为了研究梯度折射率介质对复变量双曲正弦高斯光束的传输影响,利用广义惠更斯-菲涅耳衍射积分法推导出了复变量双曲正弦高斯光束在梯度折射率介质中的传输场,运用空间二阶矩的定义解出了光斑尺寸及其变化率的表达式,并进行了数值模拟分析.结果表明,光斑尺寸及其变化率随传输距离的增加呈周期性变化,周期由折射率系数决定;随光束参量的改变,光斑位置不变,周期性不变,但是光斑尺寸的振荡幅度要发生改变;通过调整这些参量,可以改变光斑尺寸及其位置.此项研究对大功率半导体激光器等方面的开发应用有帮助.

In order to study influence of gradient-index medium on propagation property of complex variable sinh-Gaussian beam,propagation field of complex variable sinh-Gaussian beam in a gradient-index medium was deduced by means of generalized Huygens-Fresnel diffraction integral method.The expressions of spot size and its change rate were deduced by using the definitions of spatial second-order matrix.Then,the numerical stimulation and analysis were made.The results show that the spot size and its change rate changes with the increasing of propagation distance periodically and the periodical cycles are determined by gradient-index parameters.With the changing of beam parameters,the spot location and the periodical cycle are constant,but the oscillation amplitude of the spot size will change.The spot size and its location can be changed by adjusting these parameters.The study is helpful for development and application of high-power semiconductor lasers.