About multilayer.app
Thin-film and textured-surface optics
multilayer.app is a free online optical simulator for multilayer coatings, one-dimensional gratings, and pyramid-textured interfaces. Define the materials, geometry, and illumination to calculate how a structure reflects, transmits, 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.
- 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 plots as PNG and numerical results as CSV. Share a calculation link containing the structure and settings.
Models and their limits
| Structure | Method | Scope |
|---|---|---|
| Planar layers | Transfer matrix method (TMM) | Homogeneous, isotropic layers; coherent, incoherent, or mixed propagation. |
| 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. |
The planar engine extends Steven Byrnes’ tmm; its formulation is described in Multilayer optical calculations. Grating calculations use meent, and pyramid calculations use RayFlare.
Current limits. Gratings and ray-traced textures cannot be combined in one stack. Multilayer spheres, arbitrary 3D geometries, and general anisotropic materials are not currently supported. Available outputs depend on the solver.
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
Interactive tutorials explain standard coating designs and surface effects, with editable examples that open in the calculator. Surface-texture tutorials show analytic or effective-medium approximations; the full structures are solved in the calculator.
The preliminary Replications corpus currently holds 116 reconstructed stacks over 115 papers. One paper contributes two, because it measured the same stack in two states — a thermochromic VO2 film below and above its transition — and published a 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 a shared calculation link and the reference result you expected.