  We study the cross-sectional profiles and spatial distributions of the fields
in guided normal modes of two coupled parallel optical nanofibers. We show that
the distributions of the components of the field in a guided normal mode of two
identical nanofibers are either symmetric or antisymmetric with respect to the
radial principal axis and the tangential principal axis in the cross-sectional
plane of the fibers. The symmetry of the magnetic field components with respect
to the principal axes is opposite to that of the electric field components. We
show that, in the case of even $\mathcal{E}_z$-cosine modes, the electric
intensity distribution is dominant in the area between the fibers, with a
saddle point at the two-fiber center. Meanwhile, in the case of odd
$\mathcal{E}_z$-sine modes, the electric intensity distribution at the
two-fiber center attains a local minimum of exactly zero. We find that the
differences between the results of the coupled mode theory and the exact mode
theory are large when the fiber separation distance is small and either the
fiber radius is small or the light wavelength is large. We show that, in the
case where the two nanofibers are not identical, the intensity distribution is
symmetric about the radial principal axis and asymmetric about the tangential
principal axis.
