Application of Heisenberg uncertainty relation for the optimal modeling of surface diffraction.

Abstract

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.