The decibel scale representation of the
impulse response amplitude depends on the spectrum of the light propagating in
the grating. For simulation purpose, a theoretical light source with Gaussian
spectral shape is defined, which is determined by its central wavelength and
bandwidth. The influence of these parameters in the calculation of the impulse
response can be seen as a windowing effect applied to the Fourier transform of
the grating spectral response.
a)
Source bandwidth effect
The influence of the source bandwidth
is presented in Fig. 3-22. The FBG is homogeneous, 10 mm long with a
refractive index modulation amplitude of 2×10-4. The central wavelength of the light source is set to the Bragg
wavelength of 1300 nm. The impulse response obtained for a theoretical
source with bandwidth of 1, 5, 25 and 125 nm is shown. The impulse
response amplitude is inversely proportional to the source bandwidth. This can
be explained since for smaller bandwidth sources, the coherence length is
larger and then the coherent reflection is higher. The counterpart to higher
amplitude is a wider transition region that is observed at the grating input
and output. The convolution process with a function of higher coherence length
explains this. It is important to notice that this "smoothing" effect does not
affect the impulse response amplitude near poles (impulse response position for
which the amplitude sharply drops to zero and the phase difference has a p-shift).
Moreover, we can observe that the phase difference is not affected by the
source bandwidth.
Fig. 3-22 Source bandwidth effect on the complex impulse response amplitude
(top) and phase difference (bottom) for a 10 mm homogeneous grating with 2×10-4 refractive index modulation; 125 nm (solid
lines), 25 nm (dashed lines), 5 nm (dashed-dotted lines) and
1 nm (dotted lines) source bandwidth have been simulated
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