Laser Beam Expander Calculator

A beam expander widens a laser beam, which also reduces its divergence.

How the Math Works

The Laser Beam Expander Calculator uses the magnification formula M = f₂ ÷ f₁, where M is the magnification ratio, f₂ is the focal length of the second lens (output lens), and f₁ is the focal length of the first lens (input lens). This simple division determines how much the laser beam will expand in diameter. Once M is calculated, the output beam size is found by multiplying the input beam diameter by M, while the output divergence angle equals the input divergence divided by M, reflecting the fundamental trade-off between beam width and divergence in optical systems.

Practical Applications

To use this calculator practically, first measure or determine your input laser beam's initial diameter and divergence angle. Next, identify the focal lengths of both the input and output lenses in your beam expander system. Enter these values into the formula to calculate the magnification ratio, then apply this to find your expanded beam size and reduced divergence. This calculation is essential when designing laser systems for engraving, cutting, or medical procedures where beam characteristics directly affect process quality and safety.

Day-to-Day Use

Understanding laser beam expansion helps in everyday situations involving laser pointers, barcode scanners, and laser projectors. When you need a laser beam to travel farther without spreading out too much, or when you need a larger spot size for marking or engraving materials, knowing how beam expanders work allows you to select the right optics. This knowledge also prevents safety issues by helping you predict how a laser's power density changes as the beam expands, ensuring you maintain safe operating distances and power levels for both professional and hobbyist applications.

Worked example

f₁ = 25 mm, f₂ = 100 mm → 4× expansion (2 mm → 8 mm).

FAQ