Bound states in the continuum in a two-dimensional PT-symmetric system

Abstract

We address a two-dimensional parity-time (PT)-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. We show that such a system 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 chain of the waveguides, narrow BICs emerge when the standard defect mode, which is initially located in the finite gap, collides with another mode in a standard symmetry breaking scenario and its propagation constant enters the continuous spectrum upon increase of the strength of gain/losses. In contrast, 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. All BICs found here are the most rapidly growing modes, therefore they can be excited from noisy inputs and, importantly, should dominate the beam dynamics in experiments.

4 pages, 4 figures, to appear in Optics Letters

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• Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
• Spectral singularities of odd-$PT$-symmetric potential
• A universal form of complex potentials with spectral singularities
• Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations
• Fixed points on band structures of non-Hermitian models: Extended states in the bandgap and ideal superluminal tunneling
• Dispersive bands of bound states in the continuum
• Eigenvalues bifurcating from the continuum in two-dimensional potentials generating non-Hermitian gauge fields
• Surface Bound States in the Continuum in Dyakonov Structures