Glossary entry

Distributed Bragg reflector (DBR mirror)

A multi-layer dielectric mirror that reflects via constructive interference from many quarter-wave layer interfaces. The high-reflectivity mirror used in VCSELs, DBR lasers, and many fiber and free-space optics.

A distributed Bragg reflector is a periodic stack of two alternating dielectric materials with refractive indices $n_H$ (high) and $n_L$ (low), each layer one quarter-wavelength thick at the design wavelength:

d_H \;=\; \frac{\lambda_0}{4 n_H}, \qquad d_L \;=\; \frac{\lambda_0}{4 n_L}.

At $\lambda_0$ , partial reflections from each interface add in phase, producing high net reflectivity. Off-design wavelengths suffer partial destructive interference and the reflectivity drops.

Peak reflectivity for a stack of $N$ layer pairs on a substrate:

R \;=\; \left( \frac{1 - (n_L/n_H)^{2N} (n_s / n_0)}{1 + (n_L/n_H)^{2N} (n_s / n_0)} \right)^2,

where $n_0$ is the incident-medium index and $n_s$ is the substrate index. Higher index contrast and more layer pairs both increase the achievable reflectivity.

Stopband bandwidth.

\Delta\lambda \;=\; \frac{4 \lambda_0}{\pi} \arcsin\!\left( \frac{n_H - n_L}{n_H + n_L} \right).

For Si–SiO $_2$ (extreme index contrast): $\sim 600$ nm stopband. For AlAs–GaAs in VCSEL mirrors: $\sim 100$ nm at 850 nm. For TiO $_2$ –SiO $_2$ visible-band coating: $\sim 200$ nm.

Typical implementations:

Application	Materials	Pairs	Peak reflectivity
850 nm VCSEL top mirror	AlGaAs/AlAs	25 – 30	99.5 %
850 nm VCSEL bottom mirror	AlGaAs/AlAs	35 – 40	99.95 %
Laser line dichroic	TiO $_2$ /SiO $_2$	15 – 25	$> 99.9$ %
Fiber Bragg grating	UV-written index modulation in silica core	1000s of "pairs" via $\Delta n \sim 10^{-4}$	$> 99$ %
High-finesse cavity supermirror	Ta $_2$ O $_5$ /SiO $_2$ ion-beam-sputtered	30 – 50	$> 99.999$ %
Anti-reflection coating	Same materials, different design	1 – 4	$< 0.1$ % (low- $R$ design)

DBR mirrors are the standard high-reflectivity element where metal mirrors are unsuitable — wherever low absorption, high power handling, or wavelength-selectivity is required.

Compared to a single Bragg grating in a waveguide: the physical principle is identical (Bragg interference from a periodic index modulation), but DBR mirrors are typically deposited multilayer dielectric stacks for free-space optics or epitaxially-grown semiconductor stacks for vertical-cavity devices. Waveguide Bragg conditions refer to periodic in-plane index modulation in a guided wave.

For DBR mirrors in VCSELs: the very high reflectivities ( $> 99.5$ %) are necessary because the active region is only $\sim 100$ nm thick (one to a few quantum wells, each $\sim 10$ nm), so the single-pass gain is small. Without extreme mirror reflectivities, threshold could never be reached.