A variational solution to defect solitons in defect lattices

A variational technique is developed to study the defect solitons in defect lattices. The variational results show that the fundamental solitons can only exist in the semi-infinite gap for positive and zero defects, however, fundamental solitons can exist in both the semi-infinite gap and the first gap for negative defect. There exists a critical propagation constant bc of fundamental solitons, below which the solitons vanish. For zero defect, the value of bc is associated with the edge of the first band. The value of bc increases with the depth of defect, and bc locate in the semi-infinite gap and the first gap for the positive and the negative defect. Following numerical simulations, the variational results are in good agreement with the numerical results.