Diffraction of Electromagnetic Waves

TL;DR

This paper develops a general method to solve Maxwell's equations for electromagnetic wave diffraction, providing explicit formulas for polarization and imaging effects, including Fresnel diffraction behind a round stop.

Contribution

It introduces a novel approach using scalar representatives and modified Kirchhoff's integral to derive explicit diffraction formulas for electromagnetic waves.

Findings

New formulas for polarization in diffraction

Explicit expressions for imaging by diffraction

Ready-to-use Fresnel diffraction formulas behind a round stop

Abstract

The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these representatives. The respective integrals are then evaluated using the method of stationary phase in two dimensions. Hitherto unknown formulae for the polarization appear as well as for imaging by diffraction. Ready-to-use formulae describing Fresnel diffraction behind a round stop are presented.