Gap solitons attached to a gapless layer

Abstract

We consider linear and nonlinear modes pinned to a grating-free (gapless) layer placed between two symmetric or asymmetric semi-infinite Bragg gratings (BGs), with a possible phase shift between them, in a medium with the uniform Kerr nonlinearity. The asymmetry is defined by a difference between bandgap widths in the two BGs. In the linear system, exact defect modes (DMs) are found. Composite gap solitons pinned to the central layer are found too, in analytical and numerical forms, in the nonlinear model. In the asymmetric system, existence boundaries for the DMs and gap solitons, due to the competition between attraction to the gapless layer and repulsion from the reflectivity step, are obtained analytically. Stability boundaries for solitons in the asymmetric system are identified by means of direct simulations. Collisions of moving BG solitons with the gapless layer are studied too.