What is M Squared? See What Determines the Size of Your Beam Waist

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Use the focal spot size calculator calculator to see how M-Squared affects the size of the beam waist.

What is M² ?

M² or Beam Propagation Ratio, is a value that indicates how close a laser is to being a single mode TEM00 beam, which in turn determines how small a beam waist can be focused. For the perfect Gaussian TEM00 condition the M² equals 1.

For a laser beam propagating through space, the equation for the divergence θ0 of an unfocused beam is given by:

beam waist - What is M2?
Figure 1 - Characteristics of a laser beam as it passes through a focusing lens

θ0= M²4λ/ΠD0     (D0 is the waist diameter of the laser beam)
For a pure Gaussian TEM00 beam M² equals 1, and thus has no impact on the calculation. The calculation of the minimal beam spot after the lens is then:
d0 = 4λ/πθ     (θ is the beam divergence after the lens)

Again with M² equal to 1, the focused spot is diffraction limited. For real beams, M² will be greater than 1, and thus the minimum beam waist will be larger by the M² factor.

How is M² measured?
M² cannot be determined from a single beam profile measurement. The ISO/DIS 11146 requires that M² be calculated from a series of measurements as shown in figure 1. 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 artificially created beam waist and divergence.

To provide an accurate calculation of M², it is essential to make at least 5 measurements in the focused beam waist region, and at least 5 measurements in the far field, two Rayleigh ranges away from the waist area. The multiple measurements ensure that the minimum beam width is found. In addition, the multiple measurements enable a "curve fit" that improves the accuracy of the calculation by minimizing measurement error at any single point. An accurate calculation of M² is made by using the data from the multiple beam width measurements at known distances from a lens, coupled with the known characteristics of the focusing lens.

M² Measurement Solutions
Ophir-Spiricon have a number of solutions for the measurement of M² ranging from simple manual processes to fully automated dedicated instruments, depending on the frequency of the need to measure M² of lasers and laser systems. We have a system that will meet most needs, whether for research and development of new laser systems, manufacturing quality assurance, or maintenance and service of existing systems.

beam waist - What is M2?
Figure 2 - focusing laser beam

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