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Bound states in the continuum in PT-symmetric optical lattices

Bound states in the continuum (BIC), i.e. normalizable modes with an energy embedded in the continuous spectrum of scattered states, are shown to exist in certain optical waveguide lattices with $\mathcal{PT}$-symmetric defects. Two distinct types of BIC modes are found: BIC states that exist in the broken $\mathcal{PT}$ phase, corresponding to exponentially-localized modes with either exponentially damped or amplified optical power; and BIC modes with sub-exponential spatial localization that can exist in the unbroken $\mathcal{PT}$ phase as well. The two types of BIC modes at the $\mathcal{PT}$ symmetry breaking point behave rather differently: while in the former case spatial localization is lost and the defect coherently radiates outgoing waves with an optical power that linearly increases with the propagation distance, in the latter case localization is maintained and the optical power increase is quadratic.