Distributed Bragg Reflector - Reflectivity

Reflectivity

The DBR's reflectivity, for intensity is approximately 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,

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.

The bandwidth of the photonic stopband can be calculated by

\Delta\lambda_0 = \frac{4\lambda_o}{\pi}\arcsin\left(\frac{n_2 - n_1}{n_2 + n_1}\right),

where is the central wavelength of the band.

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.

Distributed Bragg reflectors are critical components in vertical cavity surface emitting lasers and other types of narrow-linewidth laser diodes such as distributed feedback lasers. They are also used to form the cavity resonator (or optical cavity) in fiber lasers and free electron lasers.

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