3.2        FBG synthesis and reconstruction

3.2.3       Reconstructed FBG interpretation

The complex coupling coefficients q_j are calculated from the complex reflectors r_j through the equation (3-16a). The complex coupling coefficient distribution q(z) can then be calculated by interpolation between the positions j×D. The complex coupling coefficient gives the local grating strength and its chirp and is related to the three distributions Dn_ac(z), Dn_dc(z) and q(z) by the following equations :

where f_q = Arg(q) and k has been evaluated at the design wavelength (l_d = 2 n_eff L_d). We can notice that a single reconstruction cannot distinguish a period chirp from a DC refractive index chirp. For this reason, an effective grating period L_eff for each layer is defined, which represents the chirp function :

where L_d is the design period. The local Bragg wavelength corresponds to 2L_eff×n_eff. The effective grating period can be expressed as a function of the Dn_dc and q distributions