Light scattering from a pair of conducting, osculating spheres

The fields from a system composed of two conducting, osculating spheres are derived using an extension of Mie theory. The boundary conditions are satisfied on both surfaces by expanding the fields in terms of vector spherical harmonics and translating them between the coordinate systems of the two spheres. We give explicit expressions for the far-field and the cross-sections. Order-of-scatter methods diverge when finding the scattered field coefficients, so the coefficients must be found directly. Splittings are discovered in the solutions of the scattered field, and we find very good agreement between the average of the solutions with experimental microwave backscatter measurements.