| M2, or Beam Propagation Ratio, is a value that indicates how close a laser is to being a single mode TEM00 beam. This in turn relates to
how small a spot a laser can be focused. |
| For a laser beam propagating through space, the equation for the
divergence,θ, of a pure Gaussian TEM00 unfocused beam is given by |
 |
| θ00= 4λ/ΠD00 (1) |
| where D00 is the waist size of the beam, and λ is the wavelength.
Actual beams with additional modes often start with a larger beam
waist, D0, and/or have a faster divergence θ 0. IIn this case Equation
(1) becomes |
| θ 0 = M24λ/ΠD0 (2) |
Characteristics of
a laser beam as it passes through a focusing lens. |
| where θ 0 and D0
are the divergence and width of a higher mode beam and M2
is greater than 1 and is named the "Beam Propagation Ratio" per the ISO 11146 standard. When a pure Gaussian laser beam is
focused, the width of the focused spot is defined by: |
| d00 = 4λ/ΠD00 (3) |
| where d00 is the ideal focused spot
width, f is the focal length of the lens, and D00
is the width of the input beam waist and is placed one focal length from
the lens as shown in the figure (above). However, when a distorted or multimode beam is focused, Equation (3) becomes: |
|
d00 = M24λf/ΠD0
(4) |
| |
| 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 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 artificially created beam waist and divergence. |
| To provide an accurate calculation of M2, it is essential to make more measurements in the focused beam waist region, and a number |
| Tof measurements in both the far fields. 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. |
|
| |
Multiple beam width measurements made by
M2-200 and M2-200s |
What is M2?
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