ON THE SPECTRUM OF A HOLOMORPHIC OPERATOR-VALUED FUNCTION WITH APPLICATIONS TO ABSORPTIVE PHOTONIC CRYSTALS

DOI10.1142/S0218202510004611zbMath1213.47013MaRDI QIDQ3161586

Christian Engström

Publication date: 15 October 2010

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

Maxwell equationsnonlinear eigenvalue problemFloquet theoryoperator pencilphotonic crystalBloch wave

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) General theory of partial differential operators (47F05) Electromagnetic theory (general) (78A25)

Related Items

Linearization techniques for band structure calculations in absorbing photonic crystals ⋮ Topology and shape optimization of plasmonic nano-antennas ⋮ Rational eigenvalue problems and applications to photonic crystals ⋮ Finite element calculation of photonic band structures for frequency dependent materials ⋮ Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations ⋮ Efficient and reliable hp-FEM estimates for quadratic eigenvalue problems and photonic crystal applications ⋮ Accumulation of complex eigenvalues of a class of analytic operator functions ⋮ PDE eigenvalue iterations with applications in two-dimensional photonic crystals

Cites Work

• On the basis property of the eigenvectors of a holomorphic selfadjoint operator-valued function
• The spectral properties of a certain class of self-adjoint operator functions
• Spectral theory of time dispersive and dissipative systems
• Spectral Properties of Classical Waves in High-Contrast Periodic Media
• Band structure of absorptive photonic crystals
• Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. I. Scalar Model
• On the Spectrum of an Operator Pencil with Applications to Wave Propagation in Periodic and Frequency Dependent Materials
• Partial Differential Equations with Periodic Coefficients and Bloch Waves in Crystals
• Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. II. Two-Dimensional Photonic Crystals
• A Floquet--Bloch Decomposition of Maxwell's Equations Applied to Homogenization
• Homogenization of Dispersive Material Parameters for Maxwell's Equations Using a Singular Value Decomposition
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