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Anisotropy in scattering of light from an atom into the guided modes of a nanofiber

We study the scattering of guided light from a multilevel cesium atom with the transitions between the hyperfine levels $6S_{1/2}F=4$ and $6P_{3/2}F'=5$ of the $D_2$ line into the guided modes of a nanofiber. We show that the rate of scattering of guided light from the atom in the steady-state regime into the guided modes is asymmetric with respect to the forward and backward directions and depends on the polarization of the probe field. The asymmetry between the forward and backward scattering is a result of the complex transition structure of the atom and the existence of a longitudinal component of the guided-mode profile function. In the case of a two-level atom, the rates of spontaneous emission (and consequently the rates of scattering) into the forward and backward guided modes differ from each other when the atomic dipole matrix-element vector is a complex vector in the plane that contains the fiber axis and the atomic position.