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Existence and Scattering of Gap Soliton in an Optical Lattice with Hollow Core
Preeti Agarwal and Roy Chowdhury

We introduce a model for two coupled waves propagating in a hollow core fibre – a linear dispersionless core mode and a nonlinear surface mode with an embedded optical lattice. The region for the existence of the soliton is analyzed as a function of the lattice depth and coupling between the two modes. It is observed that the propagation is not allowed for some critical values of the lattice depth and coupling strength which is a reflection of the gap soliton property. An interesting feature is that due to the variation of lattice depth, coupling and change in sign of nonlinearity the bright soliton when it exists can get converted to a dark soliton. Later the ordinary differential equations governing the evolution of width, amplitude, chirp etc are obtained using the Projection Operator technique. It is interesting to note that these parameters show a wide variation with respect to both the coupling parameter and lattice depth. The exchange of energy between the two modes is evident from the change of input and output wave power. Our analysis reveals that there exists some optimum range of values for the fibre parameters for which both the waves can propagate over a long distance.

Keywords: Gap soliton, lattice depth, lattice period, projection operator method.

PACS numbers : 42.25Lc, 42.55, 42.60, 42.65Sf,42.50Md.

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