### 2011-21

**On energy conditions for electromagnetic diffraction by apertures.**

by Gorenflo, N.; Kunik, M..

**Series:** 2011-21, Preprints

- MSC:
- 78A25 Electromagnetic theory, general
- 78A45 Diffraction, scattering
- 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
- 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and ~Wiener-Hopf type)
- 35S05 Pseudodifferential operators

**Abstract:**

The diffraction of light is considered for a plane screen with an open bounded aperture. The corresponding solution behind the screen is given explicitly in terms of the Fourier transforms of the tangential components of the electric boundary field on the screen. All components of the electric as well as the magnetic field vector are considered. We introduce solutions with global finite energy behind the screen and describe them in terms of two boundary potential functions. This new approach leads to a decoupling of the vectorial boundary equations on the screen in the case of global finite energy. For the physically admissible solutions, i.e. the solutions with local finite energy, we derive a characterisation in terms of the electric boundary fields.

**Keywords:**

Electromagnetic diffraction by apertures, Fourier analysis, Sobolev spaces, energy conditions, vectorial pseudodifferential operators