Gaussian beam

A Gaussian beam is a paraxial electromagnetic beam whose transverse field amplitude has a Gaussian profile. Its width and phase curvature change during propagation, while diffraction gives it a finite waist and divergence.

Paraxial wave equation: An approximation to the wave equation for fields propagating mainly along one axis with slowly varying transverse structure. Gaussian beams are exact solutions of this propagation equation.
Gaussian function: A function shaped like an exponential of a negative quadratic, characterized by its center and width. The beam's transverse field amplitude follows this profile.
Laser resonator: An optical cavity that sustains selected electromagnetic modes through repeated feedback. Stable resonators commonly support Gaussian transverse modes.
Higher-order Gaussian mode: A paraxial beam mode with transverse nodes described by Hermite or Laguerre polynomials multiplying a Gaussian envelope. These modes add structure absent from the fundamental Gaussian profile.
Beam waist: The location and radius of a beam's narrowest transverse profile. It anchors the beam's size and phase evolution along its propagation axis.
Electromagnetic wave: A propagating disturbance of electric and magnetic fields that carries energy and momentum. A Gaussian beam is a spatially structured electromagnetic wave.
Gaussian optics: A framework for tracing Gaussian beams through optical systems using paraxial transformations. It predicts how lenses and mirrors reshape Gaussian beam parameters.
Bessel beam: An idealized beam with a Bessel-function transverse profile that can resist diffraction over a finite range when truncated. Its central profile can remain narrow over distances where a Gaussian beam expands.
Rayleigh range: The distance from a beam waist over which the beam radius grows by a factor of the square root of two. It sets the characteristic axial scale of Gaussian-beam diffraction.
Diffraction: The spreading and reshaping of waves caused by finite apertures or spatial variation. A finite Gaussian profile necessarily spreads as it propagates.

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