Light Scattering and the electromagnetic near-field from a nanosphere near to the surface of a semi-infinite medium

Light Scattering and the near field of a linearly polarized monochromatic electromagnetic wave produced by a nanosphere of radius R located in vacuum to a distance D near to the surface of a semi-infinite homogeneous medium is studied theoretically. The space is divided in three regions: I) in the sphere, II) out of the sphere in vacuum III) out of the sphere in the homogenous medium. Using a multipolar expansion and the boundary conditions the Maxwell's equations are solved. As a consequence of the presence of the surface an image mirror of the sphere is considered, then a shift phase produced for this image sphere is assumed, therefore these fields should be written in another reference system, hence the addition theorem for vector spherical wave functions is used.