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Multilayer Optics Calculator

Free online transfer matrix method calculator for multilayer thin-film structures. Calculate reflectance, transmittance and absorptance spectra for TE, TM and unpolarized light using wavelength-dependent optical data.

Browser-based and free: 3,500+ optical-material datasets · custom n,k import · TE/TM and unpolarized light · R/T/A spectra · CSV, PNG and PDF export

Read the calculator documentation Open worked thin-film examples

Spectrum

⚠1 material does not cover the complete 400–800 nm range.
Success — total time: 1.1 ms · 2000 points

Layer stack top = light enters here

Incident medium · light source
Period repeat × 
2 layers × 6 = 12
Transmittance medium · detector
Support my work

Results

Polarization
Stack  ↓ light
Total thickness: 1572 nm

Materials

In this simulation 4
Air
Constant — n 1.0000 — k 0
SiO₂ — Malitson
Sellmeier — 210–6710 nm — built-in
TiO₂ measured
Tabulated n,k — 380–1200 nm — imported
Polymer film
Cauchy — A 1.50, B 0.005 — user
Built-in library RefractiveIndex.INFO
SiO₂ — Malitson 1965
Sellmeier — 210–6710 nm
TiO₂ — Devore 1951
Tabulated n,k — 430–1530 nm
Si — Aspnes 1983
Tabulated n,k — 210–840 nm
Al₂O₃ — Malitson 1972
Sellmeier — 200–5000 nm
Ag — Johnson & Christy 1972
Tabulated n,k — 188–1937 nm
MgF₂ — Dodge 1984
Sellmeier — 200–7000 nm
▶Appearance preview perceptual · specular
Perceptual preview under ideal specular conditions
Mode
sample
Colour#000000
Incidence angle28°
Perceptual color preview calculated using CIE 1931 2° colour matching functions, CIE D65 white light and ideal specular conditions. This is an idealized rendering and may differ significantly from the actual sample's appearance.

What does the multilayer optics calculator calculate?

The calculator uses the transfer matrix method to model the optical response of planar multilayer structures. It calculates wavelength-dependent reflectance, transmittance and absorptance for TE, TM and unpolarized light at a selected angle of incidence.

It can be used to analyse dielectric mirrors, distributed Bragg reflectors, anti-reflection coatings, Fabry–Pérot structures, absorbing films, metallic mirrors and other isotropic thin-film stacks.

Supported materials and optical data

Each layer can use a constant complex refractive index, a Cauchy model, a Sellmeier model, imported tabulated n,k data or a material selected from the built-in RefractiveIndex.INFO library.

The calculator checks whether the selected optical data cover the requested wavelength range and does not silently extrapolate unavailable values.

Transfer matrix method for thin-film optics

The transfer matrix method accounts for interference between forward- and backward-propagating waves at every interface in the multilayer stack. It is commonly used to analyse and design optical coatings composed of homogeneous, flat and parallel layers.

Assumptions and limitations

The current implementation assumes isotropic materials, coherent plane-wave illumination, specular reflection and semi-infinite incident and transmission media.

Read the documentation and calculation limitations before using the results for engineering or research decisions.

Worked multilayer examples

Open the multilayer optics calculator examples to load a quarter-wave anti-reflection coating, a TiO₂/SiO₂ distributed Bragg reflector, a silver mirror or a Fabry–Pérot structure.