Calculator Inputs
Plotly Graph
The graph shows the beam envelope using the current calculation mode.
Example Data Table
| Distance (m) | Beam Radius (mm) | Beam Diameter (mm) | FWHM Diameter (mm) |
|---|---|---|---|
| 0.000 | 0.500000 | 1.000000 | 0.832555 |
| 0.500 | 0.504033 | 1.008065 | 0.839268 |
| 1.000 | 0.516001 | 1.032002 | 0.859204 |
| 2.000 | 0.560102 | 1.120204 | 0.932628 |
Formula Used
Gaussian propagation: w(z) = w0 √[1 + (z / zR)²]
Rayleigh range: zR = π w02 / (M² λmedium)
Medium wavelength: λmedium = λ / n
Far-field divergence: θ = M² λmedium / (π w0)
Beam diameter: D = 2w(z)
FWHM diameter for Gaussian intensity: DFWHM = √(2 ln 2) · D
Focused spot estimate: wf = M² λmedium f / (π win)
Divergence sizing: D(z) = D0 + 2z tan(θ)
How to Use This Calculator
- Choose the calculation mode that matches your optical setup.
- Enter wavelength, refractive index, and beam quality M².
- Provide the required geometry values for the selected mode.
- Click Calculate Beam Size to show results above the form.
- Review the beam metrics, graph, and example table.
- Use the export buttons to download CSV or PDF output.
FAQs
1. What does beam size usually mean in optics?
Beam size usually means the 1/e² diameter or radius of a Gaussian beam. Some systems use FWHM instead. Always confirm the beam size definition before comparing specifications or measurements.
2. Why is M² important in beam calculations?
M² shows how closely a real beam matches an ideal Gaussian beam. Larger M² increases divergence and enlarges the focused spot. It is essential for realistic design work.
3. What is the Rayleigh range?
The Rayleigh range is the distance from the waist where the beam radius grows by √2. It helps identify the near-field region and depth of focus.
4. Does refractive index change beam calculations?
Yes. The wavelength shortens inside a medium by the refractive index. That changes the Rayleigh range, divergence, and focused spot calculations used in the tool.
5. Is beam diameter the same as beam radius?
No. Diameter is twice the radius. Many optical formulas use radius, while datasheets often show diameter. Convert carefully to avoid doubling or halving errors.
6. Can this calculator estimate a focused laser spot?
Yes. Use the focused spot mode with wavelength, input beam diameter, focal length, refractive index, and M². The tool estimates spot size, divergence, and Rayleigh range.
7. When should I use divergence mode?
Use divergence mode when you already know the starting diameter and divergence. It is useful for simple sizing over distance without requiring a waist-based Gaussian model.
8. Does this replace laboratory beam profiling?
No. This calculator gives design estimates and quick engineering checks. Real systems should still be verified with beam profilers, knife-edge tests, or manufacturer measurements.