Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Hobbyists & Makers · Gaussian Beam

Gaussian Beam for an LED

Built for hobbyists & makers exploring it for fun. Play with real physics and math, no license and no setup — just open and tinker. Simulate an LED live below — adjust the inputs and watch it respond, right in your browser.

Gaussian BeamLive

how a laser beam spreads

Controls

Presets

Beam waist w₀ (µm)

Wavelength (nm)

A real laser beam is not a perfect ray — it narrows to a minimum waist then spreads. Within one Rayleigh range of the waist it stays roughly collimated; beyond, it diverges at an angle set by wavelength over waist size. Tighter focus means faster spreading — the fundamental diffraction trade-off behind every laser and telescope.

▶ Run in Python

Data Inspector

Rayleigh range0.012 m

Divergence4.03 mrad

Waist50 µm

Governing equation

w (z) = w_{0} 1 + (z / z_{R})^{2}, z_{R} = \frac{π w _{0}^{2}}{λ} = 12.4 mm

Reading this result: Divergence is set by λ/(π·w₀): shrinking the waist or lengthening the wavelength both make the beam spread faster — the core diffraction trade-off.

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Frequently asked questions

Is this good for hobbyists & makers?: Yes — this version of "Gaussian Beam for an LED" is framed for hobbyists & makers exploring it for fun. Play with real physics and math, no license and no setup — just open and tinker.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.