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

Abstract

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 $\mathbf{M}$ 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 $4\times 4$ 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 $\mathbf{M}$, 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 $\mathcal{M}$ displaying perfect broadband invisibility for electromagnetic waves of arbitrary polarization provided that their wavenumber $k$ does not exceed a preassigned critical value $\alpha$, i.e., $\mathcal{M}$ behaves exactly like vacuum for $k\le \alpha$. Generalizing this phenomenon, we introduce and study $\alpha$-equivalent media that, by definition, have identical scattering features for $k\le \alpha$.

Expanded published version, 32 pages

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• Dynamical formulation of low-energy scattering in one dimension
• Exactness of the first Born approximation in electromagnetic scattering
• Modeling Nonlinear Optics with the Transfer Matrix Method
• Introducing a general method for solving electromagnetic radiation problem in an arbitrary linear medium