变迹光栅孤子速度与时延特性研究

基于非线性耦合模方程组（NLCME）的解析孤子解, 讨论了均匀布拉格光栅（FBG）中慢光栅孤子（GS）的存在性。利用双曲正切中间变迹光栅中的NLCME, 引入非相对论-绝热-准量子近似法, 将光栅孤子作为一个低速运动且能量守恒的整体进行分析, 得到了孤子的轨迹方程。对反射孤子、低速孤子和静态孤子三种情况下的速度、位移分别进行数值计算, 分析了变迹光栅孤子的速度可控性。对孤子时延进行的数值仿真表明, 50 m的变迹光栅中可产生2000 ns的时延, 平均速度仅相当于均匀光纤中的0.1倍。讨论了光栅参数和脉冲初始参数对速度、位移和时延的影响。研究结果表明：在变迹光栅中, 选取合适的光栅变迹函数和初始脉冲, 可得到速度在0～c/n之间的任意孤子, 产生需要的时延大小, 从而实现孤子光缓存。

Research on Velocity and Delay Characteristics of Solitons in Apodized Fiber Bragg Grating

Based on analytic soliton solutions of nonlinear coupled-mode equations (NLCME) in a uniform fiber Bragg grating (FBG), the existence of slow grating soliton (GS) is discussed. By introducing non-relativistic, adiabatic and quantum approximation to NLCMEs in the FBG with hyperbolic tangent apodization, and assuming the soliton as a particle with low velocity and invariant energy, the track equation of soliton is obtained. Numerical simulations of velocity and displacement of reflected soliton, slow soliton and standing soliton are carried out to analyze the controllable velocity characteristic of the GS. Results show that time delay of 2000 ns can occur in an apodized FBG with length of 50 meters and corresponding average velocity is 0.1 c/n. The influences of grating parameters and velocity and displacement of initial input pulse solitons on time delay are further discussed. By choosing proper parameters of the apodized FBG and the initial soliton pulse, GS with any velocity between 0 and c/n can be achieved, which facilitates the compact soliton-based optical Buffer.