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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 ...
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 ...
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.
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]
Laser beams spread out as they propagate, but slowly. Far away from the narrowest part of the beam, the spread is roughly linear with distance—the laser beam forms a cone of light in the "far field". The relation used to define the NA of the laser beam is the same as that used for an optical system,
A laser beam is guided like in a glass fiber. With an additional Kerr lens the beam width gets smaller. In a real laser the crystal is finite. The cavity on both sides features a concave mirror and then a relative long path to a flat mirror. The continuous-wave light exits the crystal end face with a larger beam width and slight divergence.
Gaussian optics is a technique in geometrical optics that describes the behaviour of light rays in optical systems by using the paraxial approximation, in which only rays which make small angles with the optical axis of the system are considered. [1] In this approximation, trigonometric functions can be expressed as linear functions of the angles.
It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue include acceptance, throughput, light grasp, light-gathering power, optical extent, [1] and the AΩ product. Throughput and AΩ product are especially used in radiometry and radiative transfer where it is related to the view factor (or shape factor).