Gaussian Beam & ABCD Bench

Build a customizable optical bench of lenses, mirrors, and apertures. Trace paraxial beams, view envelopes, and calculate clipping ratios.

Wavelength (λ, nm)

Waist Radius (w_0, mm)

Beam Quality Factor (M²)

lens

Position (z, mm)

Focal Length (mm)

aperture

Position (z, mm)

Diameter (mm)

observation

Position (z, mm)

Element	Position (mm)	Radius w(z) (µm)	Curvature R (mm)	Post-waist w0 (µm)	Post-waist z0 (mm)	Power fraction
Lens 1	120.0	501.65	18282	33.865	220.09	100.0%
Aperture 1	200.0	106.02	-22.375	33.865	220.09	100.0% (clipt)
Observation 1	250.0	153.34	31.442	33.865	220.09	100.0%

Gaussian Beam & ABCD Matrices Theory

\frac{1}{q(z)} = \frac{1}{R(z)} - i \frac{M^2 \lambda_0}{\pi n w(z)^2}

Combines physical waist size and wavefront curvature into a single complex coordinate.

q_{\mathrm{out}} = \frac{A q_{\mathrm{in}} + B}{C q_{\mathrm{in}} + D}

Propagates the beam parameter through refractive and reflective structures paraxially.

z_{\mathrm{waist}} = z_{\mathrm{plane}} - \mathrm{Re}(q_{\mathrm{after}})

w_0' = \sqrt{\frac{\mathrm{Im}(q_{\mathrm{after}}) M^2 \lambda_0}{\pi n}}

Extracts the location and radius of the beam waist directly from the propagated complex parameters.