Polarization and resonant absorption in intersecting cylinders and spheres

Abstract

The polarization of a pair of merging spheres and merging cylinders of any complex dielectric constant immersed in an external electric field has been solved. Any degree of intersection, including touching, is covered by the result. The method for cylinders is based on the solution of Laplace’s equation with boundary conditions on the conjugate surfaces in a modified bicylindrical frame. The result is presented as an integral over a continuum of eigenstates. For merging spherical particles solving the boundary problem requires a Miller–Fok integral transformation. Imaginary parts of polarizabilities were calculated for aluminum cylinders and spheres to assess the spectral absorption response of small merging particles. The relative spacing has a significant influence on optical response.