多色GSM光束通过杨氏双缝后谱强度的一般式

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。

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

Based on the propagation theory of partially coherent light, the spectral density formula of polychromatic Gaussian Schell-Model (GSM) beams passing though the Young’s double slits and ABCD optical system is obtained. The formula is universal, the reason for which is that it could be used not only for the case of the optical system behind the Young’s double slits being the free space, or lens and space, but also for the other cases with the optical systems being expressed as ABCD matrix, and moreover the spectral density formulae of Schell-Model beams and Gaussian beams in Young’s two-slit diffraction experiment could be got as special cases of the general formula. Analyzing the on-axis spectral density formula deduced from the general formula, it is illustrated that the reason for the axial spectral shift of the polychromatic GSM upon its propagation is that the Fresnel number is changed with the frequency. As a practical application, using the general formula and assuming the ABCD system being the free space, the on-axis spectral shift and spectral switch phenomenon in the near field and the off-axis spectral shift and spectral switch phenomenon in the far field of GSM beams are studied numerically.