Solitons in a Chiral Medium

Abstract

The dynamics of a field in a thin waveguide surrounded by helically arranged two-level atoms is studied. The interaction of the induced polarizations of atoms with the field propagating inside the waveguide is described by a system of reduced Maxwell–Bloch equations (RMBEs) in the approximation of unidirectional propagation of the field. Nonlocal dipole–dipole interaction (DDI) of the polarizations of atoms in the helix is described in the approximation of the interaction of nearest neighbors in a curvilinear medium. Soliton solutions of an integrable reduction of the system of equations describing the asymmetric propagation of field pulses in the waveguide in the forward and backward directions are found by the method of Riemann problem with zeros. It is shown that, depending on the chirality sign or the propagation direction, a field pulse in the waveguide can have either the shape of a sharp peak or a nearly rectangular shape. Solutions describing the evolution of field pulses on a nonzero pedestal show that the shape and amplitude of the field pulses can be controlled by the external pumping parameters.