Bragg Mirror / DBR Calculator

High-Reflectivity Quarter-Wave Stack

A dielectric Bragg reflector (distributed Bragg reflector, DBR) builds a high-reflectance stopband by stacking high-index TiO₂ and low-index SiO₂ quarter-wave layers on glass. Each layer is one quarter-wave thick at the design wavelength λ₀, so the partial reflections from every interface add in phase — start from a single pair and watch the stopband deepen toward near-unity reflectance as pairs are added.

Why This Design Works

A Bragg reflector stacks alternating quarter-wave layers of high (\(n_H\)) and low (\(n_L\)) index. At the design wavelength λ₀ the partial reflections from every interface return in phase, so even small per-interface contrasts add up to near-unity reflectance after a few periods. The high-reflectance stopband width is set by the index contrast, not the pair count — extra pairs only deepen reflectance inside the band.

Quarter-wave thicknesses at normal incidence, with the stopband full-width set by index contrast. The field profile below shows light decaying into the stack inside the stopband; the pair-count sweep shows reflectance saturating toward unity.

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.