By taking the vectorial property of the (time average) energy flow density into account, the first and the second intensity moments of the nonparaxial vector beams are defined. The parabolic propagation law of the second intensity moment in free space is deduced by employing the Maxwell's equations. And then, as an extension of the M2 factor of the paraxial scalar beams, the M2 factor of the nonparaxial vector beams is introduced. In the condition that the beam width is greater than a few wavelength, the relation M2 greater than 1 is proven by using the Schwarz inequality. Finally, the intensity moment theory is generalized for the propagation of general polychromatic and nonparaxial pulsed vector beams in free space except that the M2 factor of the static beams is replaced by the characterization width Wc which is defined as the product of the minimum beam width in the near field and the divergence in the far field.
"M2 factor of nonparaxial vector beams", Proc. SPIE 2870, Third International Workshop on Laser Beam and Optics Characterization, (20 November 1996); doi: 10.1117/12.259903; https://doi.org/10.1117/12.259903