  We present a unified and extended perspective of Bessel beams, irrespective
to their orbital angular momentum (OAM) -- zero, integer or noninteger -- and
mode -- scalar or vectorial, and LSE/LSM or TE/TM in the latter case. The
unification is based on the integral superposition of constituent waves along
the angular-spectrum cone of the beam, and allows to describe, compute, relate,
and implement all the Bessel beams, and even other types of beams, in a
universal fashion. The paper first establishes the integral superposition
theory. Then, it demonstrates the previously unreported existence of
noninteger-OAM TE/TM Bessel beams, compares the LSE/LSM and TE/TM modes, and
establishes useful mathematical relations between them. It also provides an
original description of the position of the noninteger-OAM singularity in terms
of the initial phase of the constituent waves. Finally, it introduces a general
technique to generate Bessel beams by an adequate superposition of properly
tuned sources. This global perspective and theoretical extension may open up
new avenues in applications such as spectroscopy, microscopy, and
optical/quantum force manipulations.
