G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciraci, C. Fang et al., Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas, Nature Photon, vol.8, p.835, 2014.

B. Bai and L. Li, J. Opt. A, vol.7, pp.271-278, 2005.

, Group-theoretic approach to enhancing the Fourier modal method for crossed gratings with one or two reflection symmetries

Q. Bai, M. Perrin, C. Sauvan, J. Hugonin, and P. Lalanne, Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure, Opt. Express, vol.21, p.27371, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00917914

G. D. Bernasconi, J. Butet, and O. J. Martin, Mode analysis of second-harmonic generation in plasmonic nanostructures, J. Opt. Soc. Am. B, vol.33, p.768, 2016.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. Hopman et al., Opt. Quant. Electron, vol.38, pp.731-759, 2006.

F. Bigourdan, J. Hugonin, and P. Lalanne, periodic-Fourier modal method for analysis of body-of-revolution photonic structures, J. Opt. Soc. Am. A, vol.31, pp.1303-1311, 2014.

A. Bonnet-ben-dhia, C. Carvalho, and P. Ciarlet, Mesh requirements for the finite element approximation of problems with sign-changing coefficients, Numer. Math, vol.138, pp.801-838, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01335153

A. Bonnet-ben-dhia, L. Chesnel, and P. Ciarlet, Two-dimensional Maxwell's equations with sign-changing coefficients, Appl. Numer. Math, vol.79, pp.29-41, 2014.

A. Bonnet-ben-dhia, L. Chesnel, and P. Ciarlet, Commun. Part. Diff. Eq, vol.39, pp.1007-1031, 2014.

Y. Brûlé, B. Gralak, and G. Demésy, Calculation and analysis of the complex band structure of dispersive and dissipative two-dimensional photonic crystals, J. Opt. Soc. Am. B, vol.33, p.691, 2016.

D. A. Bykov and L. L. Doskolovich, Numerical methods for calculating poles of the scattering matrix with applications in grating theory, J. Lightwave Technol, vol.31, p.793, 2013.

Q. Cao, P. Lalanne, and J. Hugonin, Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides, J. Opt. Soc. Am A, vol.19, pp.335-338, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00867916

R. K. Chang and A. J. Campillo, Optical processes in microcavities, 1996.

R. Chern, C. Chang, and C. Chang, Surface and bulk modes for periodic structures of negative index materials, Phys. Rev. B, vol.74, p.155101, 2006.

K. Cognée, W. Yan, F. China, D. Balestri, F. Intonti et al., Mapping Complex Mode Volumes with Cavity Perturbation Theory

S. Collin, G. Vincent, R. Haïdar, N. Bardou, S. Rommeluère et al., Nearly Perfect Fano Transmission Resonances through Nanoslits Drilled in a Metallic Membrane, Phys. Rev. Lett, vol.104, p.27401, 2010.

J. Ctyroky, S. Helfert, R. Pregla, P. Bienstman, R. Baets et al., Opt. Quantum Electronics, vol.34, pp.455-470, 2002.

, Bragg waveguide grating as a 1D photonic bandgap structure: cost 268 modelling task

L. M. Delves and J. N. Lyness, Math. Comp, vol.21, pp.543-560, 1967.

, A numerical method for locating the zeros of an analytic function

G. Demésy, F. Zolla, A. Nicolet, M. Commandré, and C. Fossati, The finite element method as applied to the diffraction by an anisotropic grating, Opt. Express, vol.15, p.18089, 2007.

G. Demésy, A. Nicolet, B. Gralak, C. Geuzaine, C. Campos et al., Eigenmode computations of frequency-dispersive photonic open structures: A non-linear eigenvalue problem

P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, IEEE Transactions on Magnetics, vol.34, pp.3395-3398, 1998.

, A general environment for the treatment of discrete problems and its application to the finite element method

R. Faggiani, J. Yang, and P. Lalanne, Quenching, Plasmonic, and Radiative Decays in Nanogap Emitting Devices, vol.2, pp.1739-7144, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01381391

M. Garcia-vergara, G. Demésy, and F. Zolla, Opt. Lett, vol.42, p.1145, 2017.

, Extracting an accurate model for permittivity from experimental data: hunting complex poles from the real line

J. Gérard, Top. Appl. Phys, vol.90, p.269, 2003.

, Solid-state cavity-quantum electrodynamics with self-assembled quantum dots

C. Geuzaine and J. Remacle, Gmsh: A 3-D finite element mesh generator with built-in pre-and post-processing facilities, International Journal for Numerical Methods in Engineering, vol.79, pp.1309-1331, 2009.

G. Granet and B. , J. Opt. Soc. Am. A, vol.13, issue.5, pp.1019-1023, 1996.

, Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization

G. Granet, J. Opt. Soc. Am. A, vol.16, pp.2510-2516, 1999.

, Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution

A. Gras and W. Yan,

V. Hernandez, J. E. Roman, and V. Vidal, SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems, ACM Trans. Math. Software, vol.31, pp.351-362, 2005.

, see the webpage of PL at LP2N

J. Hugonin and P. Lalanne, J. Opt. Soc. Am. A, vol.22, pp.1844-1849, 2005.

J. Jin, The Finite Element Method in Electromagnetics, 2002.

P. Kravanja and M. V. Barel, Computing the Zeros of Analytic Functions, Lecture Notes in Mathematics, vol.1727, 2000.

P. T. Kristensen, C. Van-vlack, and S. Hughes, Generalized effective mode volume for leaky optical cavity, Opt. Lett, vol.37, p.1649, 2012.

P. Lalanne and G. M. Morris, Highly improved convergence of the coupled-wave method for TM polarization, J. Opt. Soc. Am. A, vol.13, pp.779-784, 1996.

P. Lalanne and M. Jurek, Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization, J. Mod. Opt, vol.45, pp.1357-1374, 1998.

P. Lalanne, M. Besbes, J. P. Hugonin, S. Van-haver, O. T. Janssen et al., , vol.2, p.7022, 2007.

P. Lalanne, W. Yan, V. Kevin, C. Sauvan, and J. Hugonin, Light interaction with photonic and plasmonic resonances, vol.12, p.1700113, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01772412

P. Lalanne, S. Coudert, G. Duchateau, S. Dilhaire, K. Vynck et al., Structural slow waves: parallels between photonic crystal and plasmonic waveguides

J. R. De-lasson, J. Mørk, and P. T. Kristensen, J. Opt. Soc. Am. B, vol.30, 1996.

, Three-dimensional integral equation approach to light scattering, extinction cross sections, local density of states, and quasi-normal modes

E. Lassale, N. Bonod, T. Durt, and B. Stout, Interplay between spontaneous decay rates and Lamb shifts in open photonic systems, Opt. Lett, vol.43, p.1950, 2018.

J. R. De-lasson, L. H. Frandsen, P. Gutsche, S. Burger, O. S. Kim et al., Opt. Express, vol.26, p.11366, 2018.

G. Lecamp, J. P. Hugonin, and P. Lalanne, Theoretical and computational concepts for periodic optical waveguides, Opt. Express, vol.15, pp.11042-60, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00869734

P. T. Leung, S. Y. Liu, and K. Young, Completeness and time-independent perturbation of the quasinormal modes of an absorptive and leaky cavity, Phys. Rev. A, vol.49, p.3982, 1994.

L. Li, Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings, J. Opt. Soc. Am. A, vol.13, pp.1024-1035, 1996.

L. Li, Use of Fourier series in the analysis of discontinuous periodic structures, J. Opt. Soc. Am. A, vol.13, pp.1870-1876, 1996.

L. Li, New formulation of the Fourier modal method for crossed surface-relief gratings, J. Opt. Soc. Am. A, vol.14, pp.2758-2767, 1997.

L. Li, J. Opt. A: Pure Appl. Opt, vol.5, pp.345-355, 2003.

, Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors

Y. Li, H. Liu, H. Jia, F. Bo, G. Zhang et al., Fully vectorial modeling of cylindrical microresonators with aperiodic Fourier modal method, J. Opt. Soc. Am. A, vol.31, issue.11, pp.2459-2466, 2014.

H. Liu, DIF CODE for Modeling Light Diffraction in Nanostructures, 2010.

M. Luo and Q. H. Liu, J. Opt. Soc. Am. A, vol.27, p.1878, 2010.

B. Maes, J. Petracek, S. Burger, P. Kwiecien, J. Luksch et al., Simulations of high-Q optical nanocavities with a gradual 1D bandgap, vol.21, p.6794, 2013.

M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings, J. Opt. Soc. Am. A, vol.12, pp.1068-1076, 1995.

R. M. More, Theory of decaying states, vol.4, p.1782, 1971.

R. M. More and E. Gerjuoy, Properties of Resonance Wave Functions, vol.7, p.1288, 1973.

A. Moreau, C. Ciraci, J. J. Mock, R. T. Hill, Q. Wang et al., Nature, vol.492, p.86, 2012.

E. A. Muljarov and W. Langbein, Exact mode volume and Purcell factor of open optical systems, Phys. Rev. B, vol.94, p.235438, 2016.

J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, 2000.

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, Adaptive finite element method for simulation of optical nano structures, phys. stat. sol. (b), vol.244, 2007.

E. Popov, Gratings: Theory and Numeric Applications, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00787732

D. A. Powell, Resonant dynamics of arbitrarily shaped meta-atoms, Phys. Rev. B, vol.90, p.75108, 2014.

D. A. Powel, Interference between the Modes of an All-Dielectric Meta-Atom, vol.7, p.34006, 2017.

A. Raman and S. Fan, Phys. Rev. Lett, vol.104, p.87401, 2010.

, Photonic Band Structure of Dispersive Metamaterials Formulated as a Hermitian Eigenvalue Problem

P. Rigby and T. F. Krauss, The Vs and Qs of optical microcavities, Nature, vol.390, p.125, 1997.

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators, Phys. Rev. Lett, vol.110, p.237401, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00850459

E. Silberstein, P. Lalanne, J. Hugonin, and Q. Cao, Use of grating theories in integrated optics, J. Opt. Soc. Am. A, vol.18, pp.2865-2875, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00867923

A. W. Snyder and J. D. Love, Optical Waveguide Theory, 1983.

A. Taflove, S. G. Johnson, and A. Oskooi, Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology, 2013.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, Quasiguided modes and optical properties of photonic crystal slabs, Phys. Rev. B, vol.66, p.45102, 2002.

T. Vallius and M. Honkanen, Reformulation of the Fourier modal method with adaptative spatial resolution: application to multilevel profiles, Opt. Express, vol.10, pp.24-34, 2002.

B. Vial, A. Nicolet, F. Zolla, and M. Commandré, Quasimodal expansion of electromagnetic fields in open two-dimensional structures, Phys. Rev. A, vol.89, p.23829, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01281129

B. Vial, G. Demésy, F. Zolla, A. Nicolet, M. Commandré et al., J. Opt. Soc. Am. B, vol.31, pp.1339-1346, 2014.

, Resonant metamaterial absorbers for infrared spectral filtering: quasimodal analysis, design, fabrication, and characterization

J. P. Webb and B. Forgahani, Hierarchal scalar and vector tetrahedral, IEEE Transactions on Magnetics, vol.29, pp.1495-1498, 1993.

T. Weiss, G. Granet, N. A. Gippius, S. G. Tikhodeev, and H. Giessen, Matched coordinates and adaptive spatial resolution in the Fourier modal method, Opt. Express, vol.17, pp.8051-8061, 2009.

T. Weiss, N. A. Gippius, S. G. Tikhodeev, G. Granet, and H. Giessen, Derivation of plasmonic resonances in the Fourier modal method with adaptive spatial resolution and matched coordinates, J. Opt. Soc. Am. A, vol.28, pp.238-244, 2011.

T. Weiss, M. Mesch, M. Schäferling, H. Giessen, W. Langbein et al., From dark to bright: First-order perturbation theory with analytical mode normalization for plasmonic nanoantenna arrays applied to refractive index sensing, Phys. Rev. Lett, vol.116, p.237401, 2016.

T. Weiss, M. Schäferling, H. Giessen, N. A. Gippius, S. G. Tikhodeev et al., Phys. Rev. B, vol.96, p.45129, 2017.

, Analytical normalization of resonant states in photonic crystal slabs and periodic arrays of nanoantennas at oblique incidence

T. Weiss and E. A. Muljarov, How to calculate the pole expansion of the optical scattering matrix from the resonant states, Phys. Rev. B, vol.98, p.85433, 2018.

D. M. Whittaker and I. S. Culshaw, Scattering-matrix treatment of patterned multilayer photonic structures, Phys. Rev. B, vol.60, pp.2610-2618, 1999.

W. Yan, R. Faggiani, and P. Lalanne, Rigorous modal analysis of plasmonic resonances, Phys. Rev. B, vol.97, p.205422, 2018.

R. Zhao, Y. Luo, A. I. Fernández-domínguez, and J. B. Pendry, Description of van der Waals Interactions Using Transformation Optics, vol.111, p.33602, 2013.

X. Zheng, V. K. Valev, N. Verellen, V. Volskiy, L. O. Herrmann et al., Implementation of the natural mode analysis for nanotopologies using a volumetric method of moments, IEEE Photonics J, vol.6, p.4, 2014.

J. Zimmerling, L. Wei, P. Urbach, and R. Remis, J. Comput. Phys, vol.315, pp.348-362, 2016.

, A Lanczos model-order reduction technique to efficiently simulate electromagnetic wave propagation in dispersive media

J. Zimmerling, L. Wei, P. Urbach, and R. Remis, Appl. Phys. A, vol.122, p.158, 2016.

, Efficient computation of the spontaneous decay of arbitrarily shaped 3D nanosized resonators: a Krylov model-order reduction approach

F. Zolla, G. Renversez, A. Nicolet, B. Kuhlmey, S. Guenneau et al., Foundation of Photonic Crystal Fibers, 2005.

F. Zolla, G. Demésy, and A. Nicolet, Photonics in highly dispersive media: The exact modal expansion, Opt. Lett, vol.43, p.5813, 2018.

L. Zschiedrich, S. Burger, B. Kettner, and F. Schmidt, Advanced finite element method for nano-resonators, Proc. SPIE, vol.6115, p.611515, 2006.

L. Zschiedrich, F. Binkowski, N. Nikolay, O. Benson, G. Kewes et al., Riesz-projection-based theory of light-matter interaction in dispersive nanoresonators, Phys. Rev. A, vol.98, p.43806, 2018.