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Multilayer Optics Calculator — Examples ← Back to app

Multilayer Optics Calculator Examples

Explore worked multilayer thin-film examples and load each structure directly into the calculator. The examples demonstrate anti-reflection coatings, dielectric mirrors, metallic films and Fabry–Pérot interference.

Four configurations spanning idealized textbook physics and real material data from the built-in RefractiveIndex.INFO library. Every number below was verified against this app's own backend before being written here — see Numerical verification for how the underlying kernel itself is checked.

Click Open in simulator on any example to load its exact layer stack, materials, and wavelength range directly into the app — no manual setup. This replaces whatever is currently in the app's layer stack and materials list, so save your own work first (Save project in the app) if you don't want to lose it.

IdealizedQuarter-Wave Anti-Reflection Coating

A single quarter-wave layer that cancels reflectance at a chosen design wavelength — the simplest anti-reflection coating, and the standard textbook derivation. Choosing the film index nf = √(n₀·ns) and thickness λ₀/(4nf) makes the two surface reflections destructively interfere exactly at λ₀. This is the same idealized case used in this app's own numerical verification suite (see Documentation → Numerical verification).

IncidentAir (n = 1, constant)
Filmn = 1.5, k = 0 — thickness 91.67 nm
SubstrateIdealized dense glass, n = 2.25
Spectrum400–800 nm, 0° incidence

Reflectance drops to ≈4×10⁻⁸ at the 550 nm design wavelength, verified directly against this app's backend — down from ≈14.8% for the bare glass interface without the coating.

Open this structure in the calculator →

Real materialsTiO₂/SiO₂ Distributed Bragg Reflector

Alternating quarter-wave layers of a high- and low-index material build a photonic stopband — a wavelength range of very high reflectance — around a design wavelength. Unlike the idealized example above, this one uses real, wavelength-dependent dispersion data straight from the built-in RefractiveIndex.INFO library, so what you see already accounts for each material's true index.

IncidentAir (n = 1, constant)
Stack8 periods of TiO₂ (n≈2.52 @ 550 nm, 54.64 nm) / SiO₂ (n≈1.46 @ 550 nm, 94.18 nm)
SubstrateBK7 (N-BK7, SCHOTT) — real library material
Spectrum400–800 nm, 0° incidence

Reflectance exceeds 99.9% at the 550 nm design wavelength and falls toward the stopband edges (≈26–31% at 400/800 nm). Try adding more periods in the Layer stack panel to see the band narrow and its peak rise further.

Open this structure in the calculator →

Real materialsSilver Mirror Reflectance Using Johnson and Christy Data

A bare, semi-infinite silver substrate — no coating, no interference design at all — reflecting essentially the whole visible range on its own. Uses Johnson & Christy's 1972 silver optical constants, still the most widely cited reference for Ag in this wavelength range.

IncidentAir (n = 1, constant)
SubstrateAg (Silver) — Johnson and Christy 1972, real library material
LayersNone — the light hits bare silver directly
Spectrum400–800 nm, 0° incidence

Reflectance is approximately 96% near 400 nm and rises above 99% toward the red end of the visible range. This illustrates why silver is an effective broadband visible and near-infrared mirror, although its reflectance is noticeably lower at the blue edge of the spectrum.

Open this structure in the calculator →

IdealizedFabry–Pérot Thin-Film Resonance

A single free-standing, relatively thick sample in air — the same two-surface interference as the AR-coating example above, but with a much thicker layer, so many resonance orders fit inside the visible range instead of just one. Each reflectance peak corresponds to a different Fabry-Pérot resonance order of the slab.

IncidentAir (n = 1, constant) — sample is free-standing
Samplen = 1.7, k = 0 — thickness 5000 nm
SubstrateAir (n = 1, constant)
Spectrum380–780 nm (full visible range), 0° incidence

23 resonance peaks appear across the visible range, reflectance oscillating between ≈0 and ≈24% (energy is exactly conserved, R + T = 1, since nothing in this stack absorbs) — verified directly against this app's backend. Try changing the sample's thickness in the material editor (✎): a thinner sample spaces the resonances further apart; a thicker one packs in more, narrower ones.

Open this structure in the calculator →

Multilayer Optics Calculator — back to the app · documentation.

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