2.2        Fiber Bragg grating

2.2.1        Bragg reflections

In the study of crystals, it is known that X rays are reflected at well-defined directions due to the periodic arrangement of the atoms and these reflections are described by the Bragg equation. In the same way but at larger wavelengths, a periodic refractive index variation in the core of an optical fiber will exhibit specific reflections at the Bragg condition with an angle p (i.e. back-reflection)

where l_b is the peak reflection amplitude wavelength, n_eff the effective refractive index of the guided mode, L the grating period (Fig. 2-3) and m = 1, 2 , 3, … is the Bragg reflection order. For this reason these structures are called fiber Bragg gratings (FBG). FBGs in silica-based optical fiber (with approximate effective refractive index of 1.45) have a grating period between 450 and 500 nm for the lowest Bragg reflection order in the 1300-1500 nm range. Higher orders of reflection are possible but not considered here. Fig. 2-3 shows that a broadband light around the Bragg wavelength launched in the fiber (in(l)) is partly back-reflected (r(l)) with a resonance peak at the Bragg wavelength; the remaining light is instead transmitted (t(l)). In the coupled-mode formalism [2-2], the FBG can be seen as a coupling perturbation between the forward and backward waves traveling in the fiber (Appendix C). It should be noted that a small part of the back-reflected light is also coupled in the cladding. For much larger grating periods, tens or hundreds of microns instead of half micron, the coupling of energy between the forward propagating core mode and the forward propagating cladding modes is possible. Such kind of grating is called long-period grating (LPG).

Fig. 2-3 Fiber Bragg grating and spectral effects