Diffraction Diffraction is the bending and spreading of waves from apertures or obstructions, including interference of the waves.

Diffraction for increasing screen distance Aperture 200x100  z screen 20  z screen 100  z screen 500  z screen 2500  Looks like the aperture with fringes! (Fresnel) “Far field” looks like |FT| 2 of aperture!  Fraunhoffer diffraction)

Diffraction How could we solve with no approximations? plus boundary conditions. …but there are easier approximations!

1678 Huygens’ principle 1678 Every point on a wavefront acts like a “forward spherical” scalar source. Conceptual tool: gave Snell’s law, finds diffraction maxes, mins Fresnel’s update --- make it formal:

Obeys a scalar wave equation Helmholtz equation vs Works when: essentially single frequency E doesn’t change significantly over a distance of Forget about polarization Hard to solve (if we further required small, we’d get the Eikenol equation…then no diffraction)

Fresnel-Kirchoff diffraction formula Kirchhoff found the factor: Put on firm math foundation with Green’s theorem and Helmholtz equation Fresnel’s diffraction model: add these Huygen waves…it works pretty well! meaning?

Fresnel approximation Becomes : (know how to do this step with small angle/binomial approx’s) restrictions: a (size of aperture) >  [scalar wave approx] z of screen > a (but if get far enough, becomes simpler Fraunhofer) x,y of screen <<z, so angles on screen are small

Aperture 200x100  z screen 20  z screen 100  z screen 500  z screen 2500  Looks like the aperture with fringes! (Fresnel diffraction) “Far field” looks like |FT| 2 of aperture!  Fraunhoffer diffraction) Diffraction for increasing z, using Fresnel equations

Fresnel diffraction for slit, increasing z

Babinet’s principle for all diffraction patterns

Complimentarity principle The diffraction pattern for an aperture is similar (but not identical) to the pattern for a block of the same shape The principle describes the fields, not intensities

Circular hole diffraction a = 1 to 4 mm, screen 1 meter away, HeNe light Center alternates bright/dark

Complimentarity principle Center is always bright…similar but not identical Poisson’s spot in shadow of ball bearing