Beams of a high angle of convergence and divergence are called high-apertur
e beams. Different ways of defining high-aperture generalizations to paraxi
al beams are reviewed for both scalar beams and electromagnetic beams. The
different approaches are divided into three types. The particular examples
of Gaussian beams and Bessel beams are discussed. For Gaussian beams, beams
that exhibit a Gaussian variation in the waist necessarily include evanesc
ent components, which rules out their use in describing propagation over al
l space. Generalizations of the definitions of beam width and the beam-prop
agation factor M-2 for high-aperture beams are described. The similarities
among the three types of high-aperture beams and the different models of ul
trashort-pulsed beams are discussed. (C) 2001 Optical Society of America.