English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Achieving exact unidirectional invisibility in a finite frequency band hasbeen an outstanding problem for many years. We offer a simple solution to thisproblem in two dimensions that is based on our solution to another more basicopen problem of scattering theory, namely finding scattering potentials$v(x,y)$ in two dimensions whose scattering problem is exactly solvable forenergies not exceeding a critical value $E_c$. This extends the notion ofquasi-exact solvability to scattering theory and yields a simple conditionunder which the first Born approximation gives the exact expression for thescattering amplitude whenever the wavenumber for the incident wave is notgreater than $\alpha:=\sqrt{E_c}$. Because this condition only restricts the$y$-dependence of $v(x,y)$, we can use it to determine classes of suchpotentials that have certain desirable scattering features. This leads to apartial inverse scattering scheme that we employ to achieve perfect broadbandunidirectional invisibility in two dimensions. We discuss an opticalrealization of the latter by identifying a class of two-dimensional isotropicactive media that do not scatter incident TE waves with wavenumber in the range$(\alpha/\sqrt 2,\alpha]$ and source located at $x=\infty$, while scatteringthe same waves if their source is relocated to $x=-\infty$.

Quasi-Exactly Solvable Scattering Problems, Exactness of the Born Approximation, and Broadband Unidirectional Invisibility in Two Dimensions