User:Lasermeasurement/Laser Beam Quality

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Laser Beam Quality new article content ... The Laser beam quality is measured by M², which is a value indicating how close a laser is to being a TEM00 single mode beam. This also indicates how small a laser can be focused.

Contents: 1. M² definitions 2. M² measurement 3. References M² Definitions The equation for the divergence, of a pure Gaussian TEM00 unfocused beam propagating through space is given by θ00 = 4λ / π D00 (1)

Where D00 is the beam waist size, and λ is the wavelength. Higher mode beams often start with a larger beam waist, D0, and/or have a faster divergence θ0. In this case Equation (1) becomes θ0 = M² 4λ / π D0 (2) Where θ0 and D0 are the divergence and waist of a higher mode beam and M2 is greater than 1 and is named the "Beam Propagation Ratio" per ISO 11146 standard. When a Gaussian laser beam is focused, the focused spot diameter is defined by: d00 = 4 λ f / π D00 (3) Where d00 is the ideal focused spot diameter, f is the focal length of the focusing lens, and D00 is the input beam waist and is placed one focal length from the lens as shown in the figure. However, when a multimode beam is focused, Equation (3) becomes: d00 = M^{2</sup? 4 λ f / π D0 (4)}

M² measurement M² cannot be determined from a single beam profile measurement. The ISO/DIS 11146 1 define that M² should be calculated from a series of measurements as shown in the figure below. M² is measured on real beams by focusing the beam with a fixed position lens of known focal length, and then measuring the characteristics of the beam waist and divergence.

The multiple measurements ensure that the minimum beam diameter is found and enable a "curve fit" that improves the accuracy of the calculation by minimizing measurement error.

M² can be measured by commercial instruments such as ^[1]