Photonics in highly dispersive media: the exact modal expansion.

We present exact modal expansions for photonic systems including highly dispersive media. The formulas, based on a simple version of the Keldyš theorem, are very general since both permeability and permittivity can be dispersive, anisotropic, and even possibly nonreciprocal. A simple dispersive test case where both plasmonic and geometrical resonances strongly interact exemplifies the numerical efficiency of our approach.

[1]  Alastair Spence,et al.  Photonic band structure calculations using nonlinear eigenvalue techniques , 2005 .

[2]  Young,et al.  Completeness and time-independent perturbation of the quasinormal modes of an absorptive and leaky cavity. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[3]  Avner Friedman,et al.  Nonlinear eigenvalue problems , 1968 .

[4]  J. E. Román,et al.  Eigenmode computations of frequency-dispersive photonic open structures: A non-linear eigenvalue problem , 2018 .

[5]  W. Beyn An integral method for solving nonlinear eigenvalue problems , 2012 .

[6]  Christophe Geuzaine,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[7]  Resonant-state expansion Born Approximation with a correct eigen-mode normalisation applied to Schrodinger's equation or general wave equations , 2015, 1508.04411.

[8]  Benjamin Vial,et al.  Quasimodal expansion of electromagnetic fields in open two-dimensional structures , 2013, 1311.3244.

[9]  Marc Van Barel,et al.  Nonlinear eigenvalue problems and contour integrals , 2016, J. Comput. Appl. Math..

[10]  Christophe Geuzaine,et al.  Non-linear eigenvalue problems with GetDP and SLEPc: Eigenmode computations of frequency-dispersive photonic open structures , 2018, Comput. Phys. Commun..

[11]  M. Perrin Eigen-energy effects and non-orthogonality in the quasi-normal mode expansion of Maxwell equations. , 2016, Optics express.

[12]  Heinrich Voss,et al.  Nonlinear Eigenvalue Problems , 2012 .

[13]  Boris Gralak,et al.  Calculation and analysis of the complex band structure of dispersive and dissipative two-dimensional photonic crystals , 2015, 1512.01508.

[14]  Philippe Lalanne,et al.  Light Interaction with Photonic and Plasmonic Resonances , 2017, Laser & Photonics Reviews.

[15]  Gerhard Unger,et al.  Convergence Orders of Iterative Methods for Nonlinear Eigenvalue Problems , 2013 .

[16]  Philippe Lalanne,et al.  Rigorous modal analysis of plasmonic nanoresonators , 2017, 1711.05011.

[17]  Vicente Hernández,et al.  SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems , 2005, TOMS.

[18]  P Lalanne,et al.  Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure. , 2013, Optics express.

[19]  Stefan Güttel,et al.  The nonlinear eigenvalue problem∗ , 2017 .

[20]  A. Bossavit Solving Maxwell equations in a closed cavity, and the question of 'spurious modes' , 1990 .

[21]  P Lalanne,et al.  Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators. , 2013, Physical review letters.

[22]  M Garcia-Vergara,et al.  Extracting an accurate model for permittivity from experimental data: hunting complex poles from the real line. , 2016, Optics letters.

[23]  Christophe Geuzaine,et al.  A general environment for the treatment of discrete problems and its application to the finite element method , 1998 .

[24]  M. Keldysh,et al.  ON THE COMPLETENESS OF THE EIGENFUNCTIONS OF SOME CLASSES OF NON-SELFADJOINT LINEAR OPERATORS , 1971 .

[25]  E. Muljarov,et al.  Resonant-state expansion of dispersive open optical systems: Creating gold from sand , 2015, 1510.01182.

[26]  Christian Engström,et al.  Rational eigenvalue problems and applications to photonic crystals , 2017 .

[27]  Vladimir Kozlov,et al.  Differential Equations with Operator Coefficients: with Applications to Boundary Value Problems for Partial Differential Equations , 1999 .

[28]  Jeff F. Young,et al.  Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics , 2013, 1312.2939.