Adiabatic Bragg soliton compression

We consider the nonlinear pulse propagation through a non-uniform fiber Bragg grating whose index modulation depth varies along the propagation direction. To form the Bragg soliton outside the photonic band gap, we reduce the NLCM equations into known nonlinear Schrödinger (NLS)-type equation. As we consider the pulse propagation in non-uniform FBG, the pulse propagation outside the photonic band gap is governed by inhomogeneous NLS (INLS) rather than NLS. We then construct the soliton solution in FBG known as Bragg soliton whose central frequency lies outside but close to the photonic band gap of the grating structure. Moreover, we discuss Bragg soliton compression due to a delicate balance between self-phase modulation with the varying grating induced dispersion and also discuss the increase in the amplitude of the pulse