Electromagnetic scattering problems on perfectly-conducting complex domains: from Rayleigh-Sommerfeld integrals toward fractal screens

Christian, JM; Middleton-Spencer, HAJ

Abstract

The diffraction of light by an aperture in an otherwise perfectly conducting plane screen of infinite extent is a phenomenon of fundamental
interest in electromagnetics. Here, we consider
classes of problems where the aperture domain is
complex (possessing self-similar structure across
a range of spatial scales) and modelled on infinite
iterations of the fractal shapes devised by Cantor and Sierpinski.
Rayleigh-Sommerfeld (RS) integrals are deployed to predict electric fields in the space behind the screen. This approach captures more
fully the details of wave scattering, eliminating
many of the approximations inherent with simpler analyses in Fraunhofer and Fresnel regimes.
The solutions are essentially exact for Cantorset apertures, at least within Kirchhoff's treatment of the boundary conditions. Diffraction
patterns from Cantor dust and Sierpinski triangle apertures are computed by transforming
integrations over the domain into circulations
around the constituent subdomain boundaries.

Citation

Christian, J., & Middleton-Spencer, H. Electromagnetic scattering problems on perfectly-conducting complex domains: from Rayleigh-Sommerfeld integrals toward fractal screens. Presented at 14th International Conference on the Mathematical and Numerical Aspects of Wave Propagation (WAVES 2019), Vienna University of Technology, Austria

• Presentation Conference Type: Lecture
• Conference Name: 14th International Conference on the Mathematical and Numerical Aspects of Wave Propagation (WAVES 2019)
• Conference Location: Vienna University of Technology, Austria
• Online Publication Date: Aug 30, 2019
• Publication Date: Aug 30, 2019
• Deposit Date: Mar 2, 2020
• Publicly Available Date: Mar 2, 2020
• Book Title: 14th International Conference on Mathematical and Numerical Aspects of Wave Propagation. Book of Abstracts
• ISBN: 9783200065116
• DOI: https://doi.org/10.34726/waves2019
• Publisher URL: https://doi.org/10.34726/waves2019
• Related Public URLs: http://waves2019.at/
• Additional Information: Event Type : Conference