The Admittance Diagram traces a path through the complex admittance plane as you walk from the substrate outward through each layer of the front coating. Every layer draws an arc, and the point where the path ends fixes the reflectance at that wavelength. Reading the shape of the locus is a classic way to build intuition about how a stack works — whether it matches the coating to the incident medium, builds up a high reflectance, or sits somewhere in between.

At one wavelength and angle of incidence, the diagram starts at the substrate admittance and applies each layer’s transfer in turn. The final endpoint is the front-surface admittance Y, from which the reflectance follows as R = |(η₀ − Y) / (η₀ + Y)|², where η₀ is the admittance of the incident medium.

Settings

Wavelength — the single wavelength at which the locus is drawn, in nm. Admittance is a single-wavelength concept, so only one value is evaluated at a time. It defaults to the design’s reference wavelength.

AOI — the angle of incidence in degrees.

Polarization — s, p, or their average. At oblique incidence the s and p loci differ; at normal incidence they coincide.

Side — trace the front coating (from the incident medium) or the back coating (from the exit medium). Each coating is its own locus on the substrate, so the two sides are drawn independently.

How to read it

Each arc is one layer, labelled L1, L2, … from the substrate outward, and colored by material. A few shapes recur:

• A quarter-wave layer sweeps a half-circle arc.
• A path that walks toward η₀ (marked η₀) is matching the coating to the incident medium — an antireflection design. An endpoint sitting exactly on η₀ means zero reflectance at that wavelength.
• A tight orbit far from η₀ is a high-reflectance stack.

The substrate admittance (η_s), the incident-medium admittance (η₀), and the final admittance (Y₀) are marked, and the panel lists the numeric admittances plus the per-layer endpoints. Pair this with the Electric Field view to see which layer carries the standing-wave peak at the same wavelength.

References

• H. A. Macleod, Thin-Film Optical Filters, 5th ed., §2.4 and §4.1 — admittance locus.