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We develop a transfer-matrix formulation of the scattering of electromagneticwaves by a general isotropic medium which makes use of a notion ofelectromagnetic transfer matrix $\mathbf{M}$ that does not involve slicing ofthe scattering medium or discretization of some of the position- ormomentum-space variables. This is a linear operator that we can express as a$4\times 4$ matrix with operator entries and identify with the S-matrix of aneffective nonunitary quantum system. We use this observation to establish thecomposition property of $\mathbf{M}$, obtain an exact solution of thescattering problem for a non-magnetic point scatterer that avoids thedivergences of the Green's function approaches, and prove a generalinvisibility theorem. The latter allows for an explicit characterization of aclass of isotropic media ${\cal M}$ displaying perfect broadband invisibilityfor electromagnetic waves of arbitrary polarization provided that theirwavenumber $k$ does not exceed a preassigned critical value $\alpha$, i.e.,${\cal M}$ behaves exactly like vacuum for $k\leq\alpha$. Generalizing thisphenomenon, we introduce and study $\alpha$-equivalent media that, bydefinition, have identical scattering features for $k\leq\alpha$.

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