  We present a systematic treatment of higher-order modes of vacuum-clad
ultrathin optical fibers. We show that, for a given fiber, the higher-order
modes have larger penetration lengths, larger effective mode radii, and larger
fractional powers outside the fiber than the fundamental mode. We calculate,
both analytically and numerically, the Poynting vector, propagating power,
energy, angular momentum, and helicity (or chirality) of the guided light. The
axial and azimuthal components of the Poynting vector can be negative with
respect to the direction of propagation and the direction of phase circulation,
respectively, depending on the position, the mode type, and the fiber
parameters. The orbital and spin parts of the Poynting vector may also have
opposite signs in some regions of space. We show that the angular momentum per
photon decreases with increasing fiber radius and increases with increasing
azimuthal mode order. The orbital part of angular momentum of guided light
depends not only on the phase gradient but also on the field polarization, and
is positive with respect to the direction of the phase circulation axis.
Meanwhile, depending on the mode type, the spin and surface parts of angular
momentum and the helicity of the field can be negative with respect to the
direction of the phase circulation axis.
