Abstract

Two compact analytical descriptions of Fresnel diffraction patterns from polygonal apertures under uniform illumination are detailed. In particular, a simple expression for the diffracted field from constituent edges is derived. These results have fundamental importance as well as specific applications, and they promise new physical insights into diffraction-related phenomena. The usefulness of the formulations is illuminated in the context of a virtual source theory that accounts for two transverse dimensions. This application permits calculation of fractal unstable-resonator modes of arbitrary order and unprecedented accuracy.

© 2006 Optical Society of America

Diffraction by fractally serrated apertures

Y. Kim, H. Grebel, and D. L. Jaggard
J. Opt. Soc. Am. A 8(1) 20-26 (1991)

Fresnel diffraction of fractal grating and self-imaging effect

Junhong Wang, Wei Zhang, Yuwei Cui, and Shuyun Teng
Appl. Opt. 53(10) 2105-2111 (2014)

Plane-wave Fresnel diffraction by elliptic apertures: a Fourier-based approach

Riccardo Borghi
J. Opt. Soc. Am. A 31(10) 2120-2130 (2014)

Diffraction by a circular aperture: a generalization of Fresnel diffraction theory

C. J. R. Sheppard and M. Hrynevych
J. Opt. Soc. Am. A 9(2) 274-281 (1992)

Simple derivation of formulas for Fraunhofer diffraction at polygonal apertures

Jiří Komrska
J. Opt. Soc. Am. 72(10) 1382-1384 (1982)