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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.
A Gaussian beam has the lowest possible BPP, /, where is the wavelength of the light. [1] The ratio of the BPP of an actual beam to that of an ideal Gaussian beam at the same wavelength is denoted M 2 ("M squared"). This parameter is a wavelength-independent measure of beam quality.
The equation for the divergence of a pure Gaussian TEM 00 unfocused beam propagating through space is given by =, (1) where D 00 is the diameter of the beam waist, and λ is the wavelength. Higher mode beams often start with a larger beam waist, D 0, and/or have a faster divergence Θ 0. In this case Equation (1) becomes
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.Beams with elliptical cross-sections, or with waists at different positions in z for the two transverse dimensions (astigmatic beams) can also be described as Gaussian beams, but with distinct values of w 0 and of the z = 0 location for ...
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]
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]
A laser beam profiler captures, displays, and records the spatial intensity profile of a laser beam at a particular plane transverse to the beam propagation path. Since there are many types of lasers— ultraviolet , visible , infrared , continuous wave , pulsed, high-power, low-power—there is an assortment of instrumentation for measuring ...
An interesting phenomenon related to the filament propagation is the refocusing of focused laser pulses after the geometrical focus. [8] [9] Gaussian Beam propagation predicts an increasing beam width bidirectionally away from the geometric focus. However, in the situation of laser filamentation, the beam will quickly recollapse.