Modulation instability in nonlinear complex parity-time symmetric periodic structures

We carry out a modulation instability (MI) analysis in nonlinear complex parity-time (PT) symmetric periodic structures. All three regimes defined by the PT-symmetry breaking point or threshold, namely, below threshold, at threshold, and above threshold, are discussed. It is found that MI exists even beyond the PT-symmetry threshold, indicating the possible existence of solitons or solitary waves, in conformity with some recent reports. We find that MI does not exist at the PT-symmetry breaking point in the case of normal dispersion below a certain nonlinear threshold. However, in the case of the anomalous dispersion regime, MI does exist even at the PT-symmetry breaking point. (C) 2014 Optical Society of America