Question

A laser operating at 3x10¹⁴ Hz passes through an aperture of 10–²m . The angular spread in radians will be what?

Answer 1

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LASER BEAM DIVERGENCE
By John Lester Miller
From Photonics Rules of Thumb: Optics, Electro-Optics, Fiber Optics, and Lasers, Second Edition
LASER BEAM DIVERGENCE
A laser beam's full divergence angle is approximately the wavelength divided by the diameter of the transmitter aperture, or


where

?

= transmitter beam width (full angle) in radians

?

= wavelength

d

= aperture diameter in the same units as the wavelength

Discussion
This is a basic result drawn from diffraction theory and does not include any of the additional aberrations that occur in real systems. However, this rule is widely used to estimate the size of a laser beam that has propagated through a vacuum and is also frequently used as a first estimate even in atmospheric applications. The rule works fine in environments in which scattering is small as compared with absorption, because, in those cases, the beam shape is not affected.

This rule provides quick estimations of minimum beam divergence. A more accurate presentation is provided below.

In the far field, the full beam width of a Gaussian beam can be approximated by


where ? o = Gaussian beam waist radius in meters

This definition of beam width is based on the location of the 1/ e points in the beam. This is one of several common ways that beam spread is defined for Gaussian laser beams. Siegman describes several, including the more conservative 99 percent criterion in which the size of the beam is defined as the area that includes 99 percent of the energy in the beam. The reader will find that this definition of beam size...