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For Students · Gaussian Beam

Gaussian Beam for a light sail

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a light sail 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.

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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 students?: Yes — this version of "Gaussian Beam for a light sail" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.