  We study the propagation of nanofiber-guided light through an array of atomic
cesium, taking into account the transitions between the hyperfine levels
$6S_{1/2}F=4$ and $6P_{3/2}F'=5$ of the $D_2$ line. We derive the coupled-mode
propagation equation, the input-output equation, the scattering matrix, the
transfer matrix, and the reflection and transmission coefficients for the
guided field in the linear, quasistationary, weak-excitation regime. We show
that, when the initial distribution of populations of atomic ground-state
sublevels is flat, the quasilinear polarizations along the principal axes $x$
and $y$, which are parallel and perpendicular, respectively, to the radial
direction of the atomic position, are not coupled to each other in the linear
coherent scattering process. When the guided probe field is quasilinearly
polarized along the major principal axis $x$, forward and backward scattering
have different characteristics. We find that, when the array period is far from
the Bragg resonance, the backward scattering is weak. Under the Bragg
resonance, most of the guided probe light can be reflected back in a broad
region of field detunings even though there is an irreversible decay channel
into radiation modes. When the atom number is large enough, two different band
gaps may be formed, whose properties depend on the polarization of the guided
probe field.
