Diffraction phenomena

Diffraction is a phenomenon by which wavefronts of propagating waves bend in the neighborhood of obstacles. Diffraction around apertures is described approximately by a mathematical formalism called scalar diffraction theory. Diffraction problems are among the most difficult encountered in optics, and exact rigorous solutions are quite rare. The first such rigorous solution was found by Sommerfeld (1896). Variants of this problem dealing with line sources, point sources, and generalization to a wedge instead of a plane were solved exactly by Carslaw (1899), MacDonald (1902), and Bromwich (1916). Mie (1908) rigorously solved scattering by a sphere having finite dielectric constant and finite conductivity [4]. Depending on the Fresnel number of a system, defined as

$$F=\frac{r^2}{\lambda L}$$ (6)

where $r$ stands for the "radius" of the aperture², $\lambda$ stands for the wavelength, and $L$ is the distance from aperture, qualitatively different types of diffraction occur. In particular, $F \ll 1$ produces a type of diffraction known as Fraunhofer diffraction or Far Field diffraction, while $F \approx 1$ produces Fresnel diffraction or Near Field diffraction. Thus in the case of Fraunhofer Diffraction, the diffraction pattern is independent of the distance to the screen, depending only on the angles to the screen from the aperture. Mathematical description of Fraunhofer Diffraction is much easier and will be partly presented later.