M squared
In laser science, the parameter M², also known as the beam quality factor, is a quantity that represents the degree of variation of a beam from an ideal Gaussian beam at the same wavelength. It is calculated from the ratio of the beam parameter product (BPP) of the beam to the BPP of a Gaussian beam.
Contents
Comparison to Gaussian beams
M² is a better guide to beam quality than Gaussian appearance, however, since there are many cases in which the beam can look Gaussian, yet have an M² value far from unity.[1] Likewise, a beam intensity profile can appear very "un-Gaussian", yet have an M² value close to unity. For a single mode TEM00 Gaussian laser beam, M² is exactly one.
The value of M² can be determined by measuring D4σ or "second moment" width. Unlike the beam parameter product, M² is unitless and does not vary with wavelength.
Multi-mode beam propagation
Real laser beams are often non-Gaussian, being multi-mode or mixed-mode. Multi-mode beam propagation is often modeled by considering a so-called "embedded" Gaussian, whose beam waist is M times smaller than that of the multimode beam. The diameter of the multimode beam is then M times that of the embedded Gaussian beam everywhere, and the divergence is M times greater, but the wavefront curvature is the same. The multimode beam has M² times the beam area but 1/M² less beam intensity than the embedded beam. This holds true for any given optical system, and thus the minimum (focussed) spot size or beam waist of a multi-mode laser beam is M times the embedded Gaussian beam waist.
Applications
The quality of a beam is important for many applications. In fiber-optic communications beams with an M2 close to 1 are required for coupling to single-mode optical fiber. Laser machine shops care a lot about the M2 parameter of their lasers because the beams will focus to an area that is M2 times larger than that of a Gaussian beam with the same wavelength; in other words, the fluence scales as 1/M2. The general rule of thumb is that M2 increases as the laser power increases. It is difficult to obtain excellent beam quality and high average power (100 W to kWs) due to thermal lensing in the laser gain medium.
The M² value for a laser beam is widely used in the laser industry as a specification, and its method of measurement is "regulated" as an ISO Standard.[2] It is especially useful for determining the degree of beam divergence of real laser beams and the minimum focussed spot size.
See also
References
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