Bragg Mirror / DBR Calculator

Setup

High-Reflectivity Quarter-Wave Stack

A dielectric Bragg reflector builds a high-reflectance stopband by stacking high-index TiO₂ and low-index SiO₂ quarter-wave layers on glass.

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.

\[\begin{aligned} d_H &= \frac{\lambda_0}{4 n_H}, \qquad d_L = \frac{\lambda_0}{4 n_L}, \\ \Delta\lambda &\approx \frac{4 \lambda_0}{\pi}\sin^{-1}\!\left(\frac{n_H - n_L}{n_H + n_L}\right) \end{aligned}\]

Quarter-wave thicknesses at normal incidence and the stopband full-width set by index contrast. With \(n_H = 2.35\) (TiO₂) and \(n_L = 1.46\) (SiO₂) at \(\lambda_0 = 0.550\) μm: \(d_H \approx 0.059\) μm, \(d_L \approx 0.094\) μm, \(\Delta\lambda \approx 0.165\) μm.

Design Sweeps

Design wavelength (µm)

TiO₂ thickness (μm)

SiO₂ thickness (μm)

Bragg pair count

Incidence angle (\({}^{\circ}\))

TiO₂ \(d_H\) 0.059 μm

SiO₂ \(d_L\) 0.094 μm

Stopband \(\Delta\lambda\) 0.165 μm

Stack

Layer Material n k Thickness (µm) Coherence Plot n&k

↓

Incident

∞

coh

↓

Substrate

∞

Open design in calculator

Results

Reflectance Spectrum

normal incidence

sp R

Electric Field Profile

0.550 μm

Pair-Count Sweep

selected λ R vs N