Page 353 - Fiber Bragg Gratings

330 Chapter 7 Chirped Fiber Bragg Gratings

and an asymmetric tanh apodized grating. The bandwidth of the asymmet-
ric apodized grating, B, is now wider than that of the symmetric apodised
grating, A, and so is the group delay difference, D. The peak reflectivity
of B is 98%, whereas that of A is 90%. There is also a small ripple acquired
in both the reflection and group-delay spectra (C and D). With lower
reflectivity, the ripple in the asymmetrically apodized grating increases,
rather than decreasing as is the case with the symmetrically apodized
grating [41].

7.2.2 Effect of nonuniform refractive index
modulation on grating period

During fabrication, it is necessary to ensure that the grating receives the
correct UV dose along its length. If the dose varies, so does the effective
refractive index modulation and therefore K ac. A constant increase in
the UV dose with length merely chirps the grating. However, random
variations are generally common with pulsed lasers, since the UV radia-
tion has hot spots across the beam, with the result that the grating is no
longer uniformly exposed. While this may not be a problem for many
filtering applications, it does degrade the performance of the group delay
in chirped gratings, limiting performance. Ouellette [4] reported the effect
of a noisy refractive index profile and dither in the period of the grating
on the reflection and dispersion characteristics. It was found that, apart
from a general increase in the out-of-band reflection, the group delay was
also degraded. A period variation of 0.03 nm (—5%) over a length scale
of 1 mm degraded the delay spectrum substantially. This is a serious
issue for the fabrication of high-quality gratings. Even with perfect phase
masks, such factors as the random variations in the effective index of the
mode, UV dose, or vibration during fabrication will cause deterioration
in the quality of the grating.
We consider the likely effect of a maximum variation of ~10% of the
5
refractive index modulation amplitude, ATI (7.5 X 10~ ), but over different
scale lengths of 50,100, and 200 microns. These are expected to be typical
regions over which the refractive index modulation varies. In order to
model this behavior, we have assumed that each section of the scale length
varies in the index modulation entirely at random with a maximum value
5
of 1 X 10~ . This is realistic despite the averaging effect of multiple pulse
exposure, since the peak UV intensities can fluctuate over several orders.
The results of the simulations of the deviation from linearity of the delay