Model laser beam spread with precise optical inputs. Compute waist, divergence, Rayleigh range, intensity quickly. Export results and plots for design and testing today.
Use known waist mode, or compute a focused waist from a lens.
Try these typical values to verify outputs.
| Scenario | λ (nm) | M² | w₀ (mm) | z (mm) | P (W) | r (mm) |
|---|---|---|---|---|---|---|
| Near-ideal infrared beam | 1064 | 1.0 | 0.50 | 500 | 10 | 0.25 |
| Visible beam with modest M² | 532 | 1.3 | 0.30 | 200 | 2 | 0.10 |
| Lens focusing example | 1550 | 1.1 | — | 0 | 1 | 0 |
For the lens row, switch to lens mode and use w_in=2.0 mm, f=100 mm.
Beam divergence scales directly with wavelength, so longer infrared light spreads faster for a fixed waist. Here, λ sets Rayleigh range and far-field angle. Doubling λ doubles θ while shrinking zR by half when w₀ is constant. If you must deliver a small spot at long stand-off, shorter wavelengths reduce growth.
Laboratory beams rarely stay diffraction limited. The M² factor increases divergence and reduces effective Rayleigh range the same way as increasing wavelength. If M² rises from 1.0 to 1.5, divergence rises 50% and depth of focus drops to two thirds. Use measured M² from a profiler to keep designs realistic.
The Rayleigh range zR is the distance where the beam radius grows by √2. Many alignment and processing tasks operate inside ±zR because spot size and intensity remain comparatively stable there. The confocal parameter 2zR is often quoted for machining and microscopy because it approximates the usable focus window for a chosen waist.
When you know the beam radius at a lens, the thin-lens estimate w_f = (M² λ f)/(π w_in) predicts the focused waist. Increasing input radius at the lens tightens the focus, while longer focal length loosens it. This relation helps compare optics early, before full ABCD modeling or tolerance analysis.
On-axis intensity varies as 1/w(z)², so modest spot changes create large energy-density shifts. At constant power, a 20% reduction in radius raises I₀ by about 56%. Off-axis intensity follows the exp(−2r²/w²) envelope, letting you estimate edge exposure, sensor saturation, or safety margins at specific radii. Use r to evaluate a detector pixel position or a burn threshold at a known offset.
Validate inputs by measuring waist and M² using standard characterization practice and record wavelength from the laser specification. Then sweep z values to compare predicted w(z) against profiler data. If results disagree, check definitions: this tool uses the 1/e² radius, not FWHM. Also confirm that z is referenced to the waist or the focused spot, not the lens. Consistent units and definitions produce reliable decisions in alignment, cutting.
w(z) is the 1/e² intensity radius of a TEM00 Gaussian beam at distance z. The diameter shown is 2w(z), which is common for beam size specifications.
At the waist, the wavefront is locally planar, so curvature is effectively zero and the radius of curvature tends to infinity. Away from the waist, the beam becomes curved.
Yes. Negative z represents positions before the waist location. The radius w(z) is symmetric in z, while the Gouy phase changes sign with z.
It is a thin-lens, paraxial approximation using the beam radius at the lens. It is useful for quick comparisons, but it ignores aberrations, truncation, and misalignment.
No. The intensity uses the entered optical power and assumes an ideal Gaussian profile without transmission losses. If your system has losses, reduce the power input accordingly.
For a Gaussian intensity profile, FWHM ≈ w·√(2 ln 2). Therefore, w ≈ FWHM / √(2 ln 2). Use the converted w as the waist radius input.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.