Interestingly, there are two Braggs, father (W.H) and son (W.L.), for whom the Bragg Grating is named. Actually, the grating is named after the Bragg equation, developed in 1912, that describes the reflection of light in a three-dimensional grating:

nλ=2dsinΘ

Where d is the distance between parallel planes of crystal and Θ is the glancing angle.

What this basically means is that a Bragg Grating is a lattice of crystals arranged in a way that they filter light by internal reflection. In other words, you can arrange a grid of crystals (or other highly-structured material) so that light going into it will bounce around in such a way that only the light with the wavelength you want will come out of it.

An excellent example of this occurs in nature, visible in the colors of a butterfly's wing. They don't have any pigment in them, as their color comes from the way light is selectively absorbed and reflected by microscopic structures on their surfaces. Another example is the colors you see on the surface of a soap bubble.

A Bragg Grating is extremely useful, as it allows one to filter light without using pigment-based filters. Applications range from filters for fiber-optic communications, where they can be created in the fiber itself, to the recent experimentation in iridescent display technology, where each pixel in the display is a tunable Bragg Grating, reflecting the color desired to create the image.

Fiber Bragg Gratings are created by exposing a short length of the fiber to intense ultraviolet light. A mask with a periodic pattern is placed over the fiber, and the 240 to 260 nm light alters the refractive index of the fiber's core. The mask is made in relation to the wavelengths of light upon which the filter is to operate. The period of the pattern should be half the period of the light upon which filter is to act. Most light pass through the filter with ease, but the selected wavelength will be strongly reflected. The performance of the grating depends on the strength of the changes to the refractive index, the number of periods used in the grating, and the precision of the filter's creation.

Bragg Gratings used as fiber optic filters can typically have a near zero insertion loss for unfiltered wavelengths, with a 50 dB loss at the set wavelength. High quality gratings can have 0.2 nm bandwidths and reflect 99.9% of the light in that band. Other gratings can be made to reflect less light, or have a wider band, allowing wavelength-specific precision attenuation. The low insertion loss of Bragg Gratings and the narrow bandwidths they offer make them ideal for use in wavelength division multiplexing. The biggest drawbacks to these filters is that they must be kept at a consistant temperature.

To use a Bragg Grating in a WDM application, there are multiple approaches. One option is to use an optical circulator, like so:

```                 Clockwise Circulator
___
/   \    Bragg
λ1, λ2, λ3, λ4 >--------|    |----||||--> λ1, λ3, λ4
\___/
|
|
v
λ2
```
Although this approach is effective, the cost of circulators makes it often desirable to find a cheaper alternative, like the Mach-Zehnder Interferometer. The Mach-Zehnder approach uses a coupler-like structure with waveguides. Although this method is cheaper, it is much more complex to build.

Another use for Bragg Gratings in fiber is to filter the output of the pump lasers in optical amplifiers, and to flatten the gain of the amplifier's output. A long period Bragg Grating couples the high-gain wavelengths into the cladding, causing all wavelengths to show the same gain at the output.

Yet another use in fiber optics is compensating for chromatic dispersion. By carefully varying the periods along the length of the grating, different amounts of delay can be added to different wavelengths. Done properly, this will tighten the pulse.

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