${\cal P}{\cal T}$-Symmetric Waveguides With Tunable Parameters

We propose a physical setting for a PT-symmetric waveguide with spatially varying parameters and mode structure. The system consists of a mixture of isotopes of Rubidium Λ-atoms loaded in a cell with Bragg cladding and exposed to laser fields ensuring Raman excitations, controlling the real and imaginary parts of the refractive index of the system. It is shown that the system parameters can be designed to support different numbers of propagating modes in different parts of the waveguide as well as to create localized defects. We study the wave transition between different wave guide configurations. We address two types of defects in more details:1) tunable defects, which are related to the variation of the refractive index inside the waveguide, and 2) fixed defects created by changes of a Bragg cladding. We demonstrate that the change of the waveguide toward the increase of the number of guided modes can support and even enhance the light propagation. However, if a transition, or a defect, results in a reduction of the number of guiding modes, strong attenuation of guided beams can be observed. As a result, the proposed waveguides may support unidirectional propagation of light and operate as switches and amplifiers.