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Bragg Mirrors

Acronym: DBR = distributed Bragg reflector

Definition: mirror structures based on Bragg reflection at a period structure

More general term: distributed mirrors

German: Bragg-Spiegel

Category: photonic devices

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A Bragg mirror (also called distributed Bragg reflector) is a mirror structure which consists of an alternating sequence of layers of two different optical materials. The most frequently used design is that of a quarter-wave mirror, where each optical layer thickness corresponding to one quarter of the wavelength for which the mirror is designed. The latter condition holds for normal incidence; if the mirror is designed for larger angles of incidence, accordingly thicker layers are needed.

The principle of operation can be understood as follows. Each interface between the two materials contributes a Fresnel reflection. For the design wavelength, the optical path length difference between reflections from subsequent interfaces is half the wavelength; in addition, the amplitude reflection coefficients for the interfaces have alternating signs. Therefore, all reflected components from the interfaces interfere constructively, which results in a strong reflection. The reflectance (reflectivity) achieved is determined by the number of layer pairs and by the refractive index contrast between the layer materials. The reflection bandwidth is determined mainly by the index contrast.

Figure 1 shows the field penetration into a Bragg mirror made of eight layer pairs of TiO2 and SiO2. The blue curve shows the intensity distribution of a wave with the design wavelength of 1000 nm, incident from the right-hand side. Note that the intensity is oscillating outside the mirror due to the interference of the counterpropagating waves. The gray curve shows the intensity distribution for 800 nm, where a significant part of the light can get through the mirror coating.

field penetration in a Bragg mirror
Figure 1: Field penetration into a Bragg mirror, calculated with the software RP Coating.

Figure 2 shows the reflectance and the group delay dispersion as functions of the wavelength. The reflectance is high over some optical bandwidth, which depends on the refractive index contrast of the materials used and on the number of layer pairs. The dispersion is calculated from the second derivative of the reflection phase with respect to the optical frequency. It is small near the center of the reflection band, but grows rapidly near the edges.

reflectance and dispersion of a Bragg mirror
Figure 2: Reflectance (black curve) and chromatic dispersion (blue curve) of the same mirror as above.

Figure 3 shows with a color scale how the optical field penetrates into the mirror. It can be seen that there is little field penetration well within the reflection band.

field penetration in a Bragg mirror
Figure 3: Field penetration into the Bragg mirror as a function of wavelength. The colors indicate the optical intensity inside the mirror.

Figure 4 shows reflectance spectra of a Bragg mirror for different angles of incidence. The larger that angle, the more the reflection spectrum is shifted towards shorter wavelengths.

Bragg mirror reflectance vs. incidence angle
Figure 4: The reflectance spectrum of a Bragg mirror for different incidence angles from normal incidence (red) up to 60° (blue) in steps of 10°.

Types of Bragg Mirrors

Bragg mirrors can be fabricated with different technologies:

There are other multilayer mirror designs which deviate from the simple quarter-wave design. They generally have a lower reflectance for the same number of layers, but can be optimized e.g. as dichroic mirrors or as dispersive chirped mirrors for dispersion compensation.

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[1]Analysis of a Bragg mirror with the RP Coating software
[2]R. Paschotta, case study on a Bragg mirror

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See also: mirrors, Bragg gratings, fiber Bragg gratings, dielectric mirrors, crystalline mirrors, chirped mirrors, dispersive mirrors, laser mirrors, distributed Bragg reflector lasers, distributed feedback lasers
and other articles in the category photonic devices


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