Nonlocal effects in waveguide arrays with PT-symmetric defects

Photonic structures composed of coupled waveguides with loss and gain regions offer new possibilities for shaping optical beams and pulses compared to conservative structures [1, 2]. Such structures can be designed as optical analogues of complex parity-time (or PT) symmetric potentials, which can have a real spectrum corresponding to the conservation of power for optical eigenmodes, for the magnitude of gain/loss below a certain threshold. When gain/loss is increased above the threshold, PT symmetry breaking occurs, corresponding to amplification of certain eigenmodes. The PT symmetry breaking transition was recently demonstrated experimentally for directional couplers composed of two waveguides [3, 4]. PT-symmetric potentials appear in many physical contexts, and one feature actively investigated in the context of quantum theories is the property of nonlocality, where PT-defect dynamics can be sensitive to potential profile at distant locations, and it was questioned the observability of such behavior in real physical systems [5, 6]. In this work, we reveal that effective nonlocality of PT-symmetric structures with gain and loss elements can lead to pronounced differences for optical beam dynamics in arrays of coupled waveguides with the same characteristics but different topology.