Local Fields in Dielectric Nanospheres from a Microscopic and Macroscopic Point of View

We simulated dielectric nanospheres with a microscopic local field method and compared the results to the macroscopic mean field theory. From Maxwell´s equations we find uniform local fields inside a sphere exposed to an electric field E_a which was homogeneous before the sphere was brought in. The present paper raises the question about the validity of the macroscopic assumption. The dielectric spheres consist of neutral atoms on cubic lattice sites which show induced electronic polarization. For reasons of symmetry, the local field caused by the dipoles in the center of the sphere should be different from those at off-center locations resulting in an inhomogeneous polarization. This question about the validity is addressed by the microscopic method of local fields. With regard to dielectric nanospheres or other geometrical shapes which are used for nanodielectric composites the application of the microscopic local field method can calculate the actual local fields and polarizations whereas a macroscopic mean field calculation can yield misleading results.