Gaussian Laser Beam Waist & Divergence Propagation Calculator

A Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity distributions are described by Gaussian functions.

Unlike ray optics, wave diffraction dictates that tightly focused laser beams diverge rapidly away from the focal waist.

At the waist (z = 0), the wavefront is planar (R = infinity) and the beam has its smallest spot radius w0.

Over the Rayleigh range zR, the cross-sectional area doubles and the beam radius grows by sqrt(2) (approx. 1.414 * w0).

In the far field (z >> zR), the beam expands linearly at the divergence half-angle theta.

Spot radius w(z) gives the 1/e2 (approx. 86.5% enclosed power) radius at target distance.

Rayleigh range indicates the depth of focus over which the beam remains reasonably collimated.

Divergence half-angle (in mrad) defines beam spread for long-distance optical delivery.

• Waist size trade-off: Tightly focused laser waists diverge proportionally faster; doubling w0 halves divergence and quadruples Rayleigh range.
• Wavelength: Shorter wavelengths (UV/visible) achieve tighter focus and longer depth of focus than infrared lasers.
• Beam quality factor M2: Real non-ideal laser beams diverge M2 times faster than a theoretical diffraction-limited TEM00 beam.

• Designing industrial laser cutting heads, 3D printing optical scanners, and confocal microscopes.
• Free-space optical communication link budgets and fiber coupling lens design.

• Assumes ideal diffraction-limited fundamental TEM00 spatial mode (M2 = 1.0).
• Valid within the paraxial approximation (waist w0 >> lambda).