Distributed Bragg reflector
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A distributed Bragg reflector (DBR) is a high quality reflector used in waveguides, such as optical fibers. It is a structure formed from multiple layers of alternating materials with varying refractive index, or by periodic variation of some characteristic (such as height) of a dielectric waveguide, resulting in periodic variation in the effective refractive index in the guide. Each layer boundary causes a partial reflection of an optical wave. For waves whose wavelength is close to four times the optical thickness of the layers, the many reflections combine with constructive interference, and the layers act as a high-quality reflector. The range of wavelengths that are reflected is called the photonic stopband. Within this range of wavelengths, light is "forbidden" to propagate in the structure.
[edit] Reflectivity
The reflectivity (R) of the DBR is given by
![R= \left[\frac{n_o (n_2)^{2N} - n_s (n_1)^{2N}}{n_o (n_2)^{2N} + n_s (n_1)^{2N}}\right]^2,](../../../math/a/8/3/a83652da1d8f2fc207e0c51367ff373f.png)
where 
and 
are the respective refractive indices of the surrounding medium, the two alternating materials, and the substrate; and N is the number of repeated pairs of low/high refractive index material.
The bandwidth Δν0 of the photonic stopband can be calculated by
where νo is the central frequency of the band.
Thus increasing the number of pairs in a DBR increases the mirror reflectivity and increasing the refractive index contrast between the materials in the Bragg pairs increases both the reflectivity and the bandwidth.
Distributed Bragg reflectors are critical components in vertical cavity surface emitting lasers and other types of narrow-linewidth laser diodes. They are also used to form the cavity resonator (or optical cavity) in fiber lasers and free electron lasers.
