Abstract
This chapter focuses on the mathematics underlying the scattering of electromagnetic waves. An electromagnetic wave is comprised of an electric field and a magnetic field, both of which are functions of time and space as the wave propagates. The direction of propagation and the directions of these fields form a mutually orthogonal triad. When an electromagnetic field encounters an electron bound to a molecule, the electron is accelerated by the electric field of the wave. An accelerated electron will also radiate electromagnetic energy in the form of waves in all directions (to some extent)—this is known as scattered radiation. The chapter first considers Maxwell's equations of electromagnetic theory before discussing the vector Helmholtz equation for electromagnetic waves, the Lorentz-Mie solution and its construction, the Rayleigh scattering limit, and the radiation field generated by a Hertzian dipole.
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