3.1 Experimental results of side diffraction interference 3.1.1 3dB Gaussian apodized grating
A 3dB Gaussian apodized grating made by a uniform phase mask is studied first.
The power of the first order diffracted beam along the fiber axis is measured by the side diffraction method and the measurement results are shown in Figure 3.1. Because the intensity distribution of the UV laser beam is a Gaussian profile. We can see that the measured side diffraction ac index profile is also a Gaussian profile. The e-1 width of the UV beam is about 6.4~7.1cm and the e-1 width of the measured profile is about 7cm. The total width of the UV beam is about 20cm and the total width of the measured profile is about 10.5cm. By Fourier transforming the interference pattern and get the peak amplitude of the ac term we obtain the side interference ac index, as shown in Figure 3.2. Fig 3.2 also shows the repetibility of the measurement. The e-1 width of the side interference ac index profile is about 8cm and the total width of that is about 13cm. We can see that the side interference method can detect smaller index amplitudes the than side diffraction method, as shown in Figure 3.3.
The period of the interference pattern( CCD pixel) measured along the fiber axis is also measured. By
er
f f
int
, 1 tan
2 θ λ
λ =
= Λ
∆Λ we can obtain the side interference
grating period and the results are shown in Figure 3.4. The grating period distribution along the grating is almost a constant, in consistence with the use of the uniform phase mask. The resolution of the grating period measurement is about 0.01nm.
3.1.2 5dB linear chirp Gaussian apodized grating
A 5dB linear chirp Gaussian apodized grating made by a uniform phase mask is then characterized. The power of the first order diffracted beam along the fiber axis is measured, and the results of side diffraction method are shown in Figure 3.5. Because the intensity distribution of the UV laser beam is a Gaussian profile. We can see that the measured side diffraction ac index profile is also a Gaussian profile. The e-1 width of the UV beam is about 6.4~7.1cm and the e-1 width of the measured profile is about 6.5cm. The total width of the UV beam is about 20cm and the total width of the measured profile is about 10.5cm. By performing Fourier transform of the interference pattern and get the peak amplitude of the ac term we obtain the side interference ac index, as shown in Figure 3.6. Fig 3.6 also shows the repetibility of the measurement. The e-1 width of the side interference ac index profile is about 7.5cm and the total width of that is about 12cm. Again we can see that the side interference method can detect smaller index variation than the side diffraction method as shown in Figure 3.7.
The period of the interference pattern( CCD pixel) measured along the fiber axis is measured, and the results are shown in Figure 3.8. The grating period distribution along the grating is linearly increased, in consistence with the use of the linear phase mask. The chirp rate of the measured grating period is 0.7049/1.22 = 0.5778(nm/cm) and the linear chirp rate of the phase mask is 0.5(nm/cm).
3.2 Simulation results of transfer matrix method 3.2.1 3dB Gaussian apodized grating
The ac index profile of the 3dB Gaussian apodized grating made by the uniform phase mask is used to simulate the corresponding reflection and transmission spectra by transfer matrix method. First we use the side diffraction ac index profile as shown in Figure 3.1. Because the power of +1 and -1 order beam is 70% of the total power, we represent the dc refractive index profile as ( )
3 ) 4
(z n n z
ndc = core+ ∆ ac . When
Δnac,max = 0.00005925, the simulated transmission spectrum and the transmission spectrum measured by the optical spectrum analyzer are shown in Figure 3.9. The simulated reflection spectrum and the reflection spectrum measured by the optical spectrum analyzer are shown in Figure 3.10. The reflection and transmission spectra simulated by the transfer matrix method and the structure parameters obtained are in good agreement with those measured by optical spectrum analyzer. Then by fitting the curve in Figure 3.1, we obtain the fitting side diffraction ac index as shown in Figure 3.11. With the same procedure above, whenΔnac,max = 0.000062, the simulated transmission spectrum from the fitting result and the simulated transmission spectrum in Figure 3.9 are compared as shown in Figure 3.12. The simulated reflection spectrum from the fitting result and the simulated reflection spectrum in Figure 3.10 are compared as shown in Figure 3.13. We can observe that the difference of the two spectra in Fig 3.12 and 3.13 is only the height of the side lobes in the longer wavelength region. The similarity between them shows that the optical performance of many fiber Bragg grating devices are only affected by errors that occur over a relatively large (millimeter) length scale.
Next we use the side interference ac index profile as shown in Figure 3.2. When Δnac,max = 0.000054, the simulated transmission spectrum and the transmission spectrum measured by the optical spectrum analyzer are shown in Figure 3.14. The simulated reflection spectrum and the reflection spectrum measured by the optical spectrum analyzer are shown in Figure 3.15. The reflection and transmission spectra simulated by the transfer matrix method and the structure parameters obtained are in good agreement with those measured by optical spectrum analyzer. Then by fitting the curve in Figure 3.2 we obtain the fitting side interference ac index as shown in Figure 3.16. With the same simulation model above, when Δnac,max = 0.00005, the simulated transmission spectrum from the fitting result and the simulated transmission spectrum in Figure 3.14 are compared as shown in Figure 3.17. The simulated reflection spectrum from the fitting result and the simulated reflection spectrum in Figure 3.15 are compared as shown in Figure 3.18. We can observe that the difference of the two spectra in Fig 3.17 and 3.18 is only the height of the side lobes in the longer wavelength region. The similarity between them shows that the optical performance of many fiber Bragg grating devices are only affected by errors that occur over a relatively large (millimeter) length scale..
3.2.2 5dB linear chirp Gaussian apodized grating
The ac index profile of the 5dB linear chirp Gaussian apodized grating made by the linear phase mask is also used to simulate the corresponding reflection and transmission spectra by transfer matrix method. First we use the side diffraction ac index profile as shown in Figure 3.5 and the side interference grating period as shown in Figure 3.8. Again we represent the dc refractive index profile as
) 3 (
) 4
(z n n z
ndc = core+ ∆ ac . When Δnac,max = 0.000218, the simulated transmission
spectrum and the transmission spectrum measured by optical spectrum analyzer are shown in Figure 3.19. The simulated reflection spectrum and the reflection spectrum measured by optical spectrum analyzer are shown in Figure 3.20. The reflection and transmission spectra simulated by the transfer matrix method and the structure parameters obtained are again in good agreement with those measured by optical spectrum analyzer. Then by fitting the curves in Figure 3.5 and 3.8 we obtain the fitting the side diffraction ac index and the fitting side interference grating period as shown in Figure 3.21. With the same procedure above, whenΔnac,max = 0.00022, the simulated transmission spectrum from the fitting result and the simulated transmission spectrum in Figure 3.19 are compared as shown in Figure 3.22. The simulated reflection spectrum from the fitting result and the simulated reflection spectrum in Figure 3.20 are compared as shown in Figure 3.23. Like 3.2.1 we can observe that the difference of the two spectra in Fig 3.22 and 3.23 is only the height of side lobes in the longer wavelength region. The similarity between them again shows that the optical performance of many fiber Bragg grating devices are only affected by errors that occur over a relatively large (millimeter) length scale.
Next we use the side interference ac index profile as shown in Figure 3.6 and side interference grating period as shown in Figure 3.8. WhenΔnac,max = 0.0002325, the simulated transmission spectrum and the transmission spectrum measured by the optical spectrum analyzer are shown in Figure 3.24. The simulated reflection spectrum and the reflection spectrum measured by the optical spectrum analyzer are shown in Figure 3.25. The reflection and transmission spectra simulated by the transfer matrix method and the structure parameters obtained are in good agreement with those measured by optical spectrum analyzer. Then by fitting the curve in Figure 3.6 and 3.8 we obtain the fitting side interference ac index and the fitting side interference grating period as shown in Figure 3.26. With the same simulation model and procedure above, when Δnac,max = 0.0002225, the simulated transmission spectrum from the fitting curve and the simulated transmission spectrum in Figure 3.24 are compared as shown in Figure 3.27. The simulated reflection spectrum from the fitting curve and the simulated reflection spectrum in Figure 3.25 are compared as shown in Figure 3.28. We can observe that the difference of the two spectra in Fig 3.27 and 3.28 is only the height of the side lobes in the longer wavelength region. The similarity between them shows that the optical performance of many fiber Bragg grating devices are only affected by errors that occur over a relatively large (millimeter) length scale once again.
3.3 Experiment results of phase measurement 3.3.1 3dB Gaussian apodized grating
The phase spectrum of the 3dB Gaussian apodized grating by the uniform phase mask is shown in Fig 3.29. The group delay spectrum is shown in Fig 3.30.
3.3.2 5dB linear chirp Gaussian apodized grating
The phase spectrum of the 5dB linear chirp Gaussian apodized grating by the linear phase mask is then shown in Fig 3.31. The group delay spectrum is shown in Fig 3.32.
3.4 Reconstruction results by discrete layer peeling 3.4.1 3dB Gaussian apodized grating
The ac index profile of the 3dB Gaussian apodized grating by the uniform phase mask is reconstructed by the discrete layer peeling method and is shown in Fig 3.33.
The target reflection spectrum and the reflection spectrum obtained by the discrete layer peeling method are shown in Fig 3.34. The target and the reconstructed phase spectra are shown in Fig 3.35.
3.4.2 5dB linear chirp Gaussian apodized grating
The ac index profile of the 5dB linear chirp Gaussian apodized grating by the linear phase mask is reconstructed by the discrete layer peeling method and the result is shown in Fig 3.36. The target reflection spectrum and the reflection spectrum obtained by the discrete layer peeling method are shown in Fig 3.37. The target and the reconstructed phase spectra are shown in Fig 3.38.
3.5 Comparison of the ac index profile from side diffraction interference and discrete layer peeling
3.5.1 3dB Gaussian apodized grating
The ac index profile of the 3dB Gaussian apodized grating by the side diffraction and the discrete layer peeling is shown in Fig 3.39. The ac index profile of the 3dB Gaussian apodized grating by the side interference and the discrete layer peeling is shown in Fig 3.40. We can observe that the values of Δnmax in Fig 3.39 and 3.40 are close. Both of them have a dip in the center of the profile. Unfortunately, because the phase measurement is not accurate enough for a uniform grating, the reconstructed ac index profile is longer than the ac index profile measured by the side diffraction interference method.
3.5.2 5dB linear chirp Gaussian apodized grating
The ac index profile of the 5dB linear chirp Gaussian apodized grating by the side diffraction and the discrete layer peeling is shown in Fig 3.41. The ac index profile of the 5dB linear chirp Gaussian apodized grating by the side interference and the discrete layer peeling is shown in Fig 3.42. We can observe that the values of Δnmax
in Fig 3.41 and 3.42 are quite the same. The shapes of Fig 3.39 and 3.40 are also quite close. The total lengths of the profiles from the side diffraction interference method and the discrete layer peeling method are also about the same.
0 5000 10000 15000 20000 side diffraction ac index
(1) (2) (3) (4) (5)
Fig.3.1 Side diffraction ac index of 3dB Gaussian apodized grating
0 5000 10000 15000 20000
0.00000 side interference ac index
(1) (2) (3) (4) (5)
Fig.3.2 Side interference ac index of 3dB Gaussian apodized grating
0 5000 10000 15000 20000
line:side interference ac index,dash:side diffraction ac index
z(um)
Fig.3.3 The comparison between side diffraction and side interference ac index
0 5000 10000 15000 20000
533.6
side interference grating period(nm) (1) (2) (3)
0 5000 10000 15000 20000 0.00000
0.00005 0.00010 0.00015 0.00020 0.00025
ac index
z(um)
5dB linear chirp
side diffraction ac index (1)
(2) (3)
Fig.3.5 Side diffraction ac index of 5dB linear chirp grating
0 5000 10000 15000 20000
0.00000 0.00005 0.00010 0.00015 0.00020 0.00025
ac index
z(um)
5dB linear chirp
side interference ac index (1)
(2) (3)
Fig.3.6 Side interference ac index of 5dB linear chirp grating
0 5000 10000 15000 20000
line:side interference ac index,dash:side diffraction ac index
z(um)
Fig.3.7 The comparison between side diffraction and side interference ac index
0 5000 10000 15000 20000
534.9
5dB linear chirp,side interference grating periode(nm) experiment chirp rate:0.7049/1.22=0.5778(nm/cm) specs chirp rate:0.5(nm/cm)
1547.00 1547.25 1547.50 1547.75 1548.00 -4
-2 0
3dB gaussian apoduzed side diffraction ac index dn=0.00005925 0 transmission spectrum(dB)
Fig.3.9 Transmission spectrum by simulation and by OSA
1547.00 1547.25 1547.50 1547.75 1548.00
-40 side diffraction ac index dn=0.00005925
reflection spectrum(dB)
Fig.3.10 Reflection spectrum by simulation and OSA
-2000 0 2000 4000 6000 8000 10000 12000 14000 16000 0.00000
0.00001 0.00002 0.00003 0.00004 0.00005 0.00006 0.00007
ac index
z(um)
3dB gaussian apodized fitting side diffraction ac index
Fig.3.11 Fitting side diffraction ac index
1547.00 1547.25 1547.50 1547.75 1548.00
-4 -2 0
3dB gaussian apodized
line:simulated by side diffraction ac index
dash:simulated by fitting side diffraction ac index
wavelength(nm)
transmission spectrum(dB)
-4 -2 0 transmission spectrum(dB)
1547.00 1547.25 1547.50 1547.75 1548.00
line:simulated by side diffraction ac index
dash:simulated by fitting side diffraction ac index
wavelength(nm)
Fig.3.13 Simulated reflection spectra
1547.00 1547.25 1547.50 1547.75 1548.00
-4 -2 0
3dB gaussian apoduzed side interference ac index dn=0.000054 0 transmission spectrum(dB)
Fig.3.14 Transmission spectrum by simulation and by OSA
1547.00 1547.25 1547.50 1547.75 1548.00 side interference ac index dn=0.000054
Fig.3.15 Reflection spectrum by simulation and OSA
0 5000 10000 15000 20000
0.00000
fitting side interference ac index
1547.00 1547.25 1547.50 1547.75 1548.00 -4
-2 0
3dB gaussian apodized
line:simulated by side interference ac index
dash:simulated by fitting side interference ac index
wavelength(nm)
transmission spectrum(dB)
-4 -2 0 transmission spectrum(dB)
Fig.3.17 Simulated transmission spectra
1547.00 1547.25 1547.50 1547.75 1548.00
-40
line:simulated by side interference ac index
dash:simulated by fitting side interference ac index
wavelength(nm)
reflection spectrum(dB)
Fig.3.18 Simulated reflection spectra
1542 1544 1546 1548 1550
side diffraction ac index,side interference grating periode(nm) dn=0.000218,dc(kk)=Neff+ddc*ac(kk)*4/3
Fig.3.19 Transmission spectrum by simulation and by OSA
1542 1544 1546 1548 1550
-40
side diffraction ac index,side interference grating periode(nm) dn=0.000218,dc(kk)=Neff+ddc*ac(kk)*4/3
0 5000 10000 15000 20000
line:fitting side diffraction ac index
dash:fitting side interference grating periode(nm)
z(um)
Fig.3.21 Fitting side diffraction ac index and fitting grating period
1542 1544 1546 1548 1550
-6 -4 -2 0
5dB linear chirp
line:simulated by side diffraction ac index
dash:simulated by fitting side diffraction ac index
wavelength(nm)
transmission spectrum(dB)
Fig.3.22 Simulated transmission spectra
1542 1544 1546 1548 1550
line:simulated by side diffraction ac index
dash:simulated by fitting side diffraction ac index
wavelength(nm)
Fig.3.23 Simulated reflection spectra
1542 1544 1546 1548 1550
-6 -4 -2 0
5dB linear chirp,line:OSA,dash:simulation side interference ac index
side interference grating periode(nm) dn=0.0002325,dc(kk)=Neff+ddc*ac(kk)*4/3
1542 1544 1546 1548 1550
side interference ac index,side interference grating periode(nm) dn=0.0002325,dc(kk)=Neff+ddc*ac(kk)*4/3
Fig.3.25 Reflection spectrum by simulation and OSA
0 5000 10000 15000 20000
0.00000
line:fitting side interference ac index
dash:fitting side interference grating periode(nm)
z(um)
Fig.3.26 Fitting side interference ac index and fitting grating period
1542 1544 1546 1548 1550
line:simulated by side interference ac index
dash:simulated by fitting side interference ac index
wavelength(nm)
transmission spectrum(dB)
Fig.3.27 Simulated transmission spectra
1542 1544 1546 1548 1550
-40
line:simulated by side interference ac index
dash:simulated by fitting side interference ac index
wavelength(nm)
1547.0 1547.1 1547.2 1547.3 1547.4 1547.5 1547.6 1547.7
Fig.3.29 The phase of the 3dB Gaussian apodized grating
1547.0 1547.1 1547.2 1547.3 1547.4 1547.5 1547.6 1547.7 0.0
Fig.3.30 The group delay time of the 3dB Gaussian apodized grating
1542 1544 1546 1548 1550
Fig.3.31 The phase of the 5dB linear chirp grating
1542 1544 1546 1548 1550
-0.1
0 5000 10000 15000 20000 25000 30000 0.00000
0.00001 0.00002 0.00003 0.00004 0.00005 0.00006
ac index
z(um)
3dB gaussian apodized discrete layer peeling ac index
Fig.3.33 The ac index profile reconstructed by discrete layer peeling method
1.5460 1.5465 1.5470 1.5475 1.5480 1.5485 1.5490 -60
-50 -40 -30 -20 -10 0
3dB gaussian apodized
line:target reflectance,dash:discrete layer peeling reflectance
wavelength(um)
target reflectance(dB)
-60 -50 -40 -30 -20 -10 0
DLP reflectance(dB)
Fig.3.34 The target reflectance and reflectance simulated by DLP
1.54734 1.54736 1.54738 1.54740 1.54742 1.54744 1.54746 120
130 140 150 160 170
3dB gaussian apodized
line:target group delay time(ps)
dash:discrete layer peeling group delay time(ps)
wavelength(nm)
target group delay time(ps)
120 130 140 150 160 170 discrete layer peeling group delay time(ps)
Fig.3.35 The target group delay time and group delay time simulated by DLP
0 5000 10000 15000 20000 25000 30000
0.00000 0.00005 0.00010 0.00015 0.00020 0.00025
ac index
z(um)
5dB linear chirp
discrete layer peeling ac index
1.542 1.544 1.546 1.548 1.550
line:target reflectance,dash:discrete layer peeling reflectance
wavelength(um)
DLP reflectance(dB)
Fig.3.37 The target reflectance and reflectance simulated by DLP
1.5456 1.5458 1.5460 1.5462 1.5464 1.5466 1.5468 120
line:target group delay time(ps)
dash:discrete layer peeling group delay time(ps)
wavelength(um)
target group delay time(ps)
120
Fig.3.38 The target group delay time and group delay time simulated by DLP
0 5000 10000 15000 20000 25000 30000
line:discrete layer peeling ac index dash:side diffraction ac index
z(um)
Fig.3.39 The ac index profile by side diffraction and discrete layer peeling
0 5000 10000 15000 20000 25000 30000
0.00000
line:discrete layer peeling ac index dash:side interference ac index
z(um)
0 5000 10000 15000 20000 25000 30000
line:discrete layer peeling ac index dash:side diffraction ac index
z(um)
Fig.3.41 The ac index profile by side diffraction and discrete layer peeling
0 5000 10000 15000 20000 25000 30000
0.00000
line:discrete layer peeling ac index dash:side interference ac index
z(um)
Fig.3.42 The ac index profile by side interference and discrete layer peeling