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The shape of a Gaussian beam of a given wavelength λ is governed solely by one parameter, the beam waist w 0. 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).
Gaussian beam width () as a function of the axial distance .: beam waist; : confocal parameter; : Rayleigh length; : total angular spread In optics and especially laser science, the Rayleigh length or Rayleigh range, , is the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled. [1]
In optics, the complex beam parameter is a complex number that specifies the properties of a Gaussian beam at a particular point z along the axis of the beam. It is usually denoted by q . It can be calculated from the beam's vacuum wavelength λ 0 , the radius of curvature R of the phase front , the index of refraction n ( n =1 for air), and ...
The NA of a Gaussian laser beam is then related to its minimum spot size ("beam waist") by NA ≃ λ 0 π w 0 , {\displaystyle {\text{NA}}\simeq {\frac {\lambda _{0}}{\pi w_{0}}},} where λ 0 is the vacuum wavelength of the light, and 2 w 0 is the diameter of the beam at its narrowest spot, measured between the e −2 irradiance points ("Full ...
Multi-mode beam propagation is often modeled by considering a so-called "embedded" Gaussian, whose beam waist is M times smaller than that of the multimode beam. The diameter of the multimode beam is then M times that of the embedded Gaussian beam everywhere, and the divergence is M times greater, but the wavefront curvature is the same.
Unlike the previous beam width definitions, the D86 width is not derived from marginal distributions. The percentage of 86, rather than 50, 80, or 90, is chosen because a circular Gaussian beam profile integrated down to 1/e 2 of its peak value contains 86% of its total power. The D86 width is often used in applications that are concerned with ...
Laser machine shops care a lot about the M 2 parameter of their lasers because the beams will focus to an area that is M 4 times larger than that of a Gaussian beam with the same wavelength and D4σ waist width; in other words, the fluence scales as 1/M 4. The rule of thumb is that M 2 increases as the laser power increases.
Gaussian laser beams are said to be diffraction limited when their radial beam divergence = / is close to the minimum possible value, which is given by [2] =, where is the laser wavelength and is the radius of the beam at its narrowest point, which is called the "beam waist". This type of beam divergence is observed from optimized laser cavities.