首次使用了离散傅里叶方法数值分析局域空心光束。用离散傅里叶方法描述单色平面波产生局域空心光束(bottle beam)的光强分布, 引入色散公式使得一定频谱宽度的LED光源同样适用。讨论抽样要求并对变量进行离散化, 导出LED产生bottle beam的离散化傅里叶公式。最后代入相关参数并用MATLAB进行数值模拟, 得到了在不同距离处光束的强度分布。设计实验进行验证, 实验结果表明: 使用LED也能够产生高质量的bottle beam。数值模拟与实验结果基本吻合, 证明了采用傅里叶方法可以精确地分析非相干光源产生bottle beam, 并且相较于传统的标量衍射理论, 它更加简洁、快速, 是研究bottle beam的一种全新又可靠的方法。

The bottle beam was analyzed by using the discrete Fourier method for the first time in this paper. The bottle beam intensity distribution was described by discrete Fourier transform, then Sellmeier formula was added to adapt to a LED light source with some spectral width. By considering sampling and discrete variables, discrete Fourier's formula of bottle beam generated by a LED light source was derived. At last, the parameters were substituted and the intensity distribution of the beam at different distance was obtained by the numerical simulation with MATLAB. Experiments were designed to verify it, and the experimental results showed that using LED as light source can produce high-quality bottle beam. Numerical simulation is in line with experimental results basically, which proves the discrete Fourier transform method is feasible to analyze bottle beam generation by incoherent light. Furthermore, compared to conventional scalar diffraction theory, it is more simple and fast. It′s a new and reliable way to study bottle beam.