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What this does: a laser beam isn't a ray — it has a narrowest point (the waist) and spreads from there.
Set your source beam, drop lenses into the path, and the plot shows the real beam width everywhere. The green dots mark
where the beam re-focuses. Use Advanced (top right) for the focused-spot solver and depth-of-focus.
Source beam
nm
–
µm
mm
mm
Lens train
| # | Position z (mm) | Focal length f (mm) |
|---|
Thin-lens model:
1/q′ = 1/q − 1/f. Use positive f for converging,
negative for diverging lenses. Lenses are applied in order of position.What this means
Beam caustic
Key results
Advanced diagnostics & focus solver expert
µm
Solver assumes a single focusing lens at the first lens position, fed by the beam width arriving there.
Segment-by-segment beam data
| Segment | Waist w₀ | Waist at z | Rayleigh zR | Divergence θ (half) | Beam at next lens |
|---|
Conventions: w is the 1/e² intensity radius. zR = πw₀²/(M²λ).
θ = M²λ/(πw₀) is the far-field half-angle. A waist reported outside its segment is virtual.
Learn: Gaussian beams & the q-parameter
A real laser beam stays narrow only near its waist w₀, then diverges. The Rayleigh range z_R = πw₀²/(M²λ) is how far it travels before its area doubles — your usable "in focus" zone.
The whole beam is captured by one complex number, the q-parameter, which a lens transforms with the same ABCD matrices used for rays: 1/q′ = 1/q − 1/f. That's how this tool propagates the beam exactly.
Tighter focus costs depth: a smaller spot has a shorter Rayleigh range (∝ w₀²). And a beam with M² > 1 can't be focused as small — its spot and divergence both scale with M².