For laser integration engineers sizing a focusing head before a cutting, welding or marking station, accurately understanding beam propagation is critical. This calculator helps quickly determine key parameters like Rayleigh length and depth of focus. For example, a 50 µm waist at 1064 nm with M² = 1.1 gives a Rayleigh length zR ≈ 6.7 mm, meaning the beam has already grown to roughly 90 µm only 10 mm from the waist. Gaussian beam propagation: Rayleigh length zR = π w₀² / (M² λ), depth of focus 2 zR, beam radius w(z) = w₀ √ (1 + (z/zR)²) and far-field divergence.
A: The Rayleigh length zR = π·w₀²/(M²·λ) is the distance from the waist over which the beam area doubles; the depth of focus is twice that, 2·zR, i.e. the full waist-to-waist span over which the beam stays within √2 of w₀.
A: Square the waist radius in metres, multiply by π, and divide by M² times the wavelength in metres: zR = π·w₀²/(M²·λ). For w₀ = 50 µm, λ = 1064 nm and M² = 1.1 this gives about 6.7 mm.
A: A beam with M² > 1 has a Rayleigh length shorter by that factor and a far-field half-angle larger by it: zR = π·w₀²/(M²·λ) and θ = M²·λ/(π·w₀). The calculator rejects any M² below 1.
A: The beam radius grows as w(z) = w₀·√(1 + (z/zR)²), so at z = zR it is w₀·√2 and it keeps expanding roughly linearly beyond that, with the sign of z making no difference to the width.