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 b c of fundamental solitons, below which the solitons vanish. For zero defect, the value of b c is associated with the edge of the first band. The value of b c increases with the depth of defect, and b c 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.