Theory
The fundamental principle behind the operation of a FBG, is Fresnel reflection. Where light traveling between media of different refractive indices may both reflect and refract at the interface.
The grating will typically have a sinusoidal refractive index variation over a defined length. The reflected wavelength, called the Bragg wavelength, is defined by the relationship,
where is the effective refractive index of the grating in the fiber core and is the grating period. The effective refractive index quantifies the velocity of propagating light as compared to its velocity in vacuum. depends not only on the wavelength but also (for multimode waveguides) on the mode in which the light propagates. For this reason, it is also called modal index.
The wavelength spacing between the first minima (nulls, see Fig. 2), or the bandwidth, is (in the strong grating limit) given by,
where is the variation in the refractive index, and is the fraction of power in the core. Note that this approximation does not apply to weak gratings where the grating length, is not large compared to \ .
The peak reflection is approximately given by,
where is the number of periodic variations. The full equation for the reflected power, is given by,
where,
Read more about this topic: Fiber Bragg Grating
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