期刊
ANNALS OF PHYSICS
卷 341, 期 -, 页码 77-85出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2013.11.008
关键词
Scattering theory; Transfer matrix; Complex potential; Spectral singularity; Anti-laser; Unidirectional invisibility
资金
- Scientific and Technological Research Council of Turkey (TUBITAK) [112T951]
- Turkish Academy of Sciences (TUBA)
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 given as solutions of a set of dynamical equations. By decoupling and partially integrating these equations, we reduce the scattering problem to a second order linear differential equation with universal initial conditions that is equivalent to an initial-value time-independent Schrodinger equation. We give explicit formulas for the reflection and transmission amplitudes in terms of the solution of either of these equations and employ them to outline an inverse-scattering method for constructing finite-range potentials with desirable scattering properties at any prescribed wavelength. In particular, we construct optical potentials displaying threshold lasing, antilasing, and unidirectional invisibility. (C) 2013 Elsevier Inc. All rights reserved.
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