Free · Physics models
Ideal Two-Lens Laser Beam Expansion
Relate focal lengths, beam diameter and full-angle divergence for an ideal beam expander.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
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Formula and method
magnification power = 5.0000; magnification = 0.20000. This worked example uses the displayed units and declared assumptions.
magnification_power = focal_length_objective/(type *focal_length_image); magnification = 1/magnification_power; output_diameter=input_diameter*magnification_power; output_divergence = input_divergence/magnification_power; diameter_at_distance_L = output_diameter + 2*L*tan(output_divergence/2)
Worked example
Enter these known values and leave the other values blank.
- Design
- 1
- Image lens' focal length (f==ɪ==)
- 20 mm
- Objective lens' focal length (f==O==)
- 100 mm
- Input diameter (D==ɪ==)
- 2 mm
- Input divergence (Θ==ɪ==)
- 5 mrad
- Distance from the expander (L)
- 10 m
- Magnification (m)
- 0.2
- Magnifying power (MP)
- 5 X
- Output diameter (D==O==)
- 10 mm
- Output divergence (Θ==O==)
- 1 mrad
- Diameter at distance (D==L==)
- 20 mm
Assumptions and limitations
- This paraxial two-lens model assumes a collimated input and ideal aligned lenses. Expansion ratio is objective focal length divided by the signed input focal length times the selected lens type.
- Divergence is the full included angle. Propagation uses straight edge rays, D(L)=D0+2L tan(theta/2); it is not Gaussian-beam waist propagation and does not include diffraction or aberration.
Common questions
What assumptions apply?
This paraxial two-lens model assumes a collimated input and ideal aligned lenses. Expansion ratio is objective focal length divided by the signed input focal length times the selected lens type.
Which unknowns can I solve?
Editable controls preserve the supported captured inverse branches. Clear the desired unknown and provide enough independent known quantities; singular or underdetermined inverses may remain incomplete.
References
Declare divergence as the full included angular width. Two symmetric edge rays each travel at theta/2, so diameter grows by 2 L tan(theta/2), with each captured inverse updated consistently. Expansion ratio and inverse divergence relation retain their paraxial lens assumptions.