Stack Formula generates a complete layer stack from a compact symbolic expression — the shorthand a coating engineer already thinks in. You type a formula, watch the parsed stack and its spectrum preview update live, then apply it to the design.

Air | (HL)^4 H | Glass             9-layer quarter-wave HR mirror
Glass | 2H 1.5L H L (HL)^3 | Air   matching layers + quarter-wave stack
Air | 0.5H L H 0.5L | Sub          fractional quarter-waves
Air | Hi Lo Hi Lo Med | Glass      custom symbols

The formula language

A formula reads incident-medium | layers | exit-medium, with the coating written between the two bars.

• Symbols H, L and M default to the high-, low- and medium-index materials at the active reference wavelength. You can map your own symbols to any material (for example Hi → TiO2, Lo → SiO2, Med → Al2O3).
• Coefficients are quarter-wave multipliers at the reference wavelength: 2H is a half-wave of the high material, 0.5L an eighth-wave of the low. A bare symbol is one quarter-wave.
• Repeat groups (...)^n expand the enclosed layers n times.
• @λ on a medium overrides the reference wavelength used for the conversion.

Settings

Reference wavelength — the wavelength at which the quarter-wave coefficients are converted to physical thickness.

Symbol assignments — a list mapping each symbol used in the formula to a material. H/L/M are pre-filled; any unknown symbol you type is surfaced automatically with a material picker, and you can add, rename or remove rows.

Incident / Substrate / Exit media — the media that bound the coating. The front coating is bounded by the incident medium and the substrate; the back coating by the substrate and the exit medium.

Start from substrate — reads the formula from the substrate outward instead of from the incident medium inward.

Apply to side — choose whether the formula populates the front coating, the back coating, or both. (A symmetric design always writes the front and mirrors it to the back.)

How to read it

As you type, the right-hand panel lists the parsed layers with their material, quarter-wave value and physical thickness, along with the layer count and total thickness, and plots the resulting T and R spectrum with the reference wavelength marked. A parse error is flagged at the character where it occurs and the preview blanks until you fix it.

When the formula is valid, apply it with Append (add the layers to the end of the current stack), Replace (overwrite the active design’s stack), or New design (create a fresh design from the formula). A classic mirror or anti-reflection coating built this way is a clean quarter-wave starting point to hand to Refinement or Needle. The stack that the formula generates lands in the Design Editor, and the formula is kept with the design so any design can be written back to a formula later.

References

• H. A. Macleod, Thin-Film Optical Filters, 5th ed., §3.1 (quarter-wave optical thickness notation), Ch. 5 (quarter-wave stacks).