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The Gaussian function has a 1/e 2 diameter (2w as used in the text) about 1.7 times the FWHM.. At a position z along the beam (measured from the focus), the spot size parameter w is given by a hyperbolic relation: [1] = + (), where [1] = is called the Rayleigh range as further discussed below, and is the refractive index of the medium.
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 ...
In laser science, the parameter M 2, also known as the beam propagation ratio or beam quality factor is a measure of laser beam quality. It represents the degree of variation of a beam from an ideal Gaussian beam. [1] It is calculated from the ratio of the beam parameter product (BPP) of the beam to that of a Gaussian beam with the same wavelength.
where Θ 0 and D 0 are the divergence and waist of a higher mode beam and M 2 is greater than 1 and is named the "Beam Propagation Ratio" per the ISO 11146 standard. When a Gaussian laser beam is focused, the focused spot diameter is defined by =, (3)
Multiple prism beam expander using r prisms M is the total beam magnification given by M = k 1 k 2 k 3 ···k r, where k is defined in the previous entry and B is the total optical propagation distance [clarification needed] of the multiple prism expander. [5]
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]
For a Gaussian beam, no simple upper integration limits exist because it theoretically extends to infinity. At r >> R, a Gaussian beam and a top-hat beam of the same R and S 0 have comparable convolution results. Therefore, r ≤ r max − R can be used approximately for Gaussian beams as well.
Propagation of a ray through a layer. The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified medium; a stack of thin films. [1] [2] This is, for example, relevant for the design of anti-reflective coatings and dielectric mirrors.