Influences on the beam propagation ratio M

A beam is described by its transverse power density distribution, its wavefront, and its transverse distribution of coherence. The beam propagation ratio, M², is expressed as the square root of the sum of each of the three beam attributes. The shape of the power density distribution governs the diffraction of the beam. The stronger it is modulated, the higher the M². In comparison to an non-aberrated beam, the M² of a beam with an aberrated wavefront is increased. Similarly, the M² of a partially coherent beam is higher than the one of a fully coherent one. A concise formula is derived. The components of M² of a mixture of Hermite–Gaussian beams and of a spherically aberrated Gaussian beam are given as examples.