Photonic Crystals: Mathematical Analysis and Numerical Approximation

Dörfler, Willy; Lechleiter, Armin; Plum, Michael; Schneider, Guido; Wieners, Christian

doi:10.1007/978-3-0348-0113-3

Cited by 58 publications

(62 citation statements)

References 24 publications

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“…In conservative systems, the permittivity ϵ is ω ‐independent and the constitutive relations reduces to

\hat{B} (x, ω) = Ĥ (x, ω), \hat{D} (x, ω) = ϵ (x) Ê (x, ω), ϵ (x) = a (x) .

This important approximation has been studied intensively and we summarize in this section some of the main mathematical results. Further information can for example be found in Kuchment …”

Section: Conservative Photonic Crystalsmentioning

confidence: 99%

Spectral properties of conservative, dispersive, and absorptive photonic crystals

Engström

Torshage

2018

GAMM-Mitteilungen

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“…In conservative systems, the permittivity ϵ is ω ‐independent and the constitutive relations reduces to

\hat{B} (x, ω) = Ĥ (x, ω), \hat{D} (x, ω) = ϵ (x) Ê (x, ω), ϵ (x) = a (x) .

This important approximation has been studied intensively and we summarize in this section some of the main mathematical results. Further information can for example be found in Kuchment …”

Section: Conservative Photonic Crystalsmentioning

confidence: 99%

Spectral properties of conservative, dispersive, and absorptive photonic crystals

Engström

Torshage

2018

GAMM-Mitteilungen

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“…Photonic crystals. Photonic crystals are artificial periodic optical media that are optical analogs of semi-conductors, which bring about major technological advances (see [111,206,245] for a nice physics introduction and bibliography, as well as [110,245] for mathematics surveys). The main equation to study here is the Maxwell operator with periodic coefficients.…”

Section: Inhomogeneous Equationsmentioning

confidence: 99%

Untitled

2016

Bull. Amer. Math. Soc.

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Abstract. The article surveys the main topics, techniques, and results of the theory of periodic operators arising in mathematical physics and other areas. Close attention is paid to studying analytic properties of Bloch and Fermi varieties, which significantly influence most spectral features of such operators.The approaches described are applicable not only to the standard model example of Schrödinger operator with periodic electric potential −Δ + V (x), but to a wide variety of elliptic periodic equations and systems, equations on graphs, ∂-operator, and other operators on abelian coverings of compact bases.Important applications are mentioned. However, due to the size restrictions, they are not dealt with in detail.

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“…In many situations these fields can -after exploiting some basic material properties -be described by Maxwell's equations in the electric field formulation [15,19] …”

Section: Maxwell's Equationsmentioning

confidence: 99%