Generalized Lorenz-Mie Theory for a sphere with an eccentrically located inclusion, and optical chaos

This paper deals with the case when a homogeneous spherical particle (called the inclusion) is embedded at an arbitrary location inside a sphere (called the main or host sphere). Similarly as for previous Generalized Lorenz-Mie Theories, many applications are expected from this theory, in particular in the field of optical particle characterization. Another interesting prospect concerns the behavior of morphology-dependent resonances (MDRs). From an electromagnetic point of view, these MDRs correspond to solutions of characteristic equations associated with boundary conditions and lead to internal fields which are concentrated near the rim of the scatterer. It is also shown that this geometrical optics approximation (expressed in terms of rays) is equivalent to a mechanical problem (expressed in terms of trajectories). This mechanical problem leads to chaotic behavior corresponding to optical chaos phenomena in the optical language. We therefore exhibit a class of particles (i) for which the electromagnetic problem is exactly solvable in the framework of a GLMT and (ii) which exhibits chaotic signatures. It is expected that these chaotic signatures would be revealed in salient features of the scattering diagrams, opening the way to refined optical particle characterization in the presence of inhomogeneities.