基于数值计算上好干涉和衍射的一堂辨析总结课

Explanation of the concepts of interference and diffraction based on numerical calculations

干涉和衍射是波动光学课程的核心内容,概念难、计算复杂。本文基于基尔霍夫衍射公式,利用次波相干叠加算法和MATLAB软件通过数值计算得到光照射到单缝、双缝等障碍物后的图案,给学生演示所获得的数值计算结果和典型光学教材中的解析结果吻合良好,让学生直观认识到单缝衍射和双缝干涉图案均可利用基尔霍夫衍射公式计算得到,进一步明确了所谓光的干涉和衍射实际上都是次波相干叠加的结果,在物理上并没有本质的差异。本文提出了抓住主要矛盾舍去次要矛盾的教学思路分别讲解干涉和衍射,继而前后呼应,并用统一算法获得典型孔径的衍射图案来讲解双缝衍射和光栅衍射。该教学手段有助于提高学生对干涉、衍射以及对复振幅线性叠加等物理现象的辨析和理解。

In this paper,the patterns of the single slit and the double slits which are illuminated by light are calculated using the Kirchhoff diffraction formula and the secondary wave coherent superposition algorithm based on MATLAB software.It can demonstrate to students that the obtained patterns fit the analytical results in the typical optical textbook very well,which means that the patterns of single slit diffraction and double slits interference can be calculated using the Kirchhoff diffraction formula and further clarifies that the interference and diffraction of light are actually the results of coherent superpositions of secondary wave,and there is no actual difference.In this work,we grasp the main contradictions and discard the minor contradictions to explain the interference and diffraction separately,and then call and response,and use a unified algorithm to obtain the diffraction pattern of the typical aperture to explain the double slit diffraction and grating diffraction.This teaching approach helps students to understand the concept of interference and diffraction together with the linear superposition of complex amplitudes.