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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.
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]
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.
To calculate the response of a light beam on a plane perpendicular to the z axis, the beam function (represented by a b × b matrix) is convolved with the impulse response on that plane (represented by an a × a matrix). Normally a is greater than b. The calculation efficiency of these two methods depends largely on b, the size of the light beam.
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]
If the beam is distributed in phase space with a Gaussian distribution, the emittance of the beam may be specified in terms of the root mean square value of and the fraction of the beam to be included in the emittance. The equation for the emittance of a Gaussian beam is: [1]: 83
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 ...