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.
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