Gaussian Beam Explorer
Physics · free browser app
How a laser beam narrows to a waist, spreads again and focuses through a lens.
Description
A laser beam is never a cylinder: it narrows to its waist and spreads again with a fixed far-field angle. The app draws that Gaussian envelope live — waist w₀, Rayleigh range, divergence and on-axis peak intensity — while you drag wavelength, waist size, beam quality M² and power. A movable probe plane reads the beam radius and intensity anywhere along the axis.
A thin lens can be dropped into the path: the app propagates the beam through it with ABCD ray-transfer matrices and shows the new waist behind the lens. Presets set up a HeNe pointer at 633 nm, a single-mode fiber output at 1550 nm and a focused high-power beam at 1064 nm; free-text entry accepts exact values far beyond the slider ranges, and the essential math is collected inside the app.
Examples
How far does a laser pointer stay collimated?
The HeNe preset starts with a 250 µm waist at 633 nm. Its Rayleigh range is about 31 cm, and a beam stays roughly collimated for two of them — over half a metre before the spread becomes obvious.
Why light from a fiber spreads so fast
The Fiber preset launches from a 5 µm waist at 1550 nm. That tiny waist makes the Rayleigh range about 50 µm, so within a fraction of a millimetre the beam is visibly conical — the smaller the waist, the faster the spread.
Focusing: a tighter spot is sharp for a shorter distance
Add the thin lens and watch the waist behind it: halving the focused spot size cuts the Rayleigh range to a quarter, since it grows with the square of the waist. That trade-off between spot size and depth of focus governs laser cutting and microscopy alike.