多色GSM光束通过杨氏双缝后谱强度的一般式

General spectral density formula of polychromatic GSM beam passing through the Young's double slits

为了统一地研究多色高斯-谢尔模型(GSM)光束通过杨氏双缝衍射后在近场和远场的光谱移动和光谱开关现象,利用部分相干光的广义衍射积分公式,得到了多色GSM光束通过杨氏双缝和ABCD光学系统后的谱强度解析表达式。从该式可看出,多色GSM光束轴上光谱移动的成因是不同频率成分的光具有不同的菲涅耳数。利用谱强度解析式并以自由空间作为ABCD光学系统的典型代表,对多色GSM光束在近场轴上和远场轴外的光谱移动和光谱开关现象作了数值计算研究。结果表明,所得谱强度解析表达式对GSM光束通过杨氏双缝衍射后的光谱移动和光谱开关现象的研究有一定的理论价值。

In order to study the spectral shift and spectral switch phenomena in the near field and far field of polychromatic Gaussian-Schell model （GSM） beam uniformly, based on the general diffraction integral formula of partially coherent light, the analytical spectral density formula of polychromatic GSM beam passing though the Young＇ s double slits and ABCD optical system was derived. From the general spectral density formula it can be shown that the Fresnel number varies with the frequency, which is the physical reason of the axial spectral shift of the polychromatic GSM beam. Taking the free space as a typical example of the ABCD optical system, the on-axis spectral shift and spectral switch in the near field and the off-axis spectral shift and spectral switch in the far field were studied numerically by means of the general formula. The result shows that the analytical spectral density formula has some theoretical value in researching spectral shift and spectral switch phenomenon of GSM beam diffracted by Young＇ s double slits.