About
multilayer.app is a free online optical simulator for multilayer coatings, one-dimensional gratings, pyramid-textured interfaces, concentric cylinders, and multilayered spheres. Define the materials, geometry, and illumination to calculate how a structure reflects, transmits, scatters, and absorbs light.
What you can calculate
- Optical spectra
- Reflectance R, transmittance T, and absorptance A for s, p, or unpolarized light. View spectra against wavelength, frequency, photon energy, or wavenumber.
- Parameter sweeps
- Vary incidence angle, layer thickness, or a surface-finish parameter and compare the resulting spectra.
- Multilayered spheres
- Extinction, scattering, and absorption efficiencies of a core with any number of concentric shells under plane-wave illumination, resolved into electric and magnetic multipoles; near-field intensity maps, the angular scattering pattern, and a sweep of one layer’s thickness.
- Concentric cylinders
- Cross sections per unit cylinder length, efficiencies, azimuthal orders, scattering patterns and electric/magnetic field maps for infinite circular cylinders, including oblique plane-wave incidence.
- Focused beams
- A beam focused through an annular (Cassegrain) or circular aperture, as in infrared microspectroscopy, on films, cylinders and spheres: the apparent absorbance against a reference (a film without its sample layers, or the empty host), the detected, reflected, transmitted, scattered and absorbed fractions of the beam power, each multipole order’s share and the near field of the spot. Coherent spot or Köhler illumination, vector or corrected scalar model; sweep the aperture, the focus or a layer. The aplanatic pupil is filled uniformly, and the medium the beam is focused and collected in must be lossless.
- Point emitters
- Electric or magnetic dipoles in films, cylinders and spheres: total decay enhancement, escaping power, guided power where present, material loss, quantum efficiency and angular emission. Sweep wavelength and source offset. The source and exterior media must be lossless; rates use the homogeneous source medium as their reference.
- Additional outputs
- Layer-resolved absorption; field profiles for planar stacks; ellipsometric Ψ and Δ for fully coherent planar stacks; planar-stack appearance color under selected observers and illuminants.
- Export & share
- Download existing plots as PNG, numerical results as CSV, and source-driven setups with resolved results as JSON. Share a calculation link containing the structure and settings.
For spheres, enter the core radius first, followed by each shell’s radial thickness; the Host is the surrounding medium. The outer radius R is the core radius plus all shell thicknesses. The efficiencies Qext, Qsca, and Qabs are cross sections divided by πR², with Qext = Qsca + Qabs. Unlike thin-film R, T, and A, these efficiencies are not fractions of incident power and can exceed one.
Models and their limits
| Structure | Method | Scope |
|---|---|---|
| Planar layers | Transfer matrix method (TMM) | Homogeneous, isotropic layers; coherent, incoherent, or mixed plane-wave propagation. Point-dipole emission requires coherent layers. |
| Effective roughness | Bruggeman effective medium + TMM | A mixed layer represents adjacent materials. It does not resolve a rough surface or its diffuse scattering. |
| Rectangular line gratings | Rigorous coupled-wave analysis (RCWA) | One-dimensional periodic interfaces. Check convergence with the number of Fourier orders. |
| Upright or random pyramids | Geometric ray tracing + interface TMM | Ray-optics regime with an incoherent bulk layer. Check convergence with the number of ray paths. |
| Concentric cylinders | Cylindrical modes, stable layer response | Infinite circular cylinders with concentric layers, a lossless exterior and plane waves or 3D point dipoles. Check angular-order and axial-spectrum convergence. |
| Multilayered spheres | Mie theory, recursive transfer matrices | Concentric homogeneous, isotropic shells in a non-absorbing host, under a plane wave or electric/magnetic point dipole. Check convergence with the multipole order ℓmax. |
The owned PyStratify engine composes planar, cylindrical and spherical layer responses. Its planar routines extend Steven Byrnes’ tmm; its formulation is described in Multilayer optical calculations. Grating calculations use meent, pyramid calculations use RayFlare, and its sphere formulation builds on STRATIFY (OSA Continuum 3, 2290 (2020)).
Current limits. Gratings and ray-traced textures cannot be combined in one stack. Arbitrary 3D geometries and general anisotropic materials are not currently supported. Point emitters require planar or concentric geometries, with a lossless source region. Available outputs depend on geometry and source.
Optical constants and data sources
Choose wavelength-dependent refractive index n and extinction coefficient k from refractiveindex.info or Palik’s Handbook of Optical Constants of Solids. You can also enter constants, define oscillator models, or upload n,k or permittivity tables.
Palik HOC I–II data come from the Palik/Bennett digital companion; HOC III tables are transcribed for this project. The Palik release is under review and may contain digitization errors. Check the selected source and its spectral range. Tabulated data are not extrapolated beyond their coverage.
Simulation accuracy depends on representative material data, geometry, and coherence assumptions. Compare convergence and parameter sensitivity before interpreting a computed spectrum as a prediction for a fabricated structure.
Examples and independent checks
Learn explains the theory section by section, from Maxwell's equations and the transfer matrix to coatings, filters, metal films, emitters and devices, and from Mie theory to the multilayered sphere; every worked example is computed by PyStratify, with every slider position computed in advance, and the classic papers of each topic open in the calculator from the section that explains them. Verification lists every check the engine is held to.
The preliminary thin-film Replications corpus currently holds 181 reconstructed stacks over 177 papers. Three papers contribute more than one structure: two VO2 stacks, each below and above the film’s transition, and a photonic-crystal sensor whose porous-silicon defect layer is computed at three gamma-ray doses, with a calculated curve for each. Each record links the paper, states the model inputs, and compares recomputed spectra with published calculated curves. Inputs are extracted with Reviewer3 and may contain errors; agreement is not experimental validation.
To check a result, inspect the cited optical data and model assumptions, export the numerical results, and compare with an independent implementation or measurement.
Project and contact
Created and maintained by Ilia Rasskazov. The calculator is free to use in a modern browser; calculations require JavaScript and a connection to the simulation service.
Report an issue or suggest an improvement. For numerical questions, include the structure, settings, and reference result you expected. A thin-film share link or the request parameters from a sphere JSON download helps reproduce the calculation.