Thin Film on Thick Substrate Calculator

Coherent Coating on a Thick Substrate

Real lab samples often pair a sub-micron coating with a millimeter-thick glass slide or polymer sheet. The coating keeps its resolved optical phase while the thick substrate is best modeled as incoherent — phase variations across its thickness exceed what any real source bandwidth or thickness uniformity can resolve.

Why This Distinction Matters

Each layer adds \(N = 2nd\cos\theta/\lambda\) round-trip phase cycles to the reflected wave. The thin coating accumulates a small fraction of a cycle, so its phase is well-defined and adds coherently. A millimeter-thick substrate accumulates thousands of cycles — more than any real source bandwidth or thickness uniformity can resolve — so its phase randomizes and it is treated incoherently: the dense Fabry–Pérot fringes wash out into a smooth intensity baseline.

When N is large and uncertain, intensities (not amplitudes) add: the substrate's two surfaces combine as incoherent reflectances. The zoomed panel shows the coherent treatment's unphysical dense fringes against the smooth incoherent baseline.

Interactive design tool

This page includes a live transfer-matrix calculator for this design. Adjust the parameters to recompute spectra, layer stack, and performance figures in the browser, then open the design in the full calculator.