Beam width
The beam diameter or beam width of an electromagnetic beam is the diameter along any specified line that is perpendicular to the beam axis and intersects it. Since beams typically do not have sharp edges, the diameter can be defined in many different ways. Five definitions of the beam width are in common use: D4σ, 10/90 or 20/80 knife-edge, 1/e2, FWHM, and D86. The beam width can be measured in units of length at a particular plane perpendicular to the beam axis, but it can also refer to the angular width, which is the angle subtended by the beam at the source. The angular width is also called the beam divergence.
Beam diameter is usually used to characterize electromagnetic beams in the optical regime, and occasionally in the microwave regime, that is, cases in which the aperture from which the beam emerges is very large with respect to the wavelength.
Beam diameter usually refers to a beam of circular cross section, but not necessarily so. A beam may, for example, have an elliptical cross section, in which case the orientation of the beam diameter must be specified, for example with respect to the major or minor axis of the elliptical cross section. The term "beam width" may be preferred in applications where the beam does not have circular symmetry.
The angle between the maximum peak of radiated power and the first null (no power radiated in this direction) is called the Rayleigh beamwidth.
The simplest way to define the width of a beam is to choose two diametrically opposite points at which the irradiance is a specified fraction of the beam's peak irradiance, and take the distance between them as a measure of the beam's width. An obvious choice for this fraction is ½ (−3 dB), in which case the diameter obtained is the full width of the beam at half its maximum intensity (FWHM). This is also called the half-power beam width (HPBW).
The 1/e2 width is equal to the distance between the two points on the marginal distribution that are 1/e2 = 0.135 times the maximum value. In many cases, it makes more sense to take the distance between points where the intensity falls to 1/e2 = 0.135 times the maximum value. If there are more than two points that are 1/e2 times the maximum value, then the two points closest to the maximum are chosen. The 1/e2 width is important in the mathematics of Gaussian beams, in which the intensity profile is described by .
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