The scattering of plane waves by complex domains (self-similar or fractal obstructions characterized by roughness across many scales) is a problem of fundamental interest for physicists and applied mathematicians.
In laser optics, for instance, descriptions of light fields after they have interacted with fractal screens are typically based on the well-known Fresnel diffraction equation or, more commonly, Fourier transforms and the Fraunhofer (far-field) limit. These simplified models can work well in some fairly restrictive parameter regimes, but they are not always entirely satisfactory.
Here, we develop a more general formulation for wave scattering based on the Helmholtz equation and Rayleigh-Sommerfeld integrals. Such as an approach, in conjunction with the Kirchhoff approximation, can be computationally expensive but it is free from many of the physical limitations inherant to more traditional methods.
A range of complex domains will be considered, including preliminary results for screens based on the classic fractal shapes of Cantor (sets and dusts) and Sierpinski (carpets and triangles).
James Chrsitian is a lecturer in physics at the University of Salford; his current research interests involve some theoretical problems in electromagnetics and classical fluids (www.seek.salford.ac.uk/profiles/JCHRISTIAN.jsp).
Holly Middleton-Spencer is now a PhD student at the University of Newcastle studying turbulance in superfluids; she has recently completed an MSc at Salford considering wave diffraction by Cantor screens.
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