A basic dielectric mirror is one of the simplest multilayer coatings. It uses alternating layers with high and low refractive index. In coating notation, these materials are called H and L.

This tutorial builds an eight-pair mirror for 550 nm with TFStudio's Stack Formula tool.

What an HL pair does

Each layer is one quarter-wave optical thickness at the design wavelength λ0\lambda_0:

njdj=λ04,dj=λ04nj.n_j d_j=\frac{\lambda_0}{4}, \qquad d_j=\frac{\lambda_0}{4n_j}.

At normal incidence, the reflections from the interfaces in an alternating quarter-wave stack add constructively around λ0\lambda_0. Repeating the pair raises the reflectance:

HLHLHLHL…HLHLHLHL\ldots

The letters describe optical roles, not fixed materials:

  • H is the material with the higher refractive index.
  • L is the material with the lower refractive index.
  • A bare H or L in Stack Formula means one quarter-wave optical thickness.

More pairs increase the reflectance in the high-reflectance band. The index contrast between H and L largely determines the width of that band.

Build the mirror with Stack Formula

Open Design → Formula.

Formula button with the (HL)^n icon, which opens the Stack Formula tool

Enter this formula:

(H L)^8

Set the controls as follows:

  1. Set Reference λ₀ (nm) to 550.
  2. Assign H to built-in TiO2 (anatase).
  3. Assign L to built-in SiO2 (Fused Silica).
  4. Set the incident medium to Air.
  5. Set the substrate to BK7 (Schott).
  6. Set Apply to to Front.
  7. Leave Start from substrate checked.
  8. Click New design.
Stack Formula

The parentheses group one HL pair, ^8 repeats it eight times, and TFStudio converts every quarter-wave optical thickness into a physical thickness using the selected material data at 550 nm.

The result contains 16 layers. The formula is read from the substrate outward. The Design Editor also lists the substrate-adjacent layer first, so its table appears in the same order.

Design Editor listing the 16 layers from the BK7 side: TiO2 (anatase) 54.64 nm and SiO2 (Fused Silica) 94.18 nm alternating, all quarter waves

Check the result

Open the Optical Evaluation window (Analysis → T/R/A). The reflectance curve should show a high-reflectance band centered near the design wavelength.

Optical Evaluation of the (HL)^8 mirror, 400-800 nm, with a flat high-reflectance band around 550 nm where R is 99.900%

Two quick changes show how the structure behaves:

  • Open Formula window again and change the formula to (H L)^4, click Replace. The mirror now has fewer layers and lower peak reflectance.

Optical Evaluation of the (HL)^4 mirror with 8 layers, where the band around 550 nm has a lower peak and sloping edges

  • Restore (H L)^8 and change reference λ0\lambda_0 to 800 nm either in Stack Formula or in Design Editor. Now the high-reflectance band moved to the right as physical thicknesses of layers were automatically recalculated to new reference wavelength.

Optical Evaluation of (HL)^8 after changing the reference to 800 nm: the high-reflectance band has moved right, to around 800 nm

That is the basic dielectric mirror.