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c)
Constant product of the length and the
refractive index modulation amplitude
Interesting scaling properties can be
deducted in the case of FBGs for which the product Dnac×L is kept constant. The spectral and impulse response of four
gratings with Dnac×L = 10-6 have
been calculated for grating lengths of 0.1, 1, 10 and 100 mm (the
corresponding Dnac are 10-2, 10-3, 10-4 and 10-5
respectively). The impulse amplitudes are presented in Fig. 3-14 with
respect to the OPLD on a logarithmic scale. As we can see, the shape of the
responses is identical. The amplitude level is proportional to Dnac
while the OPLD range is proportional to the grating length.
Fig. 3-14 Impulse response amplitude for constant Dnac×L = 10-6 with (L = 100 mm, Dnac = 10-5) in
dotted line, (10, 10-4) in dashed-dotted line, (1, 10-3) in dashed line,
(0.1, 10-2) in solid line
Fig. 3-15 Spectral response amplitude in [dB] and time delay in [ps] for the
four FBG's with constant constant Dnac×L of 10-6
The corresponding spectral responses
are presented in Fig. 3-15. The amplitude shape is identical, with the
same amplitude level but with different wavelength bandwidth, which is
inversely proportional to the grating length. The time delays also exhibit the
same shape, with the same bandwidth change but with an amplitude scaling factor
proportional to the grating length. The relative poor definition of the
spectral response of the 100 mm grating is due to the limited resolution
of the simulation.
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