BEAM-PROPAGATION FACTOR OF DIFFRACTED LASER-BEAMS

The recent emergence of the characterization of general optical beams by means of the variance of their transverse intensity distribution has given rise to the concept of the beam propagation factor (usually referred to as the beam quality factor), which appears as a meaningful way for comparing the divergences of optical beams having the same minimum spot size. Unfortunately, a direct calculation of this factor for a beam having sharp discontinuities in its transverse intensity profile leads to an infinite result. This difficulty is addressed by deriving a general expression for the axial dependence of the variance of the beam's transverse intensity profile in free space. A new definition for the beam propagation factor can be introduced, provided that the evanescent waves of the plane-wave spectrum of the beam are ignored. This modified beam propagation factor is then calculated for some specific diffracted intensity profiles. Finally, it is shown how the proposed definition for the variance of the plane-wave spectrum of an optical beam is connected to its far-field angular spread.