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Physics of Spectral Singularities
Ali Mostafazadeh
Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their p…
Unidirectionally Invisible Potentials as Local Building Blocks of all Scattering Potentials
Ali Mostafazadeh
We give a complete solution of the problem of constructing a scattering potential v(x) that possesses scattering properties of one's choice at an arbitrary prescribed wavenumber. O…
Generalized Unitarity and Reciprocity Relations for PT-symmetric Scattering Potentials
Ali Mostafazadeh
We derive certain identities satisfied by the left/right-reflection and transmission amplitudes, and , of general -symmetric scattering potentials. We…
Spectral Singularities and CPA-Laser Action in a Weakly Nonlinear PT-Symmetric Bilayer Slab
Ali Mostafazadeh
We study optical spectral singularities of a weakly nonlinear PT-symmetric bilinear planar slab of optically active material. In particular, we derive the lasing threshold conditio…
Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility
Ali Mostafazadeh
The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the -matrix of a two-level time-dependent non-Hermitian Hamiltonian H(…
Adiabatic Series Expansion and Higher-Order Semiclassical Approximations in Scattering Theory
Ali Mostafazadeh
The scattering properties of any complex scattering potential, v:R -> C, can be obtained from the dynamics of a particular non-unitary two-level quantum system S_v. The application…