Tool · Optical coatings

Thin-Film Reflectance Calculator

Reflectance and transmittance of any stack of dielectric layers on a substrate, computed by the characteristic-matrix method for s and p polarization at any angle: single-layer and two-layer anti-reflection coatings, quarter-wave Bragg mirrors, laser facet coatings, and free-standing etalons, with the spectrum and the angular response drawn live. Background: the characteristic matrix method, anti-reflection coating design, distributed Bragg reflectors, and the Fresnel equations.

Media and geometry

Incident medium n₀

Substrate nₛ

Design λ₀ (nm) sets quarter- and half-wave thicknesses

Wavelength λ (nm)

Angle of incidence (deg)

measured in the incident medium, from the normal

Layers (incident side first)

#	n	d (nm)	n·d / λ₀

QW and HW set a layer to a quarter or half wave of optical thickness at λ₀. Indices are taken as constant over the plotted range; dispersion is not included.

Readouts at λ, θ

Reflectance versus wavelength at the set angle

range to nm

spaverage

Reflectance versus angle at the set wavelength

Checked against

These checks run in your browser on every load. Each compares the matrix computation with an independent closed form: the Fresnel equations, the Brewster and critical angles, the quarter-wave and half-wave layer formulas, the quarter-wave stack admittance, the Airy etalon formula, energy conservation, and reciprocity.

Check	Expected	Computed