3.3        Calculated FBG spectral and impulse responses

3.3.2       Non homogeneous FBG examples

b)   Period step-chirped grating

A second non-homogeneous grating, FBG2, has been simulated to investigate the reconstruction limits. The length is 10 mm, the refractive index modulation is constant (5×10^-4) and the grating period is divided in ten sections with different values linearly distributed to give Bragg conditions between 1298 to 1302 nm. The refractive index modulation amplitude (Dn_ac) and the Bragg wavelength (2Ln_eff) distributions of such grating are seen in Fig. 3-19.

The corresponding spectral response is shown in Fig. 3-20. The amplitude exhibits a nearly rectangular response between 1298 and 1302 nm. The amplitude and the time delay responses show ripples.

The impulse response amplitude of FBG2 (Fig. 3-21) shows an important amplitude drop for the first section, but then the signal increases at the entrance of any other section and the overall level is constant in the grating region. This is explained by the fact that each section reflects a different part of the source spectrum. The amplitude drop greater than 20 dB at the grating output indicates that few photons are trapped inside the structure for several round-trips. We observe that the second derivative of the phase difference, d²Df/dOPLD² (Df is the phase difference), is negative in the grating region and then constant after the grating output. This effect is explained by the decrease of the Bragg condition distribution along the grating.

Fig. 3-19 Special FBG2 refractive index modulation amplitude (top) and local Bragg condition (bottom)

Fig. 3-20 Spectral response amplitude in dB (top) and in linear scale (middle), and time delay (bottom) for the FBG2

Fig. 3-21 Impulse response amplitude (top) and phase difference with the phase of propagation at 1300 nm (bottom) for FBG2