#PhysicsFactlet While electrodynamics is well understood, there aren't many scattering problems we can actually solve.

[j_bertolotti@mathstodon.xyz]

#PhysicsFactlet
While electrodynamics is well understood, there aren't many scattering problems we can actually solve. A plane wave scattering from a uniform dielectric sphere is one of those few, and the solution was originally found by Gustav Mie in 1908. The solution is extremely elegant (albeit cumbersome), but not very practical for larger spheres, as it takes the form of a summation, and the number of terms we need to take into account grows fast with the radius.
Nevertheless it has become the prototype for all scattering solutions, and it has been extended to coated spheres, metallic spheres, birefringent spheres, ellipsoids etc etc.

In the animation: the scattered field from a uniform, dielectric disk (the 2D equivalent of the Mie solution). The source is from the bottom, and the (linear) polarization is assumed to be out of the plane.
The numerical solution has been obtained using a hand-coded finite-difference method to solve the Helmholtz equation.

#Optics #Physics #MieScattering