The theory of second harmonic generation (SHG) in three-dimensional structures consisting of arbitrary distributions of metallic spheres made of centrosymmetric materials is developed by means of multiple scattering of electromagnetic multipole fields
The nonuniform electric field applied to the PEC or PMC will induce predominantly quadrupole and higher-order multipole fields
a fraction of a wavelength outside the circumscribing sphere, and reactive fields between [S.sub.a] and a fraction of a wavelength outside the circumscribing sphere, but with a ratio of the energy stored in the reactive fields to the power radiated by the electric dipole that increases faster with decreasing electrical size of [V.sub.a] than the same ratio for the fields induced by the uniform electric field .
This field is a function of both the applied and multipole fields
in the media.
Laplace's equations in dimensions higher than 3 correspond to electric multipole fields
of order 1, where 1 = n - 3.
If ka is below this value it cost much power to add currents that radiate multipole fields
of index l, or higher.
For the proposed setup, the volume between two nested cylinders made from magnetic multipole fields
is used to store the UCN (Fig.
studied the scattering of a Hermite-Gaussian beam by a chiral sphere by using the relations between the multipole fields
and the conventional Hermite-Gaussian beam .