Beam divergence

The beam divergence of an electromagnetic beam is an angular measure of the increase in beam diameter or radius with distance from the optical aperture or antenna aperture from which the electromagnetic beam emerges. The term is relevant only in the "far field", away from any focus of the beam. Practically speaking, however, the far field can commence physically close to the radiating aperture, depending on aperture diameter and the operating wavelength.

Beam divergence is often used to characterize electromagnetic beams in the optical regime, for cases in which the aperture from which the beam emerges is very large with respect to the wavelength. However, it is also used in the Radio Frequency (RF) regime for cases in which the antenna is operating in the so-called optical region and is likewise very large relative to a wavelength.

Beam divergence 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 divergence must be specified, for example with respect to the major or minor axis of the elliptical cross section.

The divergence of a beam can be calculated if one knows the beam diameter at two separate points far from any focus (D_i, D_f), and the distance (l) between these points. The beam divergence, ${\displaystyle \Theta }$, is given by

If a collimated beam is focused with a lens, the diameter ${\displaystyle D_{m}}$ of the beam in the rear focal plane of the lens is related to the divergence of the initial beam by

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