M squared
Encyclopedia
In laser science
, the parameter M² is the ratio of the beam parameter product
(BPP) of an actual beam to that of an ideal Gaussian beam
at the same wavelength
. It is often referred to as the beam quality factor, since its value can be used to quantify the degree of variation the actual beam is from such an ideal beam. 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. As well, a beam 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 M² value is an important measure of beam quality. It is widely used in the laser industry as a specification, and its method of measurement is "regulated" as an ISO Standard. It is especially useful for determining the degree of beam divergence
of real laser beams and the minimum focussed spot size.
The value of M² can be determined by measuring D4σ or "second moment" width
. Unlike the beam parameter product, M² is unitless and has no variance with wavelength.
Laser science
Laser science or laser physics is a branch of optics that describes the theory and practice of lasers.Laser science is principally concerned with quantum electronics, laser construction, optical cavity design, the physics of producing a population inversion in laser media, and the temporal...
, the parameter M² is the ratio of the beam parameter product
Beam parameter product
In laser science, the beam parameter product is the product of a laser beam's divergence angle and the radius of the beam at its narrowest point . The BPP quantifies the quality of a laser beam, and how well it can be focused to a small spot.A Gaussian beam has the lowest possible BPP,...
(BPP) of an actual beam to that of an ideal Gaussian beam
Gaussian beam
In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity distributions are well approximated by Gaussian functions. Many lasers emit beams that approximate a Gaussian profile, in which case the laser is said to be operating on the fundamental...
at the same wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
. It is often referred to as the beam quality factor, since its value can be used to quantify the degree of variation the actual beam is from such an ideal beam. 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. As well, a beam can appear very "un-Gaussian", yet have an M² value close to unity. For a single mode
Transverse mode
A transverse mode of a beam of electromagnetic radiation is a particular electromagnetic field pattern of radiation measured in a plane perpendicular to the propagation direction of the beam...
TEM00 Gaussian Laser beam, M² is exactly one.
The M² value is an important measure of beam quality. It is widely used in the laser industry as a specification, and its method of measurement is "regulated" as an ISO Standard. It is especially useful for determining the degree of beam divergence
Beam divergence
The beam divergence of an electromagnetic beam is an angular measure of the increase in beam diameter or radius with distance from the optical aperture or antenna aperture from which the electromagnetic beam emerges. The term is relevant only in the "far field", away from any focus of the beam...
of real laser beams and the minimum focussed spot size.
The value of M² can be determined by measuring D4σ or "second moment" width
Beam diameter
The beam diameter or beam width of an electromagnetic beam is the diameter along any specified line that is perpendicular to the beam axis and intersects it. Since beams typically do not have sharp edges, the diameter can be defined in many different ways. Five definitions of the beam width are in...
. Unlike the beam parameter product, M² is unitless and has no variance with wavelength.