Borghi Riccardo
J Opt Soc Am A Opt Image Sci Vis. 2019 Jun 1;36(6):1048-1057. doi: 10.1364/JOSAA.36.001048.
A "genuinely" paraxial version of Miyamoto-Wolf's theory aimed at dealing with sharp-edge diffraction under Gaussian beam illumination is presented. The theoretical analysis is carried out in such a way the Young-Maggi-Rubinowicz boundary diffraction wave theory can be extended to deal with Gaussian beams in an apparently straightforward way. The key for achieving such an extension is the introduction of suitable "complex angles" within the integral representations of the geometrical and boundary diffracted wave components of the total diffracted wavefield. Surprisingly enough, such a simple (although not rigorously justified) mathematical generalization seems to work well within the Gaussian realm. The resulting integrals provide meaningful quantities that, once suitably combined, give rise to predictions that are in perfect agreement with results already obtained in the past. An interesting and still open theoretical question about how to evaluate "Gaussian geometrical shadows" for arbitrarily shaped apertures is also discussed.
提出了一种旨在处理高斯光束照明下尖锐边缘衍射的宫本 - 沃尔夫理论的“真正”傍轴版本。理论分析以这样一种方式进行，即杨 - 马吉 - 鲁比诺维茨边界衍射波理论可以以一种明显直接的方式扩展以处理高斯光束。实现这种扩展的关键是在总衍射波场的几何和边界衍射波分量的积分表示中引入合适的“复角”。令人惊讶的是，这种简单（尽管没有严格论证）的数学推广在高斯领域内似乎效果良好。所得积分提供了有意义的量，一旦适当地组合，就会产生与过去已经获得的结果完全一致的预测。还讨论了一个关于如何评估任意形状孔径的“高斯几何阴影”的有趣且仍未解决的理论问题。
