PT-symmetric bound states in the continuum

We show that 2D parity-time ($\mathcal{P}$$\mathcal{T}$)-symmetric structure built as a chain of waveguides, where all waveguides except for the central one are conservative, while the central one is divided into two halves with gain and losses, admits bound states in the continuum (BICs) whose properties vary drastically with the orientation of the line separating amplifying and absorbing domains, which sets the direction of internal energy flow. When the flow is perpendicular to the waveguide chain, narrow BICs emerge when the defect mode located in the finite gap, collides with another mode in standard symmetry-breaking scenario and its eigenvalue enters the continuous spectrum upon increase of the strength of gain/losses. When the energy flow is parallel to the chain of the waveguides, the symmetry gets broken even for a small strength of the gain/losses. In that case, the most rapidly growing mode emerges inside the continuous spectrum and realizes a weakly localized BIC.