Numerical methods for calculating poles of the scattering matrix with applications in grating theory
arXiv:1206.3388 · doi:10.1109/JLT.2012.2234723
Abstract
Waveguide and resonant properties of diffractive structures are often explained through the complex poles of their scattering matrices. Numerical methods for calculating poles of the scattering matrix with applications in grating theory are discussed. A new iterative method for computing the matrix poles is proposed. The method takes account of the scattering matrix form in the pole vicinity and relies upon solving matrix equations with use of matrix decompositions. Using the same mathematical approach, we also describe a Cauchy-integral-based method that allows all the poles in a specified domain to be calculated. Calculation of the modes of a metal-dielectric diffraction grating shows that the iterative method proposed has the high rate of convergence and is numerically stable for large-dimension scattering matrices. An important advantage of the proposed method is that it usually converges to the nearest pole.
9 pages, 2 figures, 4 tables
References in corpus (1)
Cited by in corpus (28)
- Light interaction with photonic and plasmonic resonances
- Quasinormal mode solvers for resonators with dispersive materials
- Bound states in the continuum in photonic structures
- Quasimodal expansion of electromagnetic fields in open two-dimensionnal structures
- Bound states in the continuum and high-Q resonances supported by a dielectric ridge on a slab waveguide
- Coupled-wave formalism for bound states in the continuum in guided-mode resonant gratings
- Interference between the modes of an all-dielectric meta-atom
- How to calculate the pole expansion of the optical scattering matrix from the resonant states
- Light guiding above the light line in arrays of dielectric nanospheres
- Exceptional points in anisotropic planar microcavities
- Third-order Exceptional Point and Successive Switching among Three States in a Degenerate Optical Microcavity
- A roundtrip matrix method for calculating the leaky resonant modes of open nanophotonic structures
- Resonant properties of composite structures consisting of several resonant diffraction gratings
- Nanophotonic resonance modes with the nanobem toolbox
- Fano line shape in photonic crystal slabs
- Resonant-state expansion for planar photonic-crystal structures
- First-order perturbation theory for material changes in the surrounding of open optical resonators
- Optical properties of opaline photonic crystals covered by phase-change material GeSbTe
- Neutron width statistics in a realistic resonance-reaction model
- Direct S-matrix calculation for diffractive structures and metasurfaces
- How many parameters do we need to obtain a BIC in symmetric and asymmetric structures?
- Controlling the surface plasmon excitation efficiency using dielectric magneto-optical cavity
- Resonant mode coupling approximation for calculation of optical spectra of photonic crystal slabs. Part II
- Analytical design of flat-top transmission filters composed of several resonant structures
- Resonant mode approximation of the scattering matrix of photonic crystal slabs near several Wood-Rayleigh anomalies
- Evaluation of resonances: adaptivity and AAA rational approximation of randomly scalarized boundary integral resolvents
- Resonant states of structured photonic time crystals
- Inverse design of focused vector beams for mode excitation in optical nanoantennas