 # How to calculate the diameter of a laser beam?

Nov 09, 2020

The beam diameter is defined as the distance between the points opposite to the diameter of the beam diameter surface, where the power per unit area of the beam is 1/e (0.368) times the displacement power per unit area. This is the definition of the beam diameter and is used to calculate the maximum allowable exposure of the laser beam.

The beam diameter is actually about the beam waist diameter or beam waist radius of the spot. Beam waist refers to the place where Gaussian light propagates in absolute parallel. The radius refers to the cross-section of Gaussian light. When the maximum amplitude is taken as the origin, the amplitude drops to 0.36788 times of the origin, that is, 1/e times. Because the Gaussian light is symmetrical about the origin, a circle is formed at 1/e, and the radius of the circle is the radius of the spot in this cross-section; if the cross-section at the beam waist is taken for investigation, the radius at this time is half of the beam waist diameter. Along with the spot, the envelope of the radius is a hyperboloid with an asymptote.

The propagation characteristic of the Gaussian beam is that it diffuses at a specific angle along the propagation direction in the distance. This angle is the far-field divergence angle of the beam, that is, the angle between a pair of asymptotes. It is proportional to the wavelength and inversely proportional to the beam waist radius. Therefore, the smaller the beam waist radius is, the faster the spot divergence is; the larger the beam waist radius, the slower the spot divergence.

High-power continuous lasers are increasingly finding applications in the field of material processing. Now, it’s worth noting that in all these applications, understanding the effective laser beam diameter is crucial. Because the knowledge of the effective beam diameter is as important as or more important than the knowledge of the total laser power.

In fact, it can be inferred that the definition of beam diameter defines a perfect basic TEM00 mode structure for a stable cavity laser, that is, the beam has a Gaussian power distribution. It can be seen that the beam diameter is defined as the diameter when the power drops to the center value (1/e2). The previous measurement method has such distribution and perfect optics, it is possible to calculate the beam diameter from a given laser cavity after passing through a lens with a known focal length.

By convention, the use of optical diameter is wrong. The actual beam diameter will be larger than the beam diameter calculated by diffraction theory, because the finite size optics used will be truncated, and a perfect Gaussian incident mode may not appear.

Then for the Gaussian beam, the isothermal technique is used to measure the error of the spherical aberration of the beam diameter at the lens (especially for the case of F-number<7). At the minimum spot size, the difference maybe 2 or more, which is critical in terms of material processing. Many methods for measuring beam diameter have been proposed. The techniques can be divided into two groups, namely single isotherm, and multiple isotherm profiles.

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