What is M2 ? Recently, there has been an increasing emphasis on the use of the term M2 to indicate the quality of a laser s beam. Lee Laser tries to explain M2. M2 is a number, without dimension, that indicates the beam quality or the focusability of a laser beam. By definition, the value of M2 for the most ideal laser beam in the single transverse electro-magnetic mode, TEMoo, is 1.0. This is the definition of a diffraction-limited beam. A laser beam with an M2 value that is larger than 1.0 is said to be that value times the diffraction limit (i.e., a beam with M2 = 3.0 is 3.0 times the diffraction limit or 3.0 times diffraction limited). How is M2 Calculated ? The M2 value of a laser may be calculated by using the expression: M2 = D /4 where: D = diameter of a laser beam at the beam waist of the laser, in mm (for most Lee Laser products, this is at the output mirror of the laser) = far-field, full-angle divergence of the beam, in mr = wavelength of the beam, in m 1. For a Nd:YAG laser at 1064-nm (1.064- m) wavelength: M2 = 0.738D An ideal TEMoo-mode (M2 = 1.0) Nd:YAG laser at 1064 nm has diameter-divergence product: D = 1.355 2. For a Nd:YAG laser at 532-nm (0.532- m) wavelength: M2 = 1.476D An ideal TEMoo-mode Nd:YAG laser at 532 nm has diameter-divergence product: D = 0.677 2 It should be remembered that the M2 value of 1.0 for a laser is the ideal, theoretical limit. No actual laser meets this theoretical limit. Only the most sophisticated scientific lasers even approach the theoretical limit of 1.0 for M2. Why does Lee Laser not use M2 ? Lee Laser prefers not to use the value of M2 to indicate the beam quality of our laser products. M2 cannot be measured; it is a value that is calculated from other parameters that are measured. As a practical matter, it is much more difficult to use the value of M2 to determine the focus potential of a laser, or the focus spot diameter when a laser is used with a particular set of beam delivery optics: s = 4(M2) f/ D where s = diameter of the beam focus spot, in m f = focal length of the focusing lens, in mm Rather, Lee Laser prefers simply to use the values of beam diameter, D, and beam divergence, , that we publish in our specifications data sheets. With these values, the diameter of a beam focus spot may be calculated simply by the expressions: 1. Focus Spot Potential of a Laser s = FD where F = the F# of the focus lens (in this case, a beam expander must be adjusted to so that the beam completely fills the input clear aperture of the focus lens) or 2. Focus Spot Diameter (when a laser is used with a particular set of beam delivery optics) s=f 1 where 1 = full-angle divergence of the beam as it enters the focus lens (will be different from if a beam expander is used), in mr 3 M2 and Lee Laser Specifications Data Sheets Specifications data sheets for Lee Laser products do not state the M2 values of the lasers. Rather, we state the beam diameter and full-angle beam divergence values that a laser typically exhibits. This information is much more useful to our customers that must calculate the beam focus capability of a laser. This calculation from the M2 value is much more difficult. Furthermore, the value of beam waist diameter of a laser that is needed to calculate M2 is not the same as the value of beam diameter that Lee Laser states in our data sheet: 1. Beam Diameter for Data Sheet: Actual measured value about 10 inches (25 mm) from the output end of the laser. 2. Beam Diameter for M2 Calculation: This is the beam waist diameter which is located at the reflective surface of the laser output coupler. Because access is not possible to measure this dimension, it must be calculated from beam diameter measurements that are taken at different distances from the output end of the laser. Clearly, Lee Laser s published value for laser beam diameter cannot be used as the beam waist value to calculate M2. The Benefit of Using M2 What is the benefit of using the M2 value of a laser ? Within the laser industry, there exists some disagreement about the meaning of beam divergence and beam size. Some companies list in their data sheets only the half angle for beam divergence, and list only the beam radius for beam size. Therefore, the mm-mr product that is used by many laser manufacturers does not clearly define the performance of a laser, and for two identical lasers it can differ by as much as a factor of 4. However, the expression of M2 as defined above is universally recognized within the laser industry. Therefore, M2 can be a valuable tool when comparing the performance of two lasers that are manufactured by different companies, or even of two lasers by the same company.