4.2 Hamming apodized cascaded fiber Bragg grating

We will simulate the spectral characteristics of the cascaded Hamming apodized fiber Bragg grating as in Figure 5.

In this simulation the modulation index, d<sup>n</sup> ¼ 0:0003 and grating length L = 5 mm. From Figure 5 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.

Figure 5. Reflectivity spectrum for four stage hamming apodized fiber Bragg grating.

We have obtained from simulation result for one unit of fiber Bragg grating the reflectivity, R = 98% and bandwidth =0.026 nm but the side lobes is high, for two cascaded units from fiber Bragg grating the reflectivity, R = 96% and bandwidth =0.020 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 = 93% and bandwidth =0.018 nm but side lobes is decreased and for four cascaded units from fiber Bragg grating the reflectivity, R = 92%, bandwidth =0.017 nm and approximately no side lobes. Then we concluded that Reflectivity, R = 92%, bandwidth =0.017 nm and the minimum side lobes is achieved at the fourth unit of cascaded fiber Bragg grating.

4.4 Nuttall apodized cascaded fiber Bragg grating

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

fiber Bragg grating as in Figure 7.

fourth unit of cascaded fiber Bragg grating.

0

Reflectivity spectrum for four stage Nuttall apodized fiber Bragg grating.

Figure 7.

17

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Refelectivity, R

4.5 Sinc apodized cascaded fiber Bragg grating

We will simulate the spectral characteristics of the cascaded Nuttall apodized

We will simulate the spectral characteristics of the cascaded Sinc apodized fiber

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

1.5495 1.5496 1.5497 1.5498 1.5499 1.55 1.5501 1.5502 1.5503 1.5504 1.5505

Wavelength, um

x 10-6

One FBG Two FBG Three FBG Four FBG

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.

In this simulation the modulation index, d<sup>n</sup> ¼ 0:0003 and grating length L = 5 mm. from Figure 7 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 = 0.08 nm but the side lobes is high, for two cascaded units from fiber Bragg grating the reflectivity, R = 99% and bandwidth =0.063 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 = 98% and bandwidth = 0.061 nm but side lobes is decreased and for four cascaded units from fiber Bragg grating the reflectivity, R = 98%, bandwidth = 0.059 nm and approximately no side lobes. Then we concluded that Reflectivity, R = 98%, bandwidth = 0.059 nm and the minimum side lobes is achieved at the

#### 4.3 Barthan apodized cascaded fiber Bragg grating

We will simulate the spectral characteristics of the cascaded Barthan apodized fiber Bragg grating as in Figure 6.

In this simulation the modulation index, d<sup>n</sup> ¼ 0:0003 and grating length L = 5 mm. From Figure 6 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 = 100% and bandwidth = 0.083 nm but the side lobes is high, for two cascaded units from fiber Bragg grating the reflectivity, R = 99% and bandwidth =0.069 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 = 99% and bandwidth =0.066 nm but side lobes is decreased and for four cascaded units from fiber Bragg grating the reflectivity, R = 99%, bandwidth = 0.064 nm and approximately no side lobes. Then we concluded that Reflectivity, R = 99%, bandwidth =0.064 nm and the minimum side lobes is achieved at the fourth unit of cascaded fiber Bragg grating.

Figure 6. Reflectivity spectrum for four stage Barthan apodized fiber Bragg grating.

We have obtained from simulation result for one unit of fiber Bragg grating the reflectivity, R = 98% and bandwidth =0.026 nm but the side lobes is high, for two cascaded units from fiber Bragg grating the reflectivity, R = 96% and bandwidth =0.020 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 = 93% and bandwidth =0.018 nm but side lobes is decreased and for four cascaded units from fiber Bragg grating the reflectivity, R = 92%, bandwidth =0.017 nm and approximately no side lobes. Then we concluded that Reflectivity, R = 92%, bandwidth =0.017 nm and the minimum side lobes is achieved at the fourth unit of cascaded

We will simulate the spectral characteristics of the cascaded Barthan apodized

1.5495 1.5496 1.5497 1.5498 1.5499 1.55 1.5501 1.5502 1.5503 1.5504 1.5505

Wavelength, um

x 10-6

One FBG Two FBG Three FBG Four FBG

In this simulation the modulation index, d<sup>n</sup> ¼ 0:0003 and grating length L = 5 mm. From Figure 6 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 = 100% and bandwidth = 0.083 nm but the side lobes is high, for two cascaded units from fiber Bragg grating the reflectivity, R = 99% and bandwidth =0.069 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 = 99% and bandwidth =0.066 nm but side lobes is decreased and for four cascaded units from fiber Bragg grating the reflectivity, R = 99%, bandwidth = 0.064 nm and approximately no side lobes. Then we concluded that Reflectivity, R = 99%, bandwidth =0.064 nm and the minimum side lobes is achieved at the

fiber Bragg grating.

fiber Bragg grating as in Figure 6.

fourth unit of cascaded fiber Bragg grating.

0

Reflectivity spectrum for four stage Barthan apodized fiber Bragg grating.

Figure 6.

16

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Refelectivity, R

4.3 Barthan apodized cascaded fiber Bragg grating

Fiber Optic Sensing - Principle, Measurement and Applications
