Transfer-matrix formulation of the scattering of electromagnetic waves and broadband invisibility in three dimensions

We develop a transfer-matrix formulation of the scattering of electromagnetic waves by a general isotropic medium which makes use of a notion of electromagnetic transfer matrix that does not involve slicing of the scattering medium or discretization of some of the position- or momentum-space variables. This is a linear operator that we can express as a matrix with operator entries and identify with the S-matrix of an effective nonunitary quantum system. We use this observation to establish the composition property of , obtain an exact solution of the scattering problem for a non-magnetic point scatterer that avoids the divergences of the Green's function approaches, and prove a general invisibility theorem. The latter allows for an explicit characterization of a class of isotropic media displaying perfect broadband invisibility for electromagnetic waves of arbitrary polarization provided that their wavenumber k does not exceed a preassigned critical value , i.e. behaves exactly like vacuum for . Generalizing this phenomenon, we introduce and study -equivalent media that, by definition, have identical scattering features for .