Fraunhofer Diffraction by a Strip: Perturbation Method

Abstract

We investigate the diffraction modeling of a plane wave by an infinitely thin and deformed perfectly conducting strip. We show that the diffraction pattern in the Fraunhofer domain can be obtained from efficiencies calculated for a periodic surface with an interpolation relationship; the elementary pattern of the periodic surface is identical to the strip. We consider the case where the deformation amplitude of the strip is small compared to its width. In this case, the propagation equation written in a curvilinear coordinate system is solved by a perturbation method inspired from quantum physics and extended to imaginary eigenvalues for evanescent waves. In the Fraunhofer approximation domain where the only waves are the propagative waves, the diffraction pattern obtained for a sinusoidal profile strip shows the phenomenon well known as apodization. Classically this phenomenon is obtained for physical optics with a slot in a screen with a variable transparency function similar to the profile function of the strip.