We introduce a new family of spectral singularities with highly directional response in parity-time (PT) symmetric cavities. These spectral singularities support modes with infinite reflection from one side and zero reflection from the other side of the cavity, results in simultaneous unidirectional laser and unidirectional reflectionless parity-time symmetric cavity. Such unidirectional spectral singularities emerge from resonance trapping induced by the interplay between parity-time symmetry and Fano resonances.
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