4.5 Sinc apodized cascaded fiber Bragg grating

We will simulate the spectral characteristics of the cascaded Sinc apodized fiber Bragg grating as in Figure 8. In this simulation we choose modulation index, d<sup>n</sup> ¼ 0:0003 and grating length L = 5 mm. From Figure 8 we noted that as the number of cascade of fiber Bragg grating is increased the bandwidth is decreased and the side lobes are also decreased but reflectivity is decreased.

we have obtained from simulation result for one unit of fiber Bragg grating the reflectivity, R = 99% and bandwidth =0.013 nm but the side lobes is high, for two cascaded units from fiber Bragg grating the reflectivity, R = 97% and bandwidth =0.01 nm but side lobes in this case is decreased on one unit of fiber Bragg grating, for three cascaded units from fiber Bragg grating the reflectivity, R = 96% and bandwidth =0.0098 nm but side lobes is decreased and for four cascaded units from

Figure 7. Reflectivity spectrum for four stage Nuttall apodized fiber Bragg grating.

In this simulation the modulation index, d<sup>n</sup> ¼ 0:0003 and grating length L = 5 mm. From Figure 9 we noted that as the number of cascade of fiber Bragg grating is increased the bandwidth is decreased and the side lobes are also decreased but reflectivity is decreased. We have obtained from simulation result for one unit of fiber Bragg Grating the reflectivity, R = 96% and bandwidth =0.013 nm but the side lobes is high, for two cascaded units from fiber Bragg grating the reflectivity, R = 93% and bandwidth =0.0092 nm but side lobes in this case is decreased on one unit of fiber Bragg grating, for three cascaded units from fiber Bragg grating the reflectivity, R = 90% and bandwidth =0.0084 nm but side lobes is decreased and for four cascaded units from fiber Bragg grating the reflectivity, R = 87%, bandwidth =0.0081 nm and approximately no side lobes. Then we concluded that Reflectivity, R = 87%, bandwidth =0.0081 nm and the minimum side lobes is achieved at the

fourth unit of cascaded fiber Bragg grating.

Theoretic Study of Cascaded Fiber Bragg Grating DOI: http://dx.doi.org/10.5772/intechopen.83020

> Grating length and refractive index modulation

Stage number

Uniform L = 5 mm, dn = 0.0003 1st stage 99 0.22

Hamming L = 40 mm, dn = 0.0004 1st stage 98 0.026

Barthan L = 15 mm, dn = 0.0001 1st stage 100 0.083

Nuttall L = 15 mm, dn = 0.0003 1st stage 99 0.08

Sinc L = 80 mm, dn = 0.0004 1st stage 99 0.013

Proposed L = 80 mm, dn = 0.0002 1st stage 96 0.013

Comparison between reflectivity, R and bandwidth for different cascaded units of apodized fiber Bragg grating.

Reflectivity, R (%)

2nd stage 98 0.17 3rd stage 97 0.168 4th stage 96 0.16

2nd stage 96 0.02 3rd stage 93 0.018 4th stage 92 0.017

2nd stage 99 0.069 3rd stage 99 0.066 4th stage 99 0.064

2nd stage 99 0.063 3rd stage 98 0.061 4th stage 98 0.059

2nd stage 97 0.010 3rd stage 96 0.0098 4th stage 95 0.0096

2nd stage 93 0.0092 3rd stage 90 0.0084 4th stage 87 0.0081

Bandwidth (nm)

Apodization profile

Table 1.

19

Figure 8. Reflectivity spectrum for four stage sinc apodized fiber Bragg grating.

fiber Bragg grating the reflectivity, R = 95%, bandwidth =0.0096 nm and approximately no side lobes. Then we concluded that Reflectivity, R = 95%, bandwidth =0.0096 nm and the minimum side lobes is achieved at the fourth unit of cascaded fiber Bragg grating.

## 4.6 Proposed apodized cascaded fiber Bragg grating

We will simulate the spectral characteristics of the cascaded proposed apodized fiber Bragg grating as in Figure 9.

Figure 9. Reflectivity spectrum for four stage proposed apodized fiber Bragg grating.
