Laser Beam Expander Calculator

Laser Beam Expander

A beam expander uses two lenses to increase beam diameter while reducing divergence. This is essential for reducing power density, improving collimation, and matching beam size to optical components.

Formulas

$$M = \frac{f_2}{f_1}$$ $$d_{out} = M \times d_{in}$$ $$\theta_{out} = \frac{\theta_{in}}{M}$$

Magnification $M$ is the ratio of output to input lens focal lengths. Beam diameter scales up by $M$, while divergence scales down by $1/M$.

Practical Notes

A 4× expander with f₁ = 25 mm and f₂ = 100 mm quadruples beam diameter and reduces divergence to one-quarter. The product of beam diameter and divergence remains approximately constant (beam parameter product).

Frequently Asked Questions

What is beam expander magnification?

Magnification M equals the output lens focal length divided by the input lens focal length: M = f₂/f₁.

Why does divergence decrease?

Expanding the beam reduces its angular spread. Output divergence equals input divergence divided by magnification.

Can I use a beam reducer?

Yes. When f₂ < f₁, M < 1 and the beam shrinks while divergence increases proportionally.

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