M²quality factor as a key to mastering laser beam propagation

Abstract

One of the most important properties of a laser resonator is the highly collimated or spatially coherent nature of the laser output beam. The spatial beam quality of the output beam, namely beam diameter and propagation factor M² are critical parameters in a wide range of practical laser applications. This is because the spatial beam quality determines how tightly the beam can be focused or how well the beam propagates over long distances without significant spreading. It was investigated by many authors in previous years how to define and on how to measure the laser beam quality. An ISO working Draft Committee has also been organized to set-up a standard for definitions and test methods of the laser beam quality. In this work, the quality factor is studied with different methods.

Ultrashort highly localized wavepackets

“…To indicate the structure of a ringshaped light bullet, the iso-electric-field surface of 6.8-fs pulses was retrieved from spatially resolved second-order autocorrelation. For visualization purposes, a DC-field (corresponding to the maximum field amplitude) was added[64] (red circles: field maxima, d = maximum-tomaximum ring diameter, ∆τcycle = field oscillation period in time). #164986 -$15.00 USD Received 19 Mar 2012; revised 4 May 2012; accepted 4 May 2012; published 18 May 2012 (C) 2012 OSA 21 May 2012 / Vol.…”

Beam qualityM2factor matrix for non-circular symmetric laser beams

“…It can be seen from equation ( 8) that the cross terms, M xy and M yx , and the values M x 2 and M y 2 , contain the angle information between the beam principal axis and the LCS. Moreover, once the M 2 factor matrix is determined, the M 2 factor values, M xo 2 and M yo 2 , along with the principal axis x′ and y′ also can be determined uniquely. Hence, the M 2 factor matrix can fully describe the beam quality for a non-circular symmetric beams with a 2 × 2 matrix.…”

“…Thus, a reliable method for quantifying beam quality is necessary. Among various laser beam evaluation measurements, the beam propagation ratio, simply known as the M 2 factor, is one of the most widely used and accepted in the laser community [1][2][3]. The M 2 factor is defined as the ratio of the beam parameter product of an actual beam to that of an ideal Gaussian beam at the same wavelength.…”

Measurement of M2-Curve for Asymmetric Beams by Self-Referencing Interferometer Wavefront Sensor

“…Now ISO published the latest version of M 2 factor measurement Standard ISO11146-1/2/3 [4,5,6], which standardized laser beam characterization by defining all relevant quantities of laser beams including in measurement method instructions. Now M 2 factor undoubtedly becomes an acceptable characterization parameter for beam quality characterization in the laser community [7,8,9,10,11,12,13,14]. …”