Raegan Bray

2022-07-22

Why do electromagnetic waves diffract?

Monica Dennis

Getting down to it, it's a mathematical property of the wave equation. Any wave-like phenomena will experience diffraction.
$\frac{{\mathrm{\partial }}^{2}}{\mathrm{\partial }{x}^{2}}U+\frac{{\mathrm{\partial }}^{2}}{\mathrm{\partial }{y}^{2}}U+\frac{{\mathrm{\partial }}^{2}}{\mathrm{\partial }{z}^{2}}U=\frac{1}{{c}^{2}}\frac{{\mathrm{\partial }}^{2}}{\mathrm{\partial }{t}^{2}}U$
The easiest way to see why this is to consider the Fourier transform property $\frac{{\mathrm{\partial }}^{2}}{\mathrm{\partial }{x}^{2}}\to -{k}_{x}^{2}$. Since ${k}_{x}$ determines the degree of propagation in the x direction, this lends itself to the physical interpretation that field variation in the x direction leads to propagation in the x direction as well. For something like a laser beam to be self contained, it should go to 0 far away from the beam, but be nonzero at the beam. Hence, variation in the transverse profile, and propagation in the transverse profile as well.
This also explains why waves will diffract at barriers, or waves that are more closely contained will diffract more. With a bit of maniuplation, it's also easy to show that lower frequencies will diffract more than higher frequencies.

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