The exact explicit solution of the Maxwell equations for nonparaxial singul
ar beams propagating in free space or in a homogeneous isotropic medium is
considered. It is shown that, in the paraxial approximation, such solutions
for mode beams of both lower and higher orders may turn into the solutions
for guided modes or vortices of optical fibers. It is found that a variati
on of the Rayleigh length for a mode beam does not change the structure of
phase and polarization singularities; it merely transforms their coordinate
s. In the paraxial limit, the singularities are shifted off the axis to reg
ions with negligible light fluxes. (C) 2001 MAIK "Nauka/ Interperiodica".