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.

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. 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.

Square (algebra)

In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 3², which is the number 9. In some cases when superscripts are not available, as for instance in programming languages or plain text files, the notations x^2 or x**2 may be used in place of x².

The adjective which corresponds to squaring is quadratic.

The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial x + 1 is the quadratic polynomial x² + 2x + 1.

One of the important properties of squaring, for numbers as well as in many other mathematical systems, is that (for all numbers x), the square of x is the same as the square of its additive inverse −x. That is, the square function satisfies the identity x² = (−x)². This can also be expressed by saying that the squaring function is an even function.

22squared

22squared is the 4th largest independent advertising agency in the United States. Its headquarters are located in Atlanta, Georgia with a second office in Tampa, Florida. The agency has several long-standing Fortune 500 clients as well as a collection of travel, retail, casual dining and financial services clients.

History

The original agency (Tucker Wayne) was founded in Atlanta in 1922 and has operated under several names during its lifetime. In 1996, Tucker Wayne merged with The West Group of Tampa, FL and formed WestWayne. Then in the summer of 2007, the agency rebranded as 22squared. Though the agency has operated under several names over its 90-year history, it has always been independent, with continuous operation under current senior management ownership. The agency is independent and privately held.

Clients

Jim'll Paint It

Jim'll Paint It is an internet blog featured on Tumblr and other social networking sites, started on 21 February 2013 by James Murray. The blog consists of mostly humorous and surreal artwork painted by Murray using only Microsoft Paint, by request from Tumblr users. Murray has produced over 100 paintings since 2013. The first piece featured dinosaurs painting people in an art class. The title is an allusion to the BBC TV series Jim'll Fix It.

James Murray

James Murray is a speed painter from Bristol, England. The only tools he uses for his works are Paint XP and an optical mouse. In October 2014, Murray published a book on his works, with 17 paintings made especially for the book. In February 2015, he began a new blog called 30squared.

See also

References

Further reading

James Murray, Electric Dreams: The Collected Works of Jim'll Paint It (2014)

External links