DBR Cross-Validation

This article compares Dreapex TMM and Essential Macleod for the same five-pair TiO₂/MgF₂ distributed Bragg reflector (DBR). The validation covers reflectance and transmittance from 400 to 800 nm, reflection phase, and an incidence-angle sweep at 510 nm.

Validation Target and Acceptance Criteria

Five TiO₂/MgF₂ periods form the high-reflectance stopband. The two physical thicknesses are 56.12 nm and 99.64 nm, with a design reference wavelength of 510 nm.

The model is a one-dimensional planar multilayer made of linear isotropic materials.

Shared Materials and Structure

Both programs use the same wavelength-dependent n, k data for TiO₂, MgF₂, and glass. The original record used Jolivet-amorphous.nk, Dodge.nk, and N-BK7HT.nk from the Dreapex TMM database and imported the same data into Essential Macleod, removing database revision and interpolation source as comparison variables. These source material data are restricted from redistribution and are not offered for download here.

Dreapex TMM represents the TiO₂/MgF₂ period as one Layer Group with Repeat Count set to 5 and glass as the bottom medium.

Essential Macleod uses the same materials, order, and physical thicknesses and lists the fractional-wave optical thickness (FWOT) at 510 nm.

Wavelength Sweep

Shared Setup

Dreapex TMM uses Sweep wavelength mode from 400 to 800 nm in 1 nm steps at 0° incidence with the R·T·A detector enabled. Essential Macleod uses the same horizontal-axis range and sampling, with reflectance and transmittance selected in turn on the vertical axis.

Reflectance and Transmittance

Dreapex TMM reports reflectance and transmittance at 401 wavelengths. The independent reference reports the corresponding data for the same structure.

The reflectance data overlap throughout 400–800 nm. With $R\geq 99\%$ as the high-reflectance criterion, both calculations give a continuous band from 519 to 573 nm, with no visible displacement of the extrema or principal turning points.

The transmittance overlays also coincide and complement the stopband in reflectance. Because all layers are transparent in this model, that complementarity also provides an energy-conservation cross-check.

Reflection Phase

Dreapex TMM enables the Phase detector, while Essential Macleod uses Reflectance Phase (deg) as the vertical quantity. The former source output is in radians and the latter in degrees. Their raw phase signs are opposite, so this record tests numerical agreement after converting degrees to radians and changing sign. It does not infer an undocumented time-factor convention for Essential Macleod.

After the unit and sign conversion, the two phase curves overlap from 400 to 800 nm, including the rapid changes near the stopband edges.

Incidence-Angle Sweep

The angular sweep fixes the wavelength at 510 nm and covers 0–89° in 1° steps. Polarization Ratio values of 0, 0.5, and 1 in Dreapex TMM correspond respectively to s polarization, Mean, and p polarization in Essential Macleod.

When the three polarization results are plotted together, their line shapes, extrema, and turning points agree. The s and p responses separate strongly at high angles, while the equal-weight mean remains between them.

Conclusion and Scope Limits

With common materials, structure, boundary conditions, and sampling, Dreapex TMM and Essential Macleod agree in reflectance, transmittance, converted reflection phase, and the three polarization-resolved angular sweeps. The conclusion applies only to the stated one-dimensional planar stack of linear isotropic materials. Surface roughness, scattering, lateral patterning, process gradients, and uncertainty in measured optical constants are outside the model. The original record also did not retain the Essential Macleod version number.

For the DBR construction workflow, see Design a 99% DBR Mirror. For the phase definition and its relation to group delay, see Dispersion Theory.