用虚时间传输计算偶极孤子

Solutions of Dipole Solitons by the Imaginary Time Propagation Method

虚时间传播是研究孤子解的重要方法,在非线性光学和波色爱因斯坦凝聚都有广泛的应用。但是一般来说,虚时间方法仅适用于计算基态的孤子,而不适用于研究激发态的孤子。本论文通过在虚时间算法中设置宇称条件,使得虚时间方法也可以计算第一激发态的孤子。我们把这一方法应用到研究反相非线性光子晶体中的激发态晶格孤子(偶极晶格孤子),并对所得到的孤子进行稳定性分析。结果证明,引入宇称条件后的虚时间方法可以推广到研究激发态问题。

Imaginary Time Propagation （ITP） is an important method for dealing with soliton solutions, which has a wide range of applications in nonlinear optics and Bose-Einstein condensation. However, in general, ITP is suitable for figuring out the ground state soliton, and is not adapted to find the exited state solitons. By introducing parity condition to ITP in this paper, the first exited state soliton can be dealt with. This method is used to research on the excited states of lattice solitons in an inverted nonlinear photonic crystal, and the stability of the stationary solitons is numerically identified. The results show that ITP with the parity condition can be qualified to handle the exited states of lattice solitons.