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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper is concerned with the time-dependent Maxwell's equations for aplane interface between a negative material described by the Drude model andthe vacuum, which fill, respectively, two complementary half-spaces. In a firstpaper, we have constructed a generalized Fourier transform which diagonalizesthe Hamiltonian that represents the propagation of transverse electric waves.In this second paper, we use this transform to prove the limiting absorptionand limiting amplitude principles, which concern, respectively, the behavior ofthe resolvent near the continuous spectrum and the long time response of themedium to a time-harmonic source of prescribed frequency. This paper alsounderlines the existence of an interface resonance which occurs when thereexists a particular frequency characterized by a ratio of permittivities andpermeabilities equal to $-1$ across the interface. At this frequency, theresponse of the system to a harmonic forcing term blows up linearly in time.Such a resonance is unusual for wave problem in unbounded domains andcorresponds to a non-zero embedded eigenvalue of infinite multiplicity of theunderlying operator. This is the time counterpart of the ill-posdness of thecorresponding harmonic problem.

Spectral theory for Maxwell's equations at the interface of a  metamaterial. Part II: Limiting absorption, limiting amplitude principles and  interface resonance