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Rayleigh length : ウィキペディア英語版
Rayleigh length

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. A related parameter is the confocal parameter, ''b'', which is twice the Rayleigh length.〔 The Rayleigh length is particularly important when beams are modeled as Gaussian beams.
==Explanation==

For a Gaussian beam propagating in free space along the \hat axis, the Rayleigh length is given by
:z_\mathrm = \frac ,
where \lambda is the wavelength and w_0 is the beam waist, the radial size of the beam at its narrowest point. This equation and those that follow assume that the waist is not extraordinarily small; w_0 \ge 2\lambda/\pi.〔Siegman (1986) p. 630.〕
The radius of the beam at a distance z from the waist is
:w(z) = w_0 \, \sqrt} \right)}^2 } .
The minimum value of w(z) occurs at w(0) = w_0, by definition. At distance z_\mathrm from the beam waist, the beam radius is increased by a factor \sqrt and the cross sectional area by 2.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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