Laser Spot Size Calculator

The focused spot diameter for a Gaussian beam is calculated as d = (4 × M² × λ × f) / (π × D), where λ is the wavelength, f is the focal length, D is the input beam diameter, and M² is the beam quality factor. For an ideal Gaussian beam, M² = 1, giving the diffraction-limited minimum spot size.

M² is a dimensionless parameter that describes how close a real laser beam is to a perfect Gaussian (TEM₀₀) beam. An ideal Gaussian has M² = 1. Real laser beams have M² > 1, meaning their spot size and divergence are M² times larger than the diffraction limit. Single-mode fiber lasers often have M² very close to 1, while multimode lasers can have M² values of 10 or more.

The depth of field is defined as twice the Rayleigh range (z_R). The Rayleigh range is the distance from the beam waist at which the beam radius increases by a factor of √2 (i.e., the area doubles). For a Gaussian beam, z_R = π × w₀² / (M² × λ), where w₀ is the focused spot radius. A tighter focus gives a smaller depth of field.

A larger input beam diameter increases the effective numerical aperture of the focusing lens, which reduces diffraction and allows tighter focusing. This is why beam expanders are used before focusing lenses in laser systems — expanding the beam before the lens results in a smaller, more intense focal spot.

The 1/e² diameter is the standard way to measure a Gaussian laser beam's size. It is the diameter at which the beam intensity drops to 1/e² (about 13.5%) of its peak value. Approximately 86.5% of the total beam power is contained within this diameter.

Yes. A longer focal length lens produces a larger spot size but a longer depth of field, while a shorter focal length produces a tighter focus but a very short depth of field. This trade-off is important in applications like laser cutting, welding, and microfabrication where both spot size and working range matter.

The focused spot size is directly proportional to the wavelength. Shorter wavelengths (e.g., UV lasers at 355 nm) produce smaller spots than longer wavelengths (e.g., CO₂ lasers at 10.6 μm) for the same beam diameter and focal length. This is why UV lasers are preferred for microfabrication and fine engraving.

This calculator assumes the input beam is a collimated Gaussian beam (or close to one, modified by M²) with negligible aberrations in the focusing lens. The lens diameter should be at least twice the input beam diameter to avoid clipping the beam edges, which would distort the focused spot. Strong lens aberrations will also increase the effective spot size beyond what this formula predicts.