Problems with power content beam parameter product

The M2 beam propagation factor is widely used to characterize the quality of laser radiation and its propagation. When M2 is defined by the second-moments, M2 ⩾ 1 holds in the paraxial approach. For many applications it is more convenient to use the power content values (normally η = 86.5%), also proposed by ISO. For the corresponding power content Mpc2 factor, it is often assumed that Mpc2⩾1 also holds. We have demonstrated previously that for a superposition of two coherent Gauss–Laguerre modes with radial symmetry, the 86.5% value of Mpc2<1[6]. In recent years, Mpc2<1 has also been presented experimentally for a superposition of axially shifted Gaussian beams [7]. The problems with power content Mpc2 for axial superposition of Gaussian beams are discussed. In this paper it is shown that the 86.5% power content Mpc2 value can not be smaller than one for a coherent superposition of axially shifted Gaussian beams with radial symmetry presented in Ref. [7]. A superposition of two Gaussian beams with different waists and without shift is also discussed, and the corresponding Mpc2 of such beam can be smaller than one, depending strongly on the power content value η. For low power content values η   and a large (or very small) ratio of the two different waists Mpc2 approaches zero. These investigations demonstrate that Mpc2 is not a suitable parameter to characterize laser radiation.