Diffraction of Weierstrass scalar fractal waves by circular apertures : symmetry and patterns, complexity and dimension

Christian, JM; Woodroofe, EP; McDonald, GS

Abstract

The diffraction of plane waves from simple hard-edged apertures constitutes a class of boundary value problem that is well understood in optics, at least within the scalar approximation. Similarly, the diffraction of such waves from fractal apertures (amplitude or phase masks possessing structure across decades of spatial scale) has also received much attention in the literature. But the diffraction of fractal waves by simple apertures constitutes an entirely new paradigm (in optics particularly, and wave physics more generally) that remains largely unexplored. Here, we consider the diffraction of fractal waves by a hard-edged circular aperture using a range of analytical and semi-analytical methods. Fast computational techniques are used to obtain Fresnel (near field) diffraction patterns, and specialist software assists with the investigation of their properties. Key issues to be addressed include the fractal dimension of diffraction patterns, and the asymptotic emergence of Fraunhofer (far field) predictions in an appropriate limit.

Citation

Christian, J., Woodroofe, E., & McDonald, G. (2015, July). Diffraction of Weierstrass scalar fractal waves by circular apertures : symmetry and patterns, complexity and dimension. Presented at 12th International Conference on the Mathematical and Numerical Aspects of Wave Propagation, Karlsruhe, Germany

• Presentation Conference Type: Other
• Conference Name: 12th International Conference on the Mathematical and Numerical Aspects of Wave Propagation
• Conference Location: Karlsruhe, Germany
• Start Date: Jul 20, 2015
• End Date: Jul 24, 2015
• Acceptance Date: Apr 1, 2015
• Publication Date: Jul 1, 2015
• Deposit Date: Jul 7, 2015
• Publicly Available Date: Apr 5, 2016
• Related Public URLs: http://waves2015.math.kit.edu/
• Additional Information: Event Type : Conference