Rayleigh length

The propagation distance from a Gaussian beam’s waist to where its cross-sectional area doubles. It equals π times the waist radius squared divided by the wavelength.

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Gaussian beam: A beam whose transverse electric-field amplitude has a Gaussian profile. Rayleigh length describes how this beam spreads as it propagates from its waist.
Wavelength: The spatial period of a wave, measured as the distance between successive points of equal phase. A shorter wavelength increases the Rayleigh length when waist radius is fixed.
Depth of focus: The axial range over which an optical system keeps an image acceptably sharp. A beam’s Rayleigh length provides a natural scale for axial focus tolerance.
Depth of field: The range of object distances that appear acceptably sharp in an imaging system. It is an image-quality range, unlike the beam-defined distance to doubled area.
Beam waist: The location along a beam where its transverse radius reaches a minimum. Its radius sets the Rayleigh length through a square-law dependence.
Beam radius: A measure of the transverse size of a beam, commonly defined by its intensity profile. The waist radius is the squared length scale in the defining formula.
Laser beam welding: A welding process that uses a focused laser beam to melt and join materials. Rayleigh length helps determine how consistently the focused spot delivers energy through the workpiece.
Confocal parameter: The distance along a Gaussian beam spanning two Rayleigh lengths, centered on the waist. It is twice the Rayleigh length and describes the full confocal region.
Gaussian beam parameter: A complex parameter that compactly describes a Gaussian beam’s curvature and transverse size. It provides a propagation-based description that includes the Rayleigh length.
Gaussian intensity profile: A radial intensity distribution that falls off from its central maximum as a Gaussian function. Its radius convention determines where the beam’s cross-sectional area is measured.