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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.
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.
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]
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 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 ...
p is the associated Laguerre polynomial of order p and index l, and w is the spot size of the mode corresponding to the Gaussian beam radius. Cylindrical transverse mode with p=2, l=1. With p = l = 0, the TEM 00 mode is the lowest order. It is the fundamental transverse mode of the laser resonator and has the same form as a Gaussian beam.
To calculate the optical broad-beam response, the impulse response of a pencil beam is convolved with the beam function. As shown by Equation 4, this is a 2-D convolution. 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 ...