Resolving the Gibbs phenomenon via a discontinuous basis in a mode solver for open optical systems
arXiv:2005.12346 · doi:10.1016/j.jcp.2020.110004
Abstract
Partial differential equations are frequently solved using a global basis, such as the Fourier series, due to excellent convergence. However, convergence becomes impaired when discontinuities are present due to the Gibbs phenomenon, negatively impacting simulation speed and possibly generating spurious solutions. We resolve this by supplementing the smooth global basis with an inherently discontinuous basis, incorporating knowledge of the location of the discontinuities. The solution's discontinuities are reproduced with exponential convergence, expediting simulations. The highly constrained discontinuous basis also eliminates the freedom to generate spurious solutions. We employ the combined smooth and discontinuous bases to construct a solver for the modes of a resonator in an open electromagnetic system. These modes can then expand any scattering problem for any source configuration or incidence condition without further numerics, enabling ready access and physical insight into the spatial variation of Green's tensor. Solving for the modes is the most numerically intensive and difficult step of modal expansion methods, so our mode solver overcomes the last major impediment to the use of modal expansion for open systems.
arXiv comment21 pages, 13 figures
References in corpus (17)
- Light interaction with photonic and plasmonic resonances
- Rigorous modal analysis of plasmonic nanoresonators
- Brillouin-Wigner perturbation theory in open electromagnetic systems
- Resonant state expansion applied to three-dimensional open optical systems
- Steady-state Ab Initio Laser Theory: Generalizations and Analytic Results
- Quasinormal mode solvers for resonators with dispersive materials
- Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics
- Resonant state expansion applied to two-dimensional open optical systems
- Generalizing normal mode expansion of electromagnetic Green's tensor to lossy resonators in open systems
- Revisiting the boundary conditions for second-harmonic generation at metal-dielectric interfaces
- Eigenmode decomposition of the near-field enhancement in localized surface plasmon resonances of metallic nanoparticles
- Material-independent modes for electromagnetic scattering
- Resonant-state expansion applied to three-dimensional open optical systems: A complete set of static modes
- Robust Location of Optical Fiber Modes via the Argument Principle Method
- Overcoming the bottleneck for quantum computations of complex nanophotonic structures: Purcell and FRET calculations using a rigorous mode hybridization method
- An efficient solver for the generalized normal modes of non-uniform open optical resonators
- Applying the resonant-state expansion to realistic materials with frequency dispersion