  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.
