Unidirectionally Invisible Potentials as Local Building Blocks of all Scattering Potentials

TL;DR

This paper presents a method to construct scattering potentials with customizable properties at any chosen wavenumber, using a finite sum of unidirectionally invisible potentials, with applications in optical device design.

Contribution

It introduces explicit formulas for building complex scattering potentials from simple unidirectionally invisible components, enabling tailored optical functionalities.

Findings

Explicit formulas for constructing potentials with desired scattering properties.

Potential applications in designing optical devices like lasers and absorbers.

Demonstrates the versatility of unidirectionally invisible potentials as building blocks.

Abstract

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. Our solution involves expressing v(x) as the sum of at most six unidirectionally invisible finite-range potentials for which we give explicit formulas. Our results can be employed for designing optical potentials. We discuss its application in modeling threshold lasers, coherent perfect absorbers, and bidirectionally and unidirectionally reflectionless absorbers, amplifiers, and phase shifters.