** Uses two positive lenses with an internal focal point. It is longer but allows for spatial filtering (placing a pinhole at the focus) to clean up the beam profile.

Why Expand a Laser Beam?

It seems counterintuitive to make a "focused" laser beam larger, but expansion is the key to achieving smaller spot sizes and longer ranges.

Top Applications

1. Smaller Spot Sizes

Surprisingly, to focus a laser to the smallest possible point, you first need to expand it. The focused spot size is inversely proportional to the input beam diameter. A 5x expander creates a 5x smaller focal spot.

2. Reducing Divergence

For long-range pointing (LiDAR, laser comms), standard lasers spread out too much. A beam expander reduces divergence by the magnification factor (M), keeping the beam tight over kilometers.

3. Protecting Optics

Expanding the beam spreads the energy over a larger area (lower power density). This prevents damage to sensitive internal optics like mirrors and polarizers in high-power systems.

4. Beam Shaping

Beam expanders are often used to resize a laser beam to match the clear aperture of a galvo scanner or objective lens, maximizing throughput and resolution.

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