Effects of Segmentation and Step Sampling on Apodized Fiber Bragg Grating

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.

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