The KdV hierarchy in optics

17Citations
Citations of this article
6Readers
Mendeley users who have this article in their library.

Abstract

There is a well explored relationship between quantum mechanical scattering from a potential and the Korteweg-de Vries (KdV) equation of fluid dynamics: if the potential is 'evolved' according to the KdV equation then it will have the same reflectivity and transmissivity as a function of energy, for each snapshot in time. In this work we explore this connection in optics, where the permittivity plays the role of the potential. We begin by deriving the relationship between the Helmholtz equation and the KdV equation in terms of the current induced in a material when a permittivity profile is changed slightly. It is then shown that the KdV equation can be used to design a plethora of bounded complex potentials that are relfectionless from both sides for all angles of incidence, and planar periodic media that exhibit a real Bloch vector for all angles of propagation. Finally we apply the KdV equation to reduce the reflection of a wave from an interface between two media of differing refractive indices.

References Powered by Scopus

Controlling electromagnetic fields

8035Citations
N/AReaders
Get full text

Metamaterial electromagnetic cloak at microwave frequencies

6978Citations
N/AReaders
Get full text

Observation of parity-time symmetry in optics

3141Citations
N/AReaders
Get full text

Cited by Powered by Scopus

Some new families of solitary wave solutions of the generalized Schamel equation and their applications in plasma physics

104Citations
N/AReaders
Get full text

Bidirectional invisibility in Kramers-Kronig optical media

39Citations
N/AReaders
Get full text

Solitary wave solutions for the KdV-type equations in plasma: a new approach with the Kudryashov function

39Citations
N/AReaders
Get full text

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Cite

CITATION STYLE

APA

Horsley, S. A. R. (2016). The KdV hierarchy in optics. Journal of Optics (United Kingdom), 18(8). https://doi.org/10.1088/2040-8978/18/8/085104

Readers' Seniority

Tooltip

PhD / Post grad / Masters / Doc 2

40%

Researcher 2

40%

Lecturer / Post doc 1

20%

Readers' Discipline

Tooltip

Physics and Astronomy 4

80%

Computer Science 1

20%

Save time finding and organizing research with Mendeley

Sign up for free