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# Bragg Gratings

Author: the photonics expert

Definition: reflecting structures with a periodic refractive index modulation

More specific terms: fiber Bragg gratings, volume Bragg gratings, holographic bulk gratings

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

$$\frac{2\pi}\Lambda = 2 \cdot \frac{2\pi n}{\lambda} \cos \theta$$

where <$\lambda$> is the vacuum wavelength of light, <$n$> the average refractive index of the medium, <$\theta$> the propagation angle in the medium relative to the direction normal to the grating, and <$\Lambda$> 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 (from angle) Angle: calc (from period)

Enter input values with units, where appropriate. After you have modified some values, click a “calc” button to recalculate the field left of it.

Around the Bragg wavelength, even a weak refractive 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.

Is the crucial function of a Bragg grating is usually to reflect light, it can also be called a Bragg reflector.

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## Questions and Comments from Users

2023-12-02

Isn't the Bragg condition also fulfilled at integer multiples of the fundamental optical frequency?