Reflection, transmission, and absorption
Reflectance R, transmittance T, and absorptance A spectra for s, p, or unpolarized incident light.
About multilayer.app
A rigorous thin-film optics calculator for multilayer coatings
multilayer.app is a free online thin-film optics calculator and optical coating simulator based on the transfer matrix method (TMM). It calculates reflectance, transmittance, absorptance, electric fields, color, and parameter sweeps for plane-parallel multilayer stacks while keeping material data, assumptions, and calculation state visible.
The purpose is practical and modest: make thin-film interference calculations easier to inspect, reproduce, teach, and share—without presenting a model as a measurement.
From multilayer stack to evidence
A calculation should carry its assumptions
A spectrum is most useful when the geometry, optical constants, coherence treatment, and numerical settings remain attached. multilayer.app treats these as one reproducible object rather than reducing the result to a detached plot.
StackMedia, layer order, and physical thickness
n,k provenanceRefractive index, extinction coefficient, and wavelength range
TMM modelAngle, polarization, and coherence assumptions
Optical responseR, T, A, fields, color, and sensitivity
ReproduceShareable URL or literature comparison
Optical coating simulation
What the calculator computes
The calculator covers the common forward problems of planar thin-film and multilayer coating analysis, from a single interference film to lossy mixed-coherence stacks.
Spectral and design sweeps
Wavelength or frequency, incidence-angle, and layer-thickness sweeps for optical coating exploration.
Fields and layer absorption
Layer-resolved absorptance and coherent electric-field intensity |E(z)|2 inside the stack.
Materials and appearance color
Published or custom n,k data, dispersion models, effective-media roughness layers, and CIE/RGB color.
Transfer matrix method
Model and numerical basis
For each wavelength, incidence angle, and polarization, the complex refractive indices n + ik and layer thicknesses define the optical boundaries and propagation. Coherent regions use amplitude transfer matrices; mixed coherent/incoherent stacks combine coherent sub-stacks through intensity transfer or deterministic phase averaging.
The implementation extends Steven Byrnes' open-source tmm code and the derivation in Multilayer optical calculations. Mixed-coherence layer absorption follows the phase-integrated formulation reported in Coatings 9, 536 (2019).
- Critical-angle cases that make an incoherent intensity recursion singular are routed to phase averaging.
- NaN and infinite responses are rejected rather than clipped into plausible 0% or 100% values.
- Reference tests cover spectra, energy balance, layer absorption, fields, dispersion models, roughness, and colorimetry.
ñ(λ) = n(λ) + ik(λ)Complex refractive index: phase propagation plus extinction
R, TSpecular reflected and transmitted power fractions
A = 1 − R − TTotal absorptance from energy balance
|E(z)|2Position-resolved coherent field intensity
Refractive-index data
Optical constants and provenance
The material catalog resolves published tables and dispersion formulas from refractiveindex.info. Users may instead supply measured n,k tables, define oscillator models, or represent a rough interface as a Bruggeman effective-medium layer.
Thin-film refractive index n and extinction coefficient k can depend on composition, deposition, microstructure, temperature, and measurement method. For research or engineering use, the data source and wavelength range can matter as much as the layer thickness.
Literature inputs are recorded in four tiers. Documented data trace to the paper itself; matched data retain the stated material but compare every covering literature dataset; substituted data use an explicit proxy; and undetermined inputs do not support an attributable calculation. No dataset is extrapolated beyond its reviewed coverage.
Principle: a material name is not a complete optical specification.
Learning and literature
Interactive examples and replications
Ten thin-film optics tutorials turn canonical systems into live calculations: anti-reflection coatings, Bragg and dielectric mirrors, Fabry–Pérot etalons, bandpass filters, beam splitters, surface plasmon resonance, low-E glass, radiative cooling, and perovskite solar cells.
The preliminary literature Replications corpus reconstructs reported planar stacks, records the optical constants used, recomputes the stated claim, and opens the same state in the calculator. When a paper names a material without identifying an n,k dataset, the verifier recomputes the curve across every covering refractiveindex.info and reviewed Palik dataset for that same material. The published best, median, worst, and range remain together rather than silently choosing one dataset.
Interpretation: the fit score describes curve agreement; the documentation tier describes how the optical inputs were established. For matched inputs, the score range measures how much of the curve depends on n,k dataset choice rather than stack physics. Neither coordinate generalizes beyond the selected curve and inputs.
Scientific boundary
Where the TMM model applies
Direct scope
Linear, specular propagation through plane-parallel, locally homogeneous, isotropic layers with an explicit coherence treatment. Within this boundary, TMM is a standard model for thin-film interference and optical coating analysis.
Outside direct scope
Diffraction gratings, lateral photonic structures, metasurfaces, particulate or diffuse scattering, anisotropic tensors, and fabrication defects. Effective-media layers or parameter sweeps may study approximations, but cannot restore absent physics.
A computed curve is evidence about a specified model. It is not a measurement, product certification, or engineering warranty. Consequential results should be checked against input provenance, sensitivity, independent software, and—where possible—experiment.
Common questions
Thin-film calculator FAQ
What is a transfer matrix method calculator?
It solves the reflection and transmission of plane waves through a stratified stack by combining the optical response of each interface and layer. multilayer.app extends this to absorbing and mixed coherent/incoherent thin films.
Can it simulate thin-film interference and optical coatings?
Yes, when the coating is well represented by plane-parallel homogeneous layers. Common examples include anti-reflection coatings, dielectric mirrors, optical filters, beam splitters, and absorbing device stacks.
Does it calculate reflectance, transmittance, and absorption?
Yes. The reported power fractions are reflectance R, transmittance T, and absorptance A. “Reflection,” “transmission,” “absorption,” and “absorbance” are common search terms; the calculator uses the radiometric terms for precision.
How accurate is a TMM thin-film simulation?
Numerical accuracy can be high within the model, but physical accuracy depends on layer geometry, coherence, and representative wavelength-dependent n,k data. A precise calculation with unsuitable inputs is still an unsuitable model.
Project and credits
A small, independent scientific-software project
multilayer.app is designed and maintained by Ilia Rasskazov as an independent resource for thin-film optics calculations, teaching, and reproducibility.
- Transfer-matrix foundation: Steven Byrnes, sbyrnes321/tmm (MIT).
- Optical-constant catalog: refractiveindex.info; uploaded data remain attributable to their original sources.
- Appearance color: CIE observers and illuminants, chromatic adaptation, and RGB transforms cross-checked against published colorimetric references.
Corrections, counterexamples, and suggestions are welcome through the calculator feedback form.