Propagation of nanofiber-guided light through an array of atoms

TL;DR

This paper investigates how nanofiber-guided light propagates through an atomic cesium array, deriving equations for scattering and reflection, and revealing effects like polarization dependence, Bragg resonance, and band gap formation.

Contribution

It provides a detailed theoretical framework for light propagation in atom arrays coupled to nanofibers, including new insights into polarization effects and band gap formation.

Findings

Backward scattering is weak away from Bragg resonance.

Most guided light is reflected at Bragg resonance despite decay channels.

Two polarization-dependent band gaps can form in large atom arrays.

Abstract

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.