Chandezon J, Gavaix A, Parriaux O, Kneale C
J Opt Soc Am A Opt Image Sci Vis. 2019 Apr 1;36(4):594-605. doi: 10.1364/JOSAA.36.000594.
The modeling of the scattering of a plane wave at a rough aperiodic surface-as well as its diffraction by a microstructured surface-is possible only by limiting the infinite surface to a window of finite width D. We show that the scattering spectrum at infinity in the Fraunhofer zone can be obtained from the diffraction modeling of a grating of period D whose surface profile coincides with the aperiodic surface in this window. This is justified by adopting the corpuscular representation of light and resorting to Heisenberg's uncertainty relation applied to the photon's canonically conjugate variables momentum and position. This approach gives a deep and comprehensive representation of scattering phenomena, and also the limit of what can be meaningfully calculated and measured. Numerical examples of grating profiles demonstrate that results obtained under the widely used Beckmann-Kirchoff approximation are matched. The described approach can solve scattering problems that usual methods cannot, or face difficulties, such as when there is significant roughness with respect to the wavelength.
只有将无限大的表面限制在有限宽度D的窗口内，才有可能对平面波在粗糙非周期表面的散射以及其在微结构表面的衍射进行建模。我们表明，夫琅禾费区无穷远处的散射光谱可以从周期为D的光栅的衍射建模中获得，该光栅的表面轮廓与该窗口内的非周期表面一致。通过采用光的微粒表示法并诉诸应用于光子正则共轭变量动量和位置的海森堡不确定性关系，这一点得到了证明。这种方法给出了散射现象的深刻而全面的表示，同时也给出了有意义的计算和测量的极限。光栅轮廓的数值例子表明，在广泛使用的贝克曼 - 基尔霍夫近似下获得的结果是匹配的。所描述的方法可以解决常规方法无法解决或面临困难的散射问题，例如当粗糙度相对于波长很大时。
