Laser Beam Expander Calculator
Free calculate output beam diameter and divergence from magnification or focal lengths. Get instant, accurate results with our easy-to-use calculator.
Input Parameters
Results
Enter parameters to calculate
What is a Laser Beam Expander?
A laser beam expander is an optical device that increases the diameter of a laser beam while simultaneously reducing its divergence angle. This improves beam collimation and allows for better focusing over longer distances.
Beam expanders typically use two lenses: an objective lens (longer focal length) and an image lens (shorter focal length). The magnification is the ratio of these focal lengths, determining how much the beam expands.
By expanding the beam, divergence is reduced proportionally, making the beam more collimated. This is essential for applications requiring long-distance beam propagation, precise focusing, or reduced beam spread.
Beam Expander Formulas
Magnification
Output Diameter
Output Divergence
Beam Parameter Product
How to Calculate
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1
Determine magnification
Either use given M, or calculate M = f_obj / f_img from focal lengths.
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2
Calculate output diameter
D_out = M × D_in (beam expands by magnification factor).
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3
Calculate output divergence
θ_out = θ_in / M (divergence reduces by magnification factor).
Practical Examples
Example 1: 2× Beam Expander
Input: 1 mm diameter, 0.5 mrad divergence. Magnification: 2×
Solution:
D_out = 2 × 1 mm = 2 mm
θ_out = 0.5 / 2 = 0.25 mrad (50% reduction!)
Example 2: From Focal Lengths
f_obj = 100 mm, f_img = 25 mm. Calculate magnification.
Solution:
M = 100 / 25 = 4×
Beam expands 4×, divergence reduces to 1/4.
Applications
Free-Space Optics
Reducing beam spread for long-distance optical communications and laser ranging systems.
Laser Processing
Improving beam quality for cutting, welding, and material processing applications.
Optical Systems
Matching beam sizes to optical components, improving focusability, and reducing aberrations.
Research
Optimizing beam parameters for experiments, improving signal-to-noise ratios, and precise measurements.
Frequently Asked Questions
Why does divergence decrease when beam expands?
The beam parameter product (BPP = D × θ) is conserved. When diameter increases, divergence must decrease proportionally to maintain constant BPP. This is a fundamental property of beam propagation.
What is the difference between Galilean and Keplerian beam expanders?
Galilean uses a negative and positive lens (shorter, no internal focus). Keplerian uses two positive lenses (longer, has internal focus). Galilean is more compact but Keplerian allows spatial filtering.
Can I use a beam expander in reverse?
Yes! Reversing a beam expander (using it as a beam reducer) compresses the beam diameter and increases divergence by the same factor. M becomes 1/M.
Does beam expansion affect power density?
Yes! Power density (W/cm²) decreases as the square of magnification since area increases as M². Total power remains constant, but it's spread over a larger area.
What magnification should I use?
Choose magnification based on your application. For long-distance propagation, higher M reduces divergence. For focusing, match beam size to your focusing optics. Typical values: 2× to 10×.