互补Sierpinski地毯光栅夫琅和费衍射现象的研究

Study of Fraunhofer Diffraction From Complementary Sierpinski Carpet Grating

利用菲涅耳-基尔霍夫光栅衍射原理和傅里叶分析方法,对具有分形结构互补Sierpinski地毯光栅的夫琅和费衍射现象进行了探讨。导出了观察平面上的频谱函数、振幅函数以及光强函数。运用MATLAB软件对该光栅的衍射现象进行了仿真,并绘制出其幅-频特性曲线。结果表明,在各阶光栅的衍射图样中,幅度较大的部分主要集中在接收屏的中心区域,而在偏离中心的区域内,幅度值较小,在较远区域幅度值趋近于零,这说明获得的衍射图样不仅具有衍射光的基本特性,而且都呈现出明显的分形特征。

The Fraunhofer diffraction phenomenon on the complementary structure of Sierpinski carpet grating is discussed on the basis of Fresnel-Kirchhoff theory and Fourier analytical method. The frequency spectrum,amplitude and lightintensity functions are derived. The diffraction phenomenon of grating is simulated by use of the MATLAB software, and the curves of its frequency response characteristic are plotted. The result shows that in diffraction patterns of all-order gratings, the higher amplitude part is concentrated in the center area of the receiving screen and the lower amplitude in the area around the center, but in the further area far away from center it tends to 0. In the whole, the diffraction patterns manifest the obvious fractal characteristics as well as the basic features of the diffraction.