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arXiv · 1310.0592

A Dynamical Formulation of One-Dimensional Scattering Theory and Its Applications in Optics

Ali Mostafazadeh
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Abstract

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, anti-lasing, and unidirectional invisibility.

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quant-phhep-thmath-phmath.MPphysics.optics

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BibTeXRIS

Ali Mostafazadeh. 2013-10-02. A Dynamical Formulation of One-Dimensional Scattering Theory and Its Applications in Optics. https://doi.org/10.1016/j.aop.2013.11.008

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