摘要
运用自相似方法,求出了二维谐振子调制势下光束传输方程的精确解析解,并对光束在传输距离一定时其传输特性随量子数的变化规律进行了数值分析。结果表明,在谐振子势调制下,光束传播的波函数解为厄米特函数,且在能量峰值上表现出类似于亮孤子的中间能量高于外围能量的特性,在几何分布上形成矩阵或方阵式波包。波包总数受x、y方向的量子数取值影响,波包能量幅值沿x、y轴的正负向均逐渐增大且关于矩阵的对角线或x、y轴对称。
The analytical solutions of light beams under two-dimensional harmonic oscillator modulation were obtained with self-similar technique, and the change rules with the quantum number of transmission properties of light beams were discussed by numerical simulation when their transmission distance were taken fixed. It is found that, under two-dimensional harmonic oscillator modulation, the solutions of light beams are Hermite polynomials, whose energy peaks are the highest in the middle of the wave packet which is similar to the bright solitons, and the energy distribution forms a matrix wave packets or a square matrix wave packets in geometry. The total number of wave packets is influenced by the quantum numbers of x and y direction. The amplitude of wave packets energy increases gradually along the positive and negative direction of x and y axis and is diagonal symmetrical on the matrix, x axis or y axis.
出处
《量子电子学报》
CAS
CSCD
北大核心
2013年第3期323-329,共7页
Chinese Journal of Quantum Electronics
基金
湖北省教育厅科学技术项目(B201 13002)
湖北第二师范学院校立科研基金(2009B013)资助项目
湖北第二师范学院"优秀教师团队"建设项目(2012KB302)资助
关键词
非线性光学
谐振子调制
非线性薛定谔方程
厄米特多项式
nonlinear optics
harmonic oscillator modulation
nonlinear Schr5dinger equation
Hermite polynomial
作者简介
靳海芹（1980-），湖北随州人，博士，讲师，研究方向为凝聚态物理和光学。E-mail：haiqin2012@qq．com
导师简介：易林（1963-），教授，博士生导师，研究方向为凝聚态物理和光学。E-mail：yilin@mail．hust．edu．cn
