page_title: Gaussian beam
section_title: Beam waist
hierarchical_section_title: Gaussian beam / Beam parameters / Beam waist
context_page_description: In optics, a Gaussian beam is a beam of monochromatic electromagnetic radiation whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity profile. This fundamental transverse Gaussian mode describes the intended output of most lasers, as such a beam can be focused into the most concentrated spot. When such a beam is refocused by a lens, the transverse phase dependence is altered; this results in a different Gaussian beam. The electric and magnetic field amplitude profiles along any such circular Gaussian beam are determined by a single parameter: the so-called waist w₀. At any position z relative to the waist along a beam having a specified w₀, the field amplitudes and phases are thereby determined as detailed below.
  The equations below assume a beam with a circular cross-section at all values of z; this can be seen by noting that a single transverse dimension, r, appears.
context_section_description: The shape of a Gaussian beam of a given wavelength λ is governed solely by one parameter, the beam waist w₀. This is a measure of the beam size at the point of its focus (z = 0 in the above equations) where the beam width w(z) (as defined above) is the smallest (and likewise where the intensity on-axis (r = 0) is the largest). From this parameter the other parameters describing the beam geometry are determined. This includes the Rayleigh range zR and asymptotic beam divergence θ, as detailed below.
caption: Gaussian beam width w(z) as a function of the distance z along the beam, which forms a hyperbola. w0: beam waist; b: depth of focus; zR: Rayleigh range; Θ: total angular spread