3.3        Calculated FBG spectral and impulse responses

3.3.2       Non homogeneous FBG examples

We define in this section two non-homogeneous gratings that will be important to characterize the reconstruction process. The first grating exhibits discontinuities and linear variations of the refractive index modulation amplitude and of the grating period. The second grating is a period step-chirped grating.

a)   Non homogeneous grating with discontinuities and ramps

In order to study the influence of the different parameters in the reconstruction process, a particular non-homogeneous FBG has been designed. Such grating exhibits discontinuities, constant and ramp parts in the Dn_ac, Dn_dc and L distributions. The refractive index modulation and local Bragg condition are presented in Fig. 3-16. The grating is divided in six sections of 2 mm length. The average refractive index distribution Dn_dc is opposite to the refractive index modulation amplitude Dn_ac to keep the effective refractive index to a constant value of 1.45. The sections where the refractive index modulation and the Bragg condition are constant are simulated in a single layer. In the cases where a ramp exists, the section is divided in 100 layers and the varying parameter is linearly distributed. This grating is labeled FBG1.

Fig. 3-16 Special FBG1 refractive index modulation amplitude Dn_ac (top) and local Bragg condition 2n_effL (bottom)

The spectral response for this grating is presented in Fig. 3-17. The main spectral region extends from 1298 to 1302 nm and a very complicated spectral amplitude and time delay are observed.

Fig. 3-17 Spectral response amplitude [dB] (top), linear scale (middle) and time delay (bottom) for FBG1

Fig. 3-18 Impulse response amplitude [dB] (top) and phase difference of the impulse phase with respect to the phase of a propagation at 1300 nm (bottom) for FBG1 with two OPLD scales; the vertical lines in the left part of the figure indicate the grating sections limits

The impulse response of FBG1 is then presented in Fig. 3-18. The left part of the figure presents the details of the grating region, where the vertical lines indicate the limits of each section of the grating. The first section exhibits a large amplitude decrease due to the high Dn_ac. The amplitude after the first section is difficult to directly interpret due to the high grating strength that greatly modifies the pulse spectral properties during the propagation. The reconstruction for this kind of grating is then very important.