Fibre Bragg grating
A fibre Bragg grating reflects a narrow band about its Bragg wavelength, back out of the port the light came in by, and passes the rest. With a circulator it picks one wavelength out of a spectrum; two make a fibre laser's cavity.
Ports
Ports 1 and 2, one each side.
The model
The grating’s power reflectance at wavelength \(\lambda\) is a Gaussian band of peak \(R_\text{max}\), centred on the Bragg wavelength \(\lambda_B\), with a full width at half maximum \(w\):
\[R(\lambda) = R_\text{max}\exp\!\left(-4\ln 2\left(\frac{\lambda - \lambda_B}{w}\right)^{2}\right).\]It reflects the same from both sides and passes the rest, with no loss:
\[\mathbf S_{11} = \mathbf S_{22} = \sqrt{R}\;\mathbf I, \qquad \mathbf S_{12} = \mathbf S_{21} = \sqrt{1 - R}\;\mathbf I.\]Broadband light is followed in slices fine enough to resolve the band (see Fibre optics: broadband light), so the grating’s reflection of an LED or an amplifier’s ASE has the grating’s own spectrum.
Settings
| Field | Default | Meaning |
|---|---|---|
centre | 1550 | Bragg wavelength (nm) |
fwhm | 0.5 | Bandwidth (nm) |
rmax | 90 | Peak reflectance (%) |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Assumptions
- The reflection band is Gaussian, with no side lobes and no phase across it: a real uniform grating has sinc-like side lobes, and a chirped one has dispersion.
- The grating is thin: it adds no delay of its own, and both polarisations see the same band.
Related
- Circulator.
- Tunable filter and WDM.
- Fibre mirror, a broadband reflector.