Abstract

Inverse-Gaussian apodized fiber Bragg gratings (IGAFBGs) are numerically studied using the transfer matrix method and fabricated by the commonly used phase-mask scanning technique in a single-step scanning process. The IGAFBG can serve as a dual-wavelength passband filter, whose wavelength spacing can be continuously tuned by introducing a tunable chirp through applying a strain gradient in principle. Also, an IGAFBG with identical dual passbands having 0.144nm wavelength spacing is experimentally achieved. We also show that an IGAFBG can act as a multipassband filter with varied free spectral ranges (FSRs), and the largest FSR variation of this IGAFBG is nearly seven times more than that in a comparable FBG pair filter. An IGAFBG with varied FSRs of 16.125, 12.25, 8.5, and 6.375GHz is fabricated. This multipassband varying-FSR IGAFBG filter can find applications in step-tunable microwave generations.

© 2010 Optical Society of America

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2010 (1)

2009 (3)

2008 (4)

J. L. Zhou, L. Xia, X. P. Cheng, X. P. Dong, and P. Shum, “Photonic generation of tunable microwave signals by beating a dual-wavelength single longitudinal mode fiber ring laser,” Appl. Phys. B 91, 99–103 (2008).
[CrossRef]

X. M. Liu, A. X. Lin, G. Y. Sun, D. S. Moon, D. Hwang, and Y. Chung, “Identical-dual-bandpass sampled fiber Bragg grating and its application to ultranarrow filters,” Appl. Opt. 47, 5637–5643 (2008).
[CrossRef] [PubMed]

S. Feng, O. Xu, S. Lu, X. Mao, T. Ning, and S. Jian, “Single-polarization, switchable dual-wavelength erbium-doped fiber laser with two polarization-maintaining fiber Bragg gratings,” Opt. Express 16, 11830–11835 (2008).
[CrossRef] [PubMed]

D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett. 44, 459–461 (2008).
[CrossRef]

2007 (1)

D. Liu, N. Q. Ngo, S. C. Tjin, and X. Y. Dong, “A dual-wavelength fiber laser sensor system for measurement of temperature and strain,” IEEE Photonics Technol. Lett. 19, 1148–1150 (2007).
[CrossRef]

2006 (2)

L. Xia, P. Shum, and T. Cheng, “Photonic generation of microwave signals using a dual-transmission-band FBG filter with controllable wavelength spacing,” Appl. Phys. B 86, 61–64(2006).
[CrossRef]

Y. Dai, X. Chen, J. Sun, Y. Yao, and S. Xie, “Dual-wavelength DFB fiber laser based on a chirped structure and the equivalent phase shift method,” IEEE Photonics Technol. Lett. 18, 1964–1966 (2006).
[CrossRef]

2005 (3)

A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg gratings to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 52, 304–312 (2005).
[CrossRef]

D. Liu, N. Q. Ngo, X. Y. Dong, S. C. Tjin, and P. Shum, “A stable dual-wavelength fiber laser with tunable wavelength spacing using a polarization-maintaining linear cavity,” Appl. Phys. B 81, 807–811 (2005).
[CrossRef]

X. Chen, J. Yao, and Z. Deng, “Ultranarrow dual-transmission-band fiber Bragg grating filter and its application in a dual-wavelength single-longitudinal-mode fiber ring laser,” Opt. Lett. 30, 2068–2070 (2005).
[CrossRef] [PubMed]

2004 (2)

S. Y. Li, N. Q. Ngo, S. C. Tjin, P. Shum, and J. Zhang, “Thermally tunable narrow-bandpass filter based on a linearly chirped fiber Bragg grating,” Opt. Lett. 29, 29–31 (2004).
[CrossRef] [PubMed]

J. Liu, J. P. Yao, J. Yao, and T. H. Yeap, “Single-longitudinal-mode multiwavelength fiber ring laser,” IEEE Photonics Technol. Lett. 16, 1020–1022 (2004).
[CrossRef]

2003 (1)

2002 (1)

X. Y. Dong, B. O. Guan, S. Z. Yuan, X. Y. Dong, and H. Y. Tam, “Strain gradient chirp of uniform fiber Bragg grating without shift of central Bragg wavelength,” Opt. Commun. 202, 91–95 (2002).
[CrossRef]

2000 (1)

B. O. Guan, H. Y. Tam, X. M. Tao, and X. Y. Dong, “Simultaneous strain and temperature measurement using a superstructure fiber Bragg grating,” IEEE Photonics Technol. Lett. 12, 675–677 (2000).
[CrossRef]

1997 (1)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

1996 (1)

S. W. James, M. L. Dockney, and R. P. Tatam, “Simultaneous independent temperature and strain measurement using in-fibre Bragg grating sensors,” Electron. Lett. 32, 1133–1134(1996).
[CrossRef]

1995 (1)

1994 (1)

G. P. Agrawal and S. Radic, “Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photonics Technol. Lett. 6, 995–997 (1994).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal and S. Radic, “Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photonics Technol. Lett. 6, 995–997 (1994).
[CrossRef]

Bernage, P.

Bernini, R.

A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg gratings to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 52, 304–312 (2005).
[CrossRef]

Boj, S.

Chen, D.

W. Liu, M. Jiang, D. Chen, and S. He, “Dual-Wavelength single-longitudinal-mode polarization-maintaining fiber laser and its application in microwave generation,” J. Lightwave Technol. 27, 4455–4459 (2009).
[CrossRef]

D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett. 44, 459–461 (2008).
[CrossRef]

Chen, X.

Y. Dai, X. Chen, J. Sun, Y. Yao, and S. Xie, “Dual-wavelength DFB fiber laser based on a chirped structure and the equivalent phase shift method,” IEEE Photonics Technol. Lett. 18, 1964–1966 (2006).
[CrossRef]

X. Chen, J. Yao, and Z. Deng, “Ultranarrow dual-transmission-band fiber Bragg grating filter and its application in a dual-wavelength single-longitudinal-mode fiber ring laser,” Opt. Lett. 30, 2068–2070 (2005).
[CrossRef] [PubMed]

Cheng, T.

L. Xia, P. Shum, and T. Cheng, “Photonic generation of microwave signals using a dual-transmission-band FBG filter with controllable wavelength spacing,” Appl. Phys. B 86, 61–64(2006).
[CrossRef]

Cheng, X. P.

J. L. Zhou, L. Xia, X. P. Cheng, X. P. Dong, and P. Shum, “Photonic generation of tunable microwave signals by beating a dual-wavelength single longitudinal mode fiber ring laser,” Appl. Phys. B 91, 99–103 (2008).
[CrossRef]

Chung, Y.

Cusano, A.

A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg gratings to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 52, 304–312 (2005).
[CrossRef]

Dai, Y.

Y. Dai, X. Chen, J. Sun, Y. Yao, and S. Xie, “Dual-wavelength DFB fiber laser based on a chirped structure and the equivalent phase shift method,” IEEE Photonics Technol. Lett. 18, 1964–1966 (2006).
[CrossRef]

Delevaque, E.

Deng, Z.

Dockney, M. L.

S. W. James, M. L. Dockney, and R. P. Tatam, “Simultaneous independent temperature and strain measurement using in-fibre Bragg grating sensors,” Electron. Lett. 32, 1133–1134(1996).
[CrossRef]

Dong, X. P.

J. L. Zhou, L. Xia, X. P. Cheng, X. P. Dong, and P. Shum, “Photonic generation of tunable microwave signals by beating a dual-wavelength single longitudinal mode fiber ring laser,” Appl. Phys. B 91, 99–103 (2008).
[CrossRef]

Dong, X. Y.

D. Liu, N. Q. Ngo, S. C. Tjin, and X. Y. Dong, “A dual-wavelength fiber laser sensor system for measurement of temperature and strain,” IEEE Photonics Technol. Lett. 19, 1148–1150 (2007).
[CrossRef]

D. Liu, N. Q. Ngo, X. Y. Dong, S. C. Tjin, and P. Shum, “A stable dual-wavelength fiber laser with tunable wavelength spacing using a polarization-maintaining linear cavity,” Appl. Phys. B 81, 807–811 (2005).
[CrossRef]

X. Y. Dong, B. O. Guan, S. Z. Yuan, X. Y. Dong, and H. Y. Tam, “Strain gradient chirp of uniform fiber Bragg grating without shift of central Bragg wavelength,” Opt. Commun. 202, 91–95 (2002).
[CrossRef]

X. Y. Dong, B. O. Guan, S. Z. Yuan, X. Y. Dong, and H. Y. Tam, “Strain gradient chirp of uniform fiber Bragg grating without shift of central Bragg wavelength,” Opt. Commun. 202, 91–95 (2002).
[CrossRef]

B. O. Guan, H. Y. Tam, X. M. Tao, and X. Y. Dong, “Simultaneous strain and temperature measurement using a superstructure fiber Bragg grating,” IEEE Photonics Technol. Lett. 12, 675–677 (2000).
[CrossRef]

Douay, M.

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

Fang, X.

Feng, S.

Floridi, M.

Fu, H.

D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett. 44, 459–461 (2008).
[CrossRef]

Giordano, M.

A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg gratings to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 52, 304–312 (2005).
[CrossRef]

Guan, B. O.

X. Y. Dong, B. O. Guan, S. Z. Yuan, X. Y. Dong, and H. Y. Tam, “Strain gradient chirp of uniform fiber Bragg grating without shift of central Bragg wavelength,” Opt. Commun. 202, 91–95 (2002).
[CrossRef]

B. O. Guan, H. Y. Tam, X. M. Tao, and X. Y. Dong, “Simultaneous strain and temperature measurement using a superstructure fiber Bragg grating,” IEEE Photonics Technol. Lett. 12, 675–677 (2000).
[CrossRef]

Hao, J.

He, S.

W. Liu, M. Jiang, D. Chen, and S. He, “Dual-Wavelength single-longitudinal-mode polarization-maintaining fiber laser and its application in microwave generation,” J. Lightwave Technol. 27, 4455–4459 (2009).
[CrossRef]

D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett. 44, 459–461 (2008).
[CrossRef]

He, X.

Hwang, D.

James, S. W.

S. W. James, M. L. Dockney, and R. P. Tatam, “Simultaneous independent temperature and strain measurement using in-fibre Bragg grating sensors,” Electron. Lett. 32, 1133–1134(1996).
[CrossRef]

Jian, S.

Jiang, M.

Legoubin, S.

Li, L.

S. Liang, S. C. Tjin, N. Q. Ngo, C. Zhang, and L. Li, “Novel tunable fiber-optic edge filter based on modulating the chirp rate of a π-phase-shifted fiber Bragg grating in transmission,” Opt. Commun. 282, 1363–1369 (2009).
[CrossRef]

Li, S. Y.

Liang, S.

B. Lin, H. Zhang, S. C. Tjin, D. Tang, J. Hao, C. M. Tay, and S. Liang, “Inverse-Gaussian apodized fiber Bragg grating for dual wavelength lasing,” Appl. Opt. 49, 1373–1377(2010).
[CrossRef] [PubMed]

S. Liang, S. C. Tjin, N. Q. Ngo, C. Zhang, and L. Li, “Novel tunable fiber-optic edge filter based on modulating the chirp rate of a π-phase-shifted fiber Bragg grating in transmission,” Opt. Commun. 282, 1363–1369 (2009).
[CrossRef]

Liao, C.

Lin, A. X.

Lin, B.

Liu, D.

D. Liu, N. Q. Ngo, S. C. Tjin, and X. Y. Dong, “A dual-wavelength fiber laser sensor system for measurement of temperature and strain,” IEEE Photonics Technol. Lett. 19, 1148–1150 (2007).
[CrossRef]

D. Liu, N. Q. Ngo, X. Y. Dong, S. C. Tjin, and P. Shum, “A stable dual-wavelength fiber laser with tunable wavelength spacing using a polarization-maintaining linear cavity,” Appl. Phys. B 81, 807–811 (2005).
[CrossRef]

Liu, J.

J. Liu, J. P. Yao, J. Yao, and T. H. Yeap, “Single-longitudinal-mode multiwavelength fiber ring laser,” IEEE Photonics Technol. Lett. 16, 1020–1022 (2004).
[CrossRef]

Liu, W.

W. Liu, M. Jiang, D. Chen, and S. He, “Dual-Wavelength single-longitudinal-mode polarization-maintaining fiber laser and its application in microwave generation,” J. Lightwave Technol. 27, 4455–4459 (2009).
[CrossRef]

D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett. 44, 459–461 (2008).
[CrossRef]

Liu, X. M.

Lu, S.

Mao, X.

Martinelli, M.

Melloni, A.

Minardo, A.

A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg gratings to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 52, 304–312 (2005).
[CrossRef]

Moon, D. S.

Morichetti, F.

Ngo, N. Q.

S. Liang, S. C. Tjin, N. Q. Ngo, C. Zhang, and L. Li, “Novel tunable fiber-optic edge filter based on modulating the chirp rate of a π-phase-shifted fiber Bragg grating in transmission,” Opt. Commun. 282, 1363–1369 (2009).
[CrossRef]

D. Liu, N. Q. Ngo, S. C. Tjin, and X. Y. Dong, “A dual-wavelength fiber laser sensor system for measurement of temperature and strain,” IEEE Photonics Technol. Lett. 19, 1148–1150 (2007).
[CrossRef]

D. Liu, N. Q. Ngo, X. Y. Dong, S. C. Tjin, and P. Shum, “A stable dual-wavelength fiber laser with tunable wavelength spacing using a polarization-maintaining linear cavity,” Appl. Phys. B 81, 807–811 (2005).
[CrossRef]

S. Y. Li, N. Q. Ngo, S. C. Tjin, P. Shum, and J. Zhang, “Thermally tunable narrow-bandpass filter based on a linearly chirped fiber Bragg grating,” Opt. Lett. 29, 29–31 (2004).
[CrossRef] [PubMed]

Niay, P.

Ning, T.

Radic, S.

G. P. Agrawal and S. Radic, “Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing,” IEEE Photonics Technol. Lett. 6, 995–997 (1994).
[CrossRef]

Shum, P.

J. L. Zhou, L. Xia, X. P. Cheng, X. P. Dong, and P. Shum, “Photonic generation of tunable microwave signals by beating a dual-wavelength single longitudinal mode fiber ring laser,” Appl. Phys. B 91, 99–103 (2008).
[CrossRef]

L. Xia, P. Shum, and T. Cheng, “Photonic generation of microwave signals using a dual-transmission-band FBG filter with controllable wavelength spacing,” Appl. Phys. B 86, 61–64(2006).
[CrossRef]

D. Liu, N. Q. Ngo, X. Y. Dong, S. C. Tjin, and P. Shum, “A stable dual-wavelength fiber laser with tunable wavelength spacing using a polarization-maintaining linear cavity,” Appl. Phys. B 81, 807–811 (2005).
[CrossRef]

S. Y. Li, N. Q. Ngo, S. C. Tjin, P. Shum, and J. Zhang, “Thermally tunable narrow-bandpass filter based on a linearly chirped fiber Bragg grating,” Opt. Lett. 29, 29–31 (2004).
[CrossRef] [PubMed]

Sun, G. Y.

Sun, J.

X. He, X. Fang, C. Liao, D. N. Wang, and J. Sun, “A tunable and switchable single-longitudinal-mode dual-wavelength fiber laser with a simple linear cavity,” Opt. Express 17, 21773–21781 (2009).
[CrossRef] [PubMed]

Y. Dai, X. Chen, J. Sun, Y. Yao, and S. Xie, “Dual-wavelength DFB fiber laser based on a chirped structure and the equivalent phase shift method,” IEEE Photonics Technol. Lett. 18, 1964–1966 (2006).
[CrossRef]

Tam, H. Y.

X. Y. Dong, B. O. Guan, S. Z. Yuan, X. Y. Dong, and H. Y. Tam, “Strain gradient chirp of uniform fiber Bragg grating without shift of central Bragg wavelength,” Opt. Commun. 202, 91–95 (2002).
[CrossRef]

B. O. Guan, H. Y. Tam, X. M. Tao, and X. Y. Dong, “Simultaneous strain and temperature measurement using a superstructure fiber Bragg grating,” IEEE Photonics Technol. Lett. 12, 675–677 (2000).
[CrossRef]

Tang, D.

Tao, X. M.

B. O. Guan, H. Y. Tam, X. M. Tao, and X. Y. Dong, “Simultaneous strain and temperature measurement using a superstructure fiber Bragg grating,” IEEE Photonics Technol. Lett. 12, 675–677 (2000).
[CrossRef]

Tatam, R. P.

S. W. James, M. L. Dockney, and R. P. Tatam, “Simultaneous independent temperature and strain measurement using in-fibre Bragg grating sensors,” Electron. Lett. 32, 1133–1134(1996).
[CrossRef]

Tay, C. M.

Tjin, S. C.

B. Lin, H. Zhang, S. C. Tjin, D. Tang, J. Hao, C. M. Tay, and S. Liang, “Inverse-Gaussian apodized fiber Bragg grating for dual wavelength lasing,” Appl. Opt. 49, 1373–1377(2010).
[CrossRef] [PubMed]

S. Liang, S. C. Tjin, N. Q. Ngo, C. Zhang, and L. Li, “Novel tunable fiber-optic edge filter based on modulating the chirp rate of a π-phase-shifted fiber Bragg grating in transmission,” Opt. Commun. 282, 1363–1369 (2009).
[CrossRef]

D. Liu, N. Q. Ngo, S. C. Tjin, and X. Y. Dong, “A dual-wavelength fiber laser sensor system for measurement of temperature and strain,” IEEE Photonics Technol. Lett. 19, 1148–1150 (2007).
[CrossRef]

D. Liu, N. Q. Ngo, X. Y. Dong, S. C. Tjin, and P. Shum, “A stable dual-wavelength fiber laser with tunable wavelength spacing using a polarization-maintaining linear cavity,” Appl. Phys. B 81, 807–811 (2005).
[CrossRef]

S. Y. Li, N. Q. Ngo, S. C. Tjin, P. Shum, and J. Zhang, “Thermally tunable narrow-bandpass filter based on a linearly chirped fiber Bragg grating,” Opt. Lett. 29, 29–31 (2004).
[CrossRef] [PubMed]

Wang, D. N.

Wei, Y.

D. Chen, H. Fu, W. Liu, Y. Wei, and S. He, “Dual-wavelength single-longitudinal-mode erbium-doped fibre laser based on fibre Bragg grating pair and its application in microwave signal generation,” Electron. Lett. 44, 459–461 (2008).
[CrossRef]

Xia, L.

J. L. Zhou, L. Xia, X. P. Cheng, X. P. Dong, and P. Shum, “Photonic generation of tunable microwave signals by beating a dual-wavelength single longitudinal mode fiber ring laser,” Appl. Phys. B 91, 99–103 (2008).
[CrossRef]

L. Xia, P. Shum, and T. Cheng, “Photonic generation of microwave signals using a dual-transmission-band FBG filter with controllable wavelength spacing,” Appl. Phys. B 86, 61–64(2006).
[CrossRef]

Xie, S.

Y. Dai, X. Chen, J. Sun, Y. Yao, and S. Xie, “Dual-wavelength DFB fiber laser based on a chirped structure and the equivalent phase shift method,” IEEE Photonics Technol. Lett. 18, 1964–1966 (2006).
[CrossRef]

Xu, O.

Yao, J.

Yao, J. P.

J. Liu, J. P. Yao, J. Yao, and T. H. Yeap, “Single-longitudinal-mode multiwavelength fiber ring laser,” IEEE Photonics Technol. Lett. 16, 1020–1022 (2004).
[CrossRef]

Yao, Y.

Y. Dai, X. Chen, J. Sun, Y. Yao, and S. Xie, “Dual-wavelength DFB fiber laser based on a chirped structure and the equivalent phase shift method,” IEEE Photonics Technol. Lett. 18, 1964–1966 (2006).
[CrossRef]

Yeap, T. H.

J. Liu, J. P. Yao, J. Yao, and T. H. Yeap, “Single-longitudinal-mode multiwavelength fiber ring laser,” IEEE Photonics Technol. Lett. 16, 1020–1022 (2004).
[CrossRef]

Yuan, S. Z.

X. Y. Dong, B. O. Guan, S. Z. Yuan, X. Y. Dong, and H. Y. Tam, “Strain gradient chirp of uniform fiber Bragg grating without shift of central Bragg wavelength,” Opt. Commun. 202, 91–95 (2002).
[CrossRef]

Zeni, L.

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Figures (11)

Fig. 1
Fig. 1

Calculated reflection spectrum of a typical uniform FBG without apodization, which means A ( z ) = 1 . In simulation, n eff = 1.45 , L = 1.2 cm , λ D = 1550 nm , and δ n eff ¯ = 2.5 × 10 4 .

Fig. 2
Fig. 2

Calculated reflection spectrum of an IGAFBG described by Eq. (3). The inset shows the corresponding transmission spectrum of this IGAFBG. In simulation, n eff = 1.45 , L = 1.2 cm , λ D = 1550 nm , and δ n eff ¯ = 2.5 × 10 4 .

Fig. 3
Fig. 3

3 dB bandwidths of peak 1 (solid line with diamond joints) and peak 2 (solid line with square joints) and wavelength spacing between these two peaks (dashed line) versus L of an IGAFBG. In simulation, n eff = 1.45 , λ D = 1550 nm , and δ n eff ¯ = 2 × 10 4 .

Fig. 4
Fig. 4

3 dB bandwidths of peak 1 (solid line with diamond joints) and peak 2 (solid line with square joints) and wavelength spacing between these two peaks (dashed line) versus δ n eff ¯ of an IGAFBG. In simulation, n eff = 1.45 , λ D = 1550 nm , and L = 1.5 cm .

Fig. 5
Fig. 5

Calculated transmission spectra of three different IGAFBGs having two identical passbands with varied wavelength spacings: (a) Wavelength spacing of 0.104 nm and 3 dB bandwidths of 3.1 pm . This spectrum corresponds to M in Fig. 3. (b) Wavelength spacing of 0.113 nm and 3 dB bandwidths of 3.5 pm . This spectrum corresponds to N in Fig. 4. (c) Wavelength spacing of 0.17 nm and 3 dB bandwidths of 5 pm .

Fig. 6
Fig. 6

Calculated transmission spectra of IGAFBGs at (a) 0 (b) 0.1 (c) 0.15, and (d) 0.2 nm / cm chirp rate. In simulation, n eff = 1.45 , λ D = 1550 nm , δ n eff ¯ = 3 × 10 4 , and L = 1 cm .

Fig. 7
Fig. 7

Calculated transmission spectrum of an IGAFBG with three passbands. In simulation, n eff = 1.45 , L = 1.5 cm , λ D = 1550 nm , and δ n eff ¯ = 3 × 10 4 .

Fig. 8
Fig. 8

Calculated transmission spectrum of an IGAFBG having multipassbands with varied FSR values. The + 1 order dip has FSR1, and the + 2 order dip has FSR2, and so on. In simulation, n eff = 1.45 , L = 2 cm , λ D = 1550 nm , and δ n eff ¯ = 4 × 10 4 .

Fig. 9
Fig. 9

(a) Scanning speed distribution of the translation stage used in the fabrication of an IGAFBG. Solid line, experimental speed distribution; dashed line, expected speed distribution to best fit Eq. (3). (b) Transmission spectra of this IGAFBG. Solid line, measured spectrum (the argon laser output power used is 66 mW and the grating length is 12 mm ); dashed line, calculated spectrum. In simulation, n eff = 1.447 , L = 12 mm , Λ = 532.85 nm , and δ n eff ¯ = 2.7 × 10 4 .

Fig. 10
Fig. 10

Transmission spectra of an IGAFBG with varied FSRs as a multiwavelength passband filter: (a) measured spectrum (the argon laser output power used is 80 mW and the grating length is 17 mm ); (b) simulated spectrum. The + 1 order dip has FSR1, and the + 2 order dip has FSR2, and so on. In simulation, n eff = 1.447 , L = 17 mm , Λ = 532.85 nm , and δ n eff ¯ = 4.5 × 10 4 .

Fig. 11
Fig. 11

Simulated transmission spectrum of a regular FBG pair. In simulation, n eff = 1.447 , Λ = 532.85 nm , δ n eff ¯ = 4.5 × 10 4 , the length of each subgrating is 5 mm , and the separation between these two subgratings is 12 mm . The numbers 1, 2, 3, 4, and 5 in the figure do not mean the dip order, and they refer to FSR1, FSR2, FSR3, FSR4, and FSR5 only.

Tables (3)

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Table 1 Calculated Parameters of an IGAFBG Under Different Chirp Rates a

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Table 2 FSRs of an IGAFBG as a Multiwavelength Filter a

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Table 3 FSRs of a Regular FBG Pair a

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

σ ¯ ( z , λ ) = 2 π n eff ( 1 λ 1 λ D ) + 2 π λ δ n eff ¯ ( z ) + 4 π n eff z ( cr ) λ D 2 .
κ ( z , λ ) = π λ v δ n eff ¯ ( z ) ,
A ( z ) = 1 exp { [ 4 ( ln 2 ) z 2 ] / ( L / 3 ) 2 } .

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