Practical implementation of apodized fiber Bragg grating results in approximation
to the apodization profile. In this study, these profiles are simulated by sampling and
segmentation. Segmenting an ideal profile is basically producing its corresponding
piecewise linear profile. The number of segments varies with the error value, which is
defined as the maximum absolute difference between the segmented profile and the ideal
one. The relationship between the error and the number of segments is found to be one to
many. To study the process normal and DWDM gratings have been considered. The
quality of the fiber Bragg gratings was investigated through the maximum reflectivity,
the SLSR, and the bandwidth of the normal gratings, the insertion loss, the bandwidth,
and the crosstalk parameters for the DWDM gratings.
Some of the results are wlexpected. Segmentation enhances the quality of the
gratings for some error values. For example, side lobe suppression ratio for normal
grating apodized with segmented profile is improved by around 5.8dB at error of 0.015
compared to the grating apodized with smooth function. An enhancement of 0.5% on the maximum reflectivity is also achieved for these normal gratings. For DWDM gratings the
insertion loss is decreased by an amount of 0.002dB and the adjacent crosstalk is
improved by an amount of around 2.5dB for some approximated Cosine apodization
profile.
The study was also done to investigate the sampling effect. Sampling rate was
varied for a fixed value of the maximum error. The study showed a good grating quality
over a wide range of sampling. This would have an impact of relaxing the practical
implementation of such process. In order to explain the results obtained, a criteria was
formulated. This is based on the integration of error function. This criterion was
instrumental in explaining the results