Research on slow Bragg solitons in apodized gratings

On the basis of non-linear coupled-mode theory, the dispersion relation of a dimensional periodic structure is analyzed and slow Bragg soliton solutions are given. The approximation approach for non-linear coupled-mode theory is studied by assuming adiabatic evolution of the soliton passed through fiber Bragg grating which is apodized by using a hyperbolic tangent apodization function in the middle of the FBG. And in the presence of apodization, the velocity equation of Bragg soliton is found. In this paper, we have simulated the motion tracks and velocities of Bragg solitons, analyzed effects of different parameters on motion track and velocity of Bragg soliton, and obtained different time-displacement curves and time-velocity curves. It is shown that the final steady velocity of soliton can be found by choosing specifical parameters, thereby, slow Bragg solitons whose propagate velocity through the grating is far lower than the speed of light in glass can obtained. We have presented detailed simulative results that agree with theoretical analysis.