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Concept
Distributed Bragg reflector
Summary
A distributed Bragg reflector (DBR) is a reflector used in waveguides, such as optical fibers. It is a structure formed from multiple layers of alternating materials with different 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 and refraction of an optical wave. For waves whose vacuum wavelength is close to four times the optical thickness of the layers, the interaction between these beams generates 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.
The DBR's reflectivity, , for intensity is approximately given by
where and are the respective refractive indices of the originating medium, the two alternating materials, and the terminating medium (i.e. backing or substrate); and is the number of repeated pairs of low/high refractive index material. This formula assumes the repeated pairs all have a quarter-wave thickness (that is , where is the refractive index of the layer, is the thickness of the layer, and is the wavelength of the light).
The frequency bandwidth of the photonic stop-band can be calculated by
where is the central frequency of the band. This configuration gives the largest possible ratio that can be achieved with these two values of the refractive index.
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. A common choice of materials for the stack is titanium dioxide (n ≈ 2.5) and silica (n ≈ 1.5). Substituting into the formula above gives a bandwidth of about 200 nm for 630 nm light.
Official source
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