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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.
When measuring the beam parameter product and M 2, one uses the D4σ or "second moment" width of the beam to determine both the radius of the beam's waist and the divergence in the far field. [ 2 ] The BPP can be easily measured by placing an array detector or scanning-slit profiler at multiple positions within the beam after focusing it with a ...
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]
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 ...
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 beam propagation method (BPM) is an approximation technique for simulating the propagation of light in slowly varying optical waveguides. It is essentially the same as the so-called parabolic equation (PE) method in underwater acoustics. Both BPM and the PE were first introduced in the 1970s.