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# Bragg Gratings

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Definition: reflecting structures with a periodic refractive index modulation

German: Bragg-Gitter

An optical Bragg grating is a transparent device with a periodic variation of the refractive index, so that a large reflectivity may be reached in some wavelength range (bandwidth) around a certain wavelength which fulfills the Bragg condition

Figure 1: A volume Bragg grating within a glass block reflects an incident beam, if the Bragg condition is met (left-hand side). For a different angle of incidence, hardly any reflection occurs.

where λ is the vacuum wavelength of light, n the refractive index, θ the propagation angle in the medium relative to the direction normal to the grating, and Λ the grating period. If this condition is met, the wavenumber of the grating matches the difference of the wavenumbers of the incident and reflected waves.

Other wavelengths are only weakly affected by the Bragg grating, except for some side lobes in the reflection spectrum. Similarly, the reflection can nearly totally disappear when the angle of incidence is modified (see Figure 1).

## Calculator for the Bragg Condition

 Wavelength: Refractive index: Grating period: calc Angle: calc

After you have modified some values, click a "calc" button to recalculate the field left of it.

Around the Bragg wavelength, even a weak index modulation can be sufficient for achieving nearly total reflection, if the grating is sufficiently long. Due to the wavelength dependence of reflection and transmission, a Bragg grating can serve as an optical filter.

## Examples of Optical Bragg Gratings

• Bragg gratings made in a bulk piece (e.g. of some glass or polymer), usually by irradiation of a photosensitive glass with coherent ultraviolet light which is spatially modulated using an interference pattern, are called volume Bragg gratings (Figure 1). Their reflection bandwidth is much smaller than that of dielectric thin-film mirrors, since they have a low refractive index contrast, which is compensated with a correspondingly longer interaction length. (Peak reflectivities of 99.9% are possible.) Volume Bragg gratings can be used e.g. as output couplers for laser diodes; the small reflection bandwidth (e.g. below 0.1 nm) can then lead to a narrow emission bandwidth (linewidth) and a low temperature dependence of the emission wavelength, which can facilitate the pumping of solid-state lasers. One can also insert a volume Bragg grating into the laser resonator of a solid-state laser in order to stabilize or tune its emission wavelength. For high intracavity powers (e.g. tens of watts), however, detrimental thermal effects can occur, such as a shift of the reflection band and a decrease of reflectivity. For not too high power levels, volume Bragg gratings can also be used in spectral beam combining.
• There are fiber Bragg gratings, made in optical fibers. These can reflect light in fibers, or lead to various kinds of mode coupling in multimode fibers. Fiber Bragg gratings are used e.g. for fixing the wavelengths of fiber lasers, for filtering out certain wavelength components, for gain flattening of fiber amplifiers, and in fiber-optic sensors.
• There are also laser diodes with built-in Bragg gratings (based on semiconductor technology) for narrowing and stabilization of the emission wavelength (→ distributed Bragg reflector lasers, distributed feedback lasers).

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