Degeneracy and regeneracy in the axial field of a focused truncated Gaussian beam

An investigation is made of the variations in the Fresnel diffraction along the axis of a Gaussian beam that is focused by a lens-and-aperture system. The general features of these variations can be described by two processes that function in opposite directions: one is the merger (or the cancellation) of the intensity maxima and their adjacent minima and the other is the recurrence of these extreme points in the axial intensities. In low-Fresnel-number focusing systems, these two processes advance alternately as the influence of the truncation of the beam by the aperture decreases. In the operation of these processes, the oscillations and rapid transitions of the focal shift can be observed, and also a discontinuous development occurs in the axial field that transforms it from a highly fluctuating distribution into a smoother one, as predicted by the theory of focusing of a nontruncated Gaussian beam.