Diffraction of light by a planar aperture in a metallic screen
A. Drezet, J.C. Woehl, S. Huant
TL;DR
This paper provides a comprehensive derivation of Smythe's diffraction formula for electromagnetic waves passing through a planar aperture in a perfect conductor, using scalar Green functions and connecting to Huygens-Fresnel principles.
Contribution
It offers a new, general derivation of Smythe's diffraction formula applicable to any aperture shape and excitation, avoiding dyadic Green functions.
Findings
Derivation valid for any aperture shape and excitation
Connects Smythe's formula to Huygens-Fresnel theorem
Provides a scalar Green function-based proof
Abstract
We present a complete derivation of the formula of Smythe [Phys.Rev.72, 1066 (1947)] giving the electromagnetic field diffracted by an aperture created in a perfectly conducting plane surface. The reasoning, valid for any excitating field and any hole shape, makes use only of the free scalar Green function for the Helmoltz equation without any reference to a Green dyadic formalism. We compare our proof with the one previously given by Jackson and connect our reasoning to the general Huygens Fresnel theorem.
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