Which method should I use?
Compare the numerical methods available in NanophotonicsLab. Each row links to the corresponding tool.
| Method | Geometry | Physics | Best for | Fails when | Cost | Tool |
|---|---|---|---|---|---|---|
| Mie theory | Spheres (and core-shell) | Exact EM solution for homogeneous spheres. All multipolar orders, retardation included. | Spherical nanoparticles of any size. Quick spectral checks, material screening. | Non-spherical geometries, substrates, inter-particle coupling, non-local effects. | Instant | Mie Scattering → |
| Quasistatic plasmonics | Rods, disks, cages, bipyramids, rings | Electrostatic modal polarizabilities with radiative-reaction correction. Geometry-only fits. | Sub-100 nm plasmonic shapes. Fast spectral estimates, shape/material exploration. | Particles approaching or larger than the wavelength. High-order multipoles needed. | Instant | Plasmonic NPs → |
| Cylinder scattering | Infinite circular cylinders | Exact Mie-type series for plane-wave scattering. Non-retarded dielectric formalism for EELS. | Nanowires, nanotubes, cylindrical waveguides. Guided-mode dispersion. | Finite-length cylinders, non-circular cross-sections, substrates. | Instant | Cylinder → |
| BEM (Boundary Element Method) | Arbitrary 3D shapes | Full-wave retarded solution via surface integral equations. Raviart-Thomas basis on triangular mesh. | Arbitrary particle shapes, near-field maps, when Mie/quasistatic are insufficient. | Very large particles (mesh resolution limited by browser memory). Periodic structures, substrates. | Seconds to minutes (in-browser via Pyodide) | BEM Solver → |
| BPM (Beam Propagation Method) | 2D waveguide cross-sections | Paraxial scalar wave equation, Crank-Nicolson scheme. Unconditionally stable. | Weakly guiding waveguides, directional couplers, mode propagation visualization. | High-contrast waveguides, backward reflections, resonant cavities, vectorial effects. | Sub-second | BPM → |
| RCWA (Rigorous Coupled Wave Analysis) | 1D periodic gratings | Fourier modal method. Plane-wave expansion, eigenvalue solve per layer. | Diffraction gratings, photonic crystals (1D), thin-film stacks with periodicity. | 2D periodicity, very thick metallic gratings (slow convergence), aperiodic structures. | Seconds (in-browser via Pyodide + inkstone) | RCWA → |
| Photothermal (Mie + heat) | Spheres in uniform host | Exact Mie for absorption + steady-state point-source heat equation. | CW laser heating of isolated nanoparticles. Biomedical, photothermal therapy estimates. | Pulsed illumination, collective heating, temperature-dependent properties, substrates. | Instant | Photothermal → |
Not sure which method fits your problem? The Methods Assistant can help — describe your geometry and physics, and get a recommendation.