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Here we refer to a "true" in-gap dark soliton, i.e., a dark gap soliton excited by a single pump with no external feedback mechanism to reinject the output field back into the structure. This external feedback scheme indeed can lead to delocalized modes excited by two counter-propagating pumps. In this regard, it is well known that in the linear regime a multilayer structure pumped on both sides can give rise to unusual delocalized states by simply choosing a proper phase link between the incident pumps; see M. Centini et al., Phys. Rev. E 67, 036617 (2003). Therefore, in the nonlinear regime dark in-gap solitons or delocalized modes can be excited using either external feedback or two counter-propagating pumps that may cause destructive interference and a local minimum inside the structure. A very good example of external feedback that can give rise to delocalized states in the gap of a multilayer structure is discussed in H. Alatas et al., J. Nonlinear Opt Phys. Mater. 13, 259 (2004).
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