Unidirectional Invisibility and Nonreciprocal Transmission in Two and Three Dimensions

Abstract

We explore the phenomenon of unidirectional invisibility in two dimensions, examine its optical realizations, and discuss its three-dimensional generalization. In particular we construct an infinite class of unidirectionally invisible optical potentials that describe the scattering of normally incident transverse electric waves by an infinite planar slab with refractive-index modulations along both the normal directions to the electric field. A by-product of this investigation is a demonstration of nonreciprocal transmission in two dimensions. To elucidate this phenomenon we state and prove a general reciprocity theorem that applies to quantum scattering theory of real and complex potentials in two and three dimensions.

16 pages, 2 figures

References in corpus (7)

• Invisibility and PT-symmetry
• The transfer matrix: a geometrical perspective
• Wave reflection in dielectric media obeying spatial Kramers-Kronig relations
• Half-spectral unidirectional invisibility in non-Hermitian periodic optical structures
• Transfer Matrix Formulation of Scattering Theory in Two and Three Dimensions
• Generalized Unitarity and Reciprocity Relations for PT-symmetric Scattering Potentials
• Perturbative Unidirectional Invisibility

Cited by in corpus (13)

• Fundamental transfer matrix and dynamical formulation of stationary scattering in two and three dimensions
• Perfect Broadband Invisibility in Isotropic Media with Gain and Loss
• Nonlinear Scattering and Its Transfer Matrix Formulation in One Dimension
• Quasi-Exactly Solvable Scattering Problems, Exactness of the Born Approximation, and Broadband Unidirectional Invisibility in Two Dimensions
• Transfer-matrix formulation of the scattering of electromagnetic waves and broadband invisibility in three dimensions
• A Class of Exactly Solvable Scattering Potentials in Two Dimensions, Entangled State Pair Generation, and a Grazing Angle Resonance Effect
• Realization of $\mathcal{P}\mathcal{T}$-symmetric and $\mathcal{P}\mathcal{T}$-symmetry broken states in static optical lattice potentials
• Exact Solution of the Two-Dimensional Scattering Problem for a Class of $\delta$-Function Potentials Supported on Subsets of a Line
• Exactness of the first Born approximation in electromagnetic scattering
• Scattering Theory and $\mathcal{P}\mathcal{T}$-Symmetry
• Broadband directional invisibility
• Potentials with Identical Scattering Properties Below a Critical Energy
• Reciprocity Theorem and Fundamental Transfer Matrix