Diffraction of fractal light: New frontiers for the mathematics of edge waves

Mylova, M; McDonald, GS; Christian, JM

Abstract

The diffraction pattern produced by a plane wave (i.e., a perfectly uniform wavefront) scattering from an infinite hard edge is well-described by the Fresnel integral [1]. Such one-dimensional (1D) edge waves [see Fig. 1(a)] turn out to be truly elemental spatial structures in linear optical systems in the sense that patterns produced by other apertures [such as a slit – see Fig. 1(b)] can be decomposed into a sum of two interfering edge waves. Our group has previously established that such waves also play a fundamental role in the exact mathematical description of diffraction patterns generated from uniform illumination of polygonal apertures [2], whereby one superposes the waves from all constituent edges (each of which has, crucially, a finite length). Here, we report on the first steps taken toward considering a related but distinct physical problem, namely how a fractal light wave incident on an infinite edge is diffracted in both the near and far fields. Our method is based upon a Fresnel-type prescription, generalizing earlier analyses [1,2] to accommodate an illuminating field that comprises a spectrum with many distinct components (each spatial frequency contributes a characteristic scale length to the incident pattern). Our results can be readily applied to other classic 1D and 2D systems such as slits and polygons, respectively.

References
[1] M. P. Silverman and W. Strange, Am. J. Phys. 64, 773 (1996).
[2] J. G. Huang, J. M. Christian, and G. S. McDonald, J. Opt. Soc. Am. A 23, 2768 (2006).

Citation

Mylova, M., McDonald, G., & Christian, J. (2013, June). Diffraction of fractal light: New frontiers for the mathematics of edge waves. Presented at College of Science & Technology Research Showcase, University of Salford

• Presentation Conference Type: Other
• Conference Name: College of Science & Technology Research Showcase
• Conference Location: University of Salford
• Start Date: Jun 19, 2013
• Deposit Date: Jun 11, 2013
• Publicly Available Date: Apr 5, 2016
• Additional Information: Event Type : Conference