![Lasers](https://upload.wikimedia.org/wikipedia/commons/4/45/Lasers.jpeg)
In
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 popul ...
, laser beam quality defines aspects of the beam illumination pattern and the merits of a particular
laser beam
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
's propagation and transformation properties (space-bandwidth criterion). By observing and recording the beam pattern, for example, one can infer the
spatial mode
A transverse mode of electromagnetic radiation is a particular electromagnetic field pattern of the radiation in the plane perpendicular (i.e., transverse) to the radiation's propagation direction. Transverse modes occur in radio waves and microwav ...
properties of the beam and whether or not the beam is being clipped by an obstruction; By focusing the laser beam with a
lens
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
and measuring the minimum spot size, the number of times
diffraction limit
The resolution of an optical imaging system a microscope, telescope, or camera can be limited by factors such as imperfections in the lenses or misalignment. However, there is a principal limit to the resolution of any optical system, due to th ...
or focusing quality can be computed.
Anthony E. Siegman
Anthony E. Siegman (November 23, 1931 – October 7, 2011) was an electrical engineer and educator at Stanford University who investigated and taught about masers and lasers. Known to almost all as Tony Siegman, he was president of the Optical S ...
was the first to propose the formalism for a laser beam quality factor that could be measured and used to compare different beams, independent of
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
. The factor is called
beam propagation ratio (M2), and it is closely related to the
beam parameter product In laser science, the beam parameter product (BPP) is the product of a laser beam's divergence angle (half-angle) and the radius of the beam at its narrowest point (the beam waist). The BPP quantifies the quality of a laser beam, and how well it can ...
. While the M
2 factor does not give detail on the spatial characteristics of the beam, it does indicate how close it is to being a fundamental-mode
Gaussian beam
In optics, a Gaussian beam is a beam of electromagnetic radiation with high monochromaticity whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. This ...
. It also determines the smallest spot size for the beam, as well as the
beam divergence
In electromagnetics, especially in optics, beam divergence is an angular measure of the increase in beam diameter or radius with distance from the optical aperture or antenna aperture from which the beam emerges. The term is relevant only in the ...
. M
2 can also give an indication of beam distortions due to, for example, power-induced
thermal lensing
Thermal blooming, also known as thermal lensing, is an atmospheric effect, seen in high energy laser beams; It is the result of the nonlinear interaction of laser radiation with the propagation medium (e.g. air or glass), which is heated by the abs ...
in the
laser gain medium
The active laser medium (also called gain medium or lasing medium) is the source of optical gain within a laser. The gain results from the stimulated emission of photons through electronic or molecular transitions to a lower energy state from a ...
, since it will increase.
There are some limitations to the M
2 parameter as a simple quality metric. It can be difficult to measure accurately, and factors such as background noise can create large errors in M
2.
[ Tutorial presentation at the Optical Society of America Annual Meeting, Long Beach, California] Beams with power well out in the "tails" of the distribution have M
2 much larger than one would expect. In theory, an idealized
tophat laser beam has infinite M
2, although this is not true of any physically realizable tophat beam. For a pure
Bessel beam
A Bessel beam is a wave whose amplitude is described by a Bessel function of the first kind. Electromagnetic, acoustic, gravitational, and matter waves can all be in the form of Bessel beams. A true Bessel beam is non-diffractive. This means ...
, one cannot even compute M
2.
The definition of "quality" also depends on the application. While a high-quality single-mode Gaussian beam (M
2 close to unity) is optimum for many applications, for other applications a uniform multimode
tophat beam In optics, a tophat (or top-hat) beam such as a laser beam or electron beam has a near-uniform fluence (energy density) within a circular disk. It is typically formed by diffractive optical elements from a Gaussian beam. Tophat beams are often used ...
intensity distribution is required. An example is
laser surgery
Laser surgery is a type of surgery that uses a laser (in contrast to using a scalpel) to cut tissue.
Examples include the use of a laser scalpel in otherwise conventional surgery, and soft-tissue laser surgery, in which the laser beam vapori ...
.
Power-in-the-bucket and
Strehl ratio The Strehl ratio is a measure of the quality of optical image formation, originally proposed by Karl Strehl, after whom the term is named. Used variously in situations where optical resolution is compromised due to lens aberrations or due to imagi ...
are two other attempts to define beam quality. Both these methods use a
laser beam profiler
A laser beam profiler captures, displays, and records the spatial intensity profile of a laser beam at a particular plane transverse to the beam propagation path. Since there are many types of lasers — ultraviolet, visible, infrared, continuou ...
to measure how much power is delivered to a given area. There is also no simple conversion between M
2, power-in-the-bucket, and Strehl ratio.
M2 definitions
The
equation
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in ...
for the
divergence
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the ...
of a pure
Gaussian
Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below.
There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...
TEM
00 unfocused beam propagating through space is given by
:
, (1)
where ''D''
00 is the diameter of the
beam waist
In optics, a Gaussian beam is a beam of electromagnetic radiation with high monochromaticity whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. This ...
, and ''λ'' is the wavelength. Higher mode beams often start with a larger beam waist, ''D''
0, and/or have a faster divergence ''Θ''
0. In this case Equation (1) becomes
:
, (2)
where ''Θ''
0 and ''D''
0 are the divergence and waist of a higher mode beam and ''M''
2 is greater than 1 and is named the "Beam Propagation
Ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
" per the ISO 11146 standard. When a Gaussian laser beam is focused, the focused spot
diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for ...
is defined by
:
, (3)
where ''d''
00 is the ideal focused spot diameter, ''f'' is the
focal length
The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative foca ...
of the focusing lens, and ''D''
00 is the input beam waist and is placed one focal length from the lens as shown in the figure. However, when a
multimode beam is focused, Equation (3) becomes
:
. (4)
M2 measurement
M
2 cannot be determined from a single beam profile measurement. The ISO/DIS 11146 define that M
2 should be calculated from a series of measurements as shown in the figure below. M
2 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 beam waist and divergence. These measurements can be taken with a
laser beam profiler
A laser beam profiler captures, displays, and records the spatial intensity profile of a laser beam at a particular plane transverse to the beam propagation path. Since there are many types of lasers — ultraviolet, visible, infrared, continuou ...
.
[G. Langer et al., A webcam in Bayer-mode as a light beam profiler for the near infra-red, Optics and Lasers in Engineering 51 (2013) 571–575]
![Focusinglens](https://upload.wikimedia.org/wikipedia/commons/7/7f/Focusinglens.gif)
The multiple measurements ensure that the minimum beam diameter is found and enable a "curve fit" that improves the accuracy of the calculation by minimizing measurement error.
References
{{Reflist
Beam quality