梯度折射率介质中可控空心光束的传输特性

The Propagation Properties of Controllable Dark-hollow Beams in Gradient Index Media

为了研究可控空心光束在梯度折射率介质中的传输特性,采用广义惠更斯-菲涅尔积分公式,推导出可控空心光束在梯度折射率介质中通过旁轴ABCD光学系统后的一般传输公式。在此基础上,结合光强二阶矩的方法,给出了相应的一般束宽变换公式。通过数值分析研究了梯度折射率介质传输场中强度分布和均方根束宽的变化特点,讨论了介质梯度折射率系数、空心光束的阶数、控制参数p对传输特性的影响。研究结果表明,在梯度折射率介质中,可控空心光束轴上光强和束宽随着传输距离呈现周期性变化。空心光束的阶数和控制参数p对光强分布和均方根束宽影响较大。并且在光强峰值位置处,光强分布不再保持原来暗中空的特性,而是迅速变为类高斯分布。

In order to study transmission property of controllable dark-hollow beams in gradient index media, the closed-form propagation equation of controllable dark hollow beams passing through a paraxial optical ABCD system is derived with the base on the definition of complex wave number and the generalized Huygens-Fresnel diffraction integral. The beamwidth propagation formula of dark hollow beams through gradient index media are obtained on the basis of the second-order moment method. By numerical analysis, the intensity distributions and beams waist width have been studied. It can be shown that, the on-axis intensity distribution and beams waist width of dark hollow beams propagating in the gradient index media varies periodically. The intensity distribution is largely influenced by the controllable parameter and orders of dark hollow beams. Furthermore, the intensity distribution on the plane of peak intensity changs rapidly into Gaussian--like distribution,with the original nature of hollow no longer kept.