Application Note, AN-3

M2, What Is It And Why Do I Care?

I. Introduction
Most laser engineers and scientists are familiar with beam width, position, divergence angle, Gaussian fit, and such parameters for characterizing a laser beam. M2 enables a user to quantitatively evaluate the focusability of the laser beam. It is a measure of how close an actual beam is to a perfect Gaussian single mode beam and is very easy to use in predicting the focused spot properties.

II. Why Is M2 Important?

Typically, when laser modes other than the fundamental Gaussian are present, the beam does not focus as sharply. For example, when focusing a beam through an ideal lens of a given focal length, the expected waist size, or focal spot size, is predictable by Equation 1:

d0 = 4lambdafM/piDin (1)

where d0 = the focused spot width, lambda = wavelength, f = focal length of the lens, M2 is the laser "times diffraction limit", and Din = the width of the multimode beam. This is shown in Figure 1. When the beam contains modes other than the fundamental Gaussian, the spot size is M times larger than would otherwise be obtained. The intensity density at the beam waist becomes lower than expected. Also, the divergence angle of the beam in the far field becomes large 

theta= M small theta, where large theta = the real divergence angle, and small theta = divergence angle of the fundamental mode. Thus the intensity density is M2 less than otherwise at all points in the beam.

III. How Does M2 Affect A Particular Application?
The laser is focused to a small spot in industrial, cutting and welding, and scientific applications wherein the high intensity light interacts with matter. In industrial cutting applications, the holes may be M2 larger than desired, and may not penetrate as deeply as would be the case with a pure beam. In scientific applications, the experiment often depends upon the intensity squared or cubed, which would create an error of M4 or M6 in the expected results. An M2 of 1.5 could create an error greater than 3.37 X, or 237%.

Once M2 is measured, a person is able to predict what the beam will do if the focal length of the lens is changed. One can scale the effect and predict the change in the focused spot size and intensity by Equation 1.

IV. How Is M2 Measured?
In an ISO committee proposal M2 is measured on real beams by focusing the beam with a lens of known focal length, and then making multiple position measurements on the artificially created beam waist and divergence. These measurements are then projected back to the laser properties through equations that take into account the focusing lens. Spiricon has built an instrument, the M2-101, that automates this multiple measurement process.

One of the greatest errors in measuring M2 comes from measurements of the beam widths. Spiricon's LBA-100A beam analyzer uses a preferred "Knife-Edge" technique on data taken from a CCD camera. This method requires, however, that the "background" or "baseline" of the CCD camera be adjusted correctly to obtain accurate measurements. Spiricon's LBA-100A uses a very sophisticated (patent pending) "Autocalibrate" method to ensure that background errors do not contribute to beam width measurement errors.

Using a CCD camera allows simultaneous measurements of the entire beam which enables characterization of M2 on both CW and pulsed lasers.

V. What Else Do I Need Besides M2?
Spiricon does not stop at just the measurement of M2 and related properties. In addition, a user can view each individual measured frame through the waist and into the far field. This feature allows the user to "see" exactly what his beam is doing as it goes through focus. A visual view of the beam can tell a user more than the single M2 quantitative number. This is demonstrated for a diode laser, in Figure 2. It shows how the X axis is focusing more rapidly than the Y axis and that the beam shape is changing dramatically through focus. The visual displays from the M2 -101 and LBA-100A tells what the beam looks like in the "real world" conditions, but scaled in size by the actual focal length of the lens used.
For a more detailed explanation, please ask for Spiricon's 6 page M2 Application Note, AN-3

Focus minus 20mm

Focus minus 10mm

Focus

Focus plus 10mm

Focus plus 20mm

Beam profiles of a laser diode through focus. The M2-101 and LBA-100A not only give M2 but also enable complete 2D and 3D beam profile display and analysis through the critical beam waist region, and in the far field.