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

  title={Transfer-matrix formulation of the scattering of electromagnetic waves and broadband invisibility in three dimensions},
  author={Farhang Loran and Ali Mostafazadeh},
  journal={arXiv: Quantum Physics},
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… 
Fundamental transfer matrix and dynamical formulation of stationary scattering in two and three dimensions
We offer a consistent dynamical formulation of stationary scattering in two and three dimensions that is based on a suitable multidimensional generalization of the transfer matrix. This is a linear
Transfermatrix in scattering theory: a survey of basic properties and recent developments
We give a pedagogical introduction to time-independent scattering theory in one dimension focusing on the basic properties and recent applications of transfer matrices. In particular, we begin
Dynamical formulation of low-energy scattering in one dimension
The transfer matrix M of a short-range potential may be expressed in terms of the timeevolution operator for an effective two-level quantum system with a time-dependent nonHermitian Hamiltonian. This
Propagation of electromagnetic waves in stationary anisotropic media
In this paper we have investigated the fundamental properties of the solutions of Maxwell’s equations describing free electromagnetic waves in stationary anisotropic media, with tensor
Transfer matrix for long-range potentials
We extend the notion of the transfer matrix of potential scattering to a large class of long-range potentials $v(x)$ and derive its basic properties. We outline a dynamical formulation of the
Transmission of low-energy scalar waves through a traversable wormhole
We study the scattering of low-energy massless and massive minimally coupled scalar fields by an asymptotically flat traversable wormhole. We provide a comprehensive treatment of this problem


Transfer matrices as nonunitary S matrices, multimode unidirectional invisibility, and perturbative inverse scattering
We show that in one dimension the transfer matrix M of any scattering potential v coincides with the S-matrix of an associated time-dependent non-Hermitian 2 x 2 matrix Hamiltonian H(\tau). If v is
A polarized transfer matrix for electromagnetic waves in structured media
Abstract The study of electromagnetic systems with dielectric or magnetic properties that vary spatially on or below the scale set by the wavelength of the radiation considered is of interest both in
Exactness of the Born approximation and broadband unidirectional invisibility in two dimensions
Achieving exact unidirectional invisibility in a finite frequency band has been an outstanding problem for many years. We offer a simple solution to this problem in two dimensions that is based on
Transfer matrix formulation of scattering theory in two and three dimensions
In one dimension one can dissect a scattering potential $ v(x) $ into pieces $ v_i(x) $ and use the notion of the transfer matrix to determine the scattering content of $ v(x) $ from that of $ v_i(x)
Exact solution of the two-dimensional scattering problem for a class of δ-function potentials supported on subsets of a line
We use the transfer matrix formulation of scattering theory in two-dimensions to treat the scattering problem for a potential of the form $v(x,y)=\zeta\,\delta(ax+by)g(bx-ay)$ where $\zeta,a$, and
A Dynamical Formulation of One-Dimensional Scattering Theory and Its Applications in Optics
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are
Wave reflection in dielectric media obeying spatial Kramers-Kronig relations
In a recent work, S.A.R. Horsley and coworkers [Nature Photon 9, 436-439 (2015)] showed rather interestingly that planar dielectric media, for which the real and imaginary parts of the dielectric
Scattering theory of waves and particles
Much progress has been made in scattering theory since the publication of the first edition of this book fifteen years ago, and it is time to update it. Needless to say, it was impossible to
Electromagnetic wave scatterings by anisotropic metamaterials: Generalized4×4transfer-matrix method
We establish a generalized $4\ifmmode\times\else\texttimes\fi{}4$ transfer-matrix method to study the scatterings of electromagnetic (EM) waves by anisotropic metamaterials, with incident waves
Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility
The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the $S$-matrix of a two-level time-dependent non-Hermitian Hamiltonian H(t). We show that