Distributed Bragg reflector

A Bragg mirror ( distributed Bragg reflector, abbreviated by DBR ) denotes an efficient reflector is used in optical fibers or optical resonators. It consists of alternating thin layers of different refractive indices. Mostly, the layers of dielectrics. Therefore you also be used in such a reflector the term dielectric mirror. At each boundary layer part of the electromagnetic wave of light according to Fresnel formulas is reflected. When the wavelength is close to four times the optical path length of the layer, then the reflected rays interfere constructively and there is a high-quality reflector. The area in which the reflection is very high, ie stop-band. Light whose wavelength is within the stop bands can not propagate in the structure.

Reflectivity

Generally

The maximum reflectance for a wavelength is achieved when all layers have an optical density of just a quarter of wavelength. Then the reflectivity calculated for this wavelength to:

Wherein the refractive index of the surrounding medium, and the refractive indices of the two materials, and the refractive index of the substrate. is the number of layer pairs. With the proviso that the two materials have different refractive indices, results. It is possible an arbitrarily high reflectivity to achieve if only enough layer pairs are used.

The width of the stop bands is calculated as follows:

Example calculation

We consider a Bragg reflector in the air, that is, with ten double layers of silicon dioxide (), and titanium (IV ) oxide ( ) on a silica substrate (). Used in the formula results in:

These ten bilayers is reached, according to the reflectivity, which is significantly higher than that of a metallic mirror with a reflectivity of approximately 92 to 98%. However, the wavelength range in which the reflection occurs is significantly less than that of a metallic mirror. He is in this example:

Thus would this Bragg mirror when he has its maximum reflectivity at 500 nm, very well reflect only in the range of 390 nm to 610 nm.

Application

Bragg mirrors are used in many semiconductor lasers as surface emitters (VCSEL ) optically pumped semiconductor lasers ( VECSEL ), laser diodes, lasers and distributed feedback (DFB). In many lasers Bragg mirror can be used as a mirror, because the wavelength is usually well defined. Thus, one can with Bragg mirrors significantly higher reflectivity than with metallic mirrors. In addition, Bragg mirror can be used as a dichroic mirror, which almost completely reflect a color and other colors almost completely transmit. By using, instead of λ/2- λ/4-Schichten results an interference filter and, when using the dielectric materials of a dielectric filter.

Bragg mirrors can also be easily integrated into glass fibers, is called fiber Bragg gratings. Here the same rules as with other Bragg mirrors are.