The first is the usual plane wave that we're all familiar with. Starting from the full vector Maxwell equations, it is common to derive two fundamental wave solutions. This is needlessly vague and without rigor. the impulse response in 3D) is a spherical wave. In scalar diffraction theory, the starting point is usually Huygen's principle, which states that the field emanating from an infinitely small point (i.e. (These functions are for learning, not actual work!) All functions are normalized an assume a wavelength of unity. These functions will plot the phase fronts of a wave on a normalized set of axes or numberically compute diffraction given a kernel function and aperture function (in 2D). This will probably only be of much interest to people already briefly familiar with diffraction theory, though the pictures should serve as a nice illustration of what's going on with the approximations for somebody just learning diffraction theory. I also demonstrate the Fraunhofer diffraction approximation is actually completely conceptually separate from Fresnel diffraction and that it makes little sense to use the Fresnel kernel as is typically shown in books. I show that Fraunhofer diffraction can be computed using the Fourier transform simply by arguing their equivalence from an impulse response standpoint. In this Mathematica notebook, I illustrate the various approximations used in diffraction theory by focusing on the phase of the impulse responses (Green's functions) implicit in each. MIT Ultrafast Optics and Quantum Electronics Group
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