Rational eigenvalue problems and applications to photonic crystals

We establish new analytic results for a general class of rational spectral problems. They arise e.g. in modelling photonic crystals whose capability to control the flow of light depends on specific ...

[1]  C. Tretter,et al.  Variational principles and eigenvalue estimates for unbounded block operator matrices and applications , 2004 .

[2]  A. A. Shkalikov,et al.  The Essential Spectrum of Some Matrix Operators , 1994 .

[3]  Christian Wieners,et al.  A computer-assisted proof for photonic band gaps , 2009 .

[4]  Über eine Klasse polynomialer Scharen selbstadjungierter Operatoren im Hilbertraum. II , 1973 .

[5]  Stefano Giani,et al.  An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems , 2012 .

[6]  R. Mennicken,et al.  Spectral Decomposition of Symmetric Operator Matrices , 1996 .

[7]  C. Engström ON THE SPECTRUM OF A HOLOMORPHIC OPERATOR-VALUED FUNCTION WITH APPLICATIONS TO ABSORPTIVE PHOTONIC CRYSTALS , 2010 .

[8]  H. Langer,et al.  Variational principles for eigenvalues of block operator matrices , 2002 .

[9]  V. G. Sigillito,et al.  Eigenvalues of the Laplacian in Two Dimensions , 1984 .

[10]  Otto Karma,et al.  Approximation in eigenvalue problems for holomorphic fredholm operator functions I , 1996 .

[11]  K. Schmidt,et al.  Computation of the band structure of two-dimensional photonic crystals with hp finite elements , 2009 .

[12]  Mark Embree,et al.  The role of the penalty in the local discontinuous Galerkin method for Maxwell’s eigenvalue problem , 2006 .

[13]  Ryszard Buczynski,et al.  FDTD analysis of modal dispersive properties of nonlinear photonic crystal fibers , 2015 .

[14]  C. Tretter,et al.  Non-symmetric perturbations of self-adjoint operators , 2016, 1604.00293.

[15]  Steven G. Johnson,et al.  Photonic Crystals: Molding the Flow of Light , 1995 .

[16]  E B Davies,et al.  Spectral Pollution , 2002 .

[17]  Christian Lage,et al.  Concepts: An object-oriented software package for partial differential equations , 2002 .

[18]  Tosio Kato Perturbation theory for linear operators , 1966 .

[19]  Perturbation of spectra and spectral subspaces , 2003, math/0306025.

[20]  J. Hesthaven,et al.  Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications , 2007 .

[21]  Alexander Figotin,et al.  Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. II. Two-Dimensional Photonic Crystals , 1996, SIAM J. Appl. Math..

[22]  D. Kressner,et al.  Linearization techniques for band structure calculations in absorbing photonic crystals , 2012 .

[23]  Christiane Tretter,et al.  Spectral inclusion for unbounded block operator matrices , 2009 .

[24]  S. Fan,et al.  Perturbation Theory for Plasmonic Modulation and Sensing , 2010, 1009.1339.

[25]  I. Babuska,et al.  The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries , 1988 .

[26]  C. Tretter Spectral Theory Of Block Operator Matrices And Applications , 2008 .

[27]  M. A. Kaashoek,et al.  Minimal Factorization of Matrix and Operator Functions , 1980 .

[28]  A. Buffa,et al.  Discontinuous Galerkin approximation of the Laplace eigenproblem , 2006 .

[29]  Chao Yang,et al.  ARPACK users' guide - solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods , 1998, Software, environments, tools.

[30]  Variational Principles for Eigenvalues of Self-adjoint Operator Functions , 2004 .

[31]  J. Osborn Spectral approximation for compact operators , 1975 .

[32]  Chan,et al.  Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials. , 1994, Physical review. B, Condensed matter.

[33]  Douglas N. Arnold,et al.  Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems , 2001, SIAM J. Numer. Anal..

[34]  Otto Karma,et al.  Approximation in eigenvalue problems for holomorphic fredholm operator functions Ii (Convergence Rate) , 1996 .

[35]  A. Markus,et al.  Introduction to the Spectral Theory of Polynomial Operator Pencils , 2012 .

[36]  P. Kuchment Floquet Theory for Partial Differential Equations , 1993 .

[37]  Andrew V. Knyazev,et al.  New A Priori FEM Error Estimates for Eigenvalues , 2006, SIAM J. Numer. Anal..

[38]  H. Latifi,et al.  Bandgap generation and enhancement in polaritonic cylinder square-lattice photonic crystals , 2012 .

[39]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[40]  M. Solomjak,et al.  Spectral theory of selfadjoint operators in Hilbert space , 1987 .

[41]  J. Joannopoulos,et al.  Nature of lossy Bloch states in polaritonic photonic crystals , 2004 .