Abstract

A new technique to design an all-fiber temporal differentiator that has a large bandwidth and an arbitrary differentiation order is proposed and investigated. The proposed temporal differentiator is a special fiber Bragg grating (FBG) that is designed by controlling its magnitude and phase responses with the discrete layer peeling (DLP) method. There are three important features of this technique: 1) the temporal differentiator has an arbitrary magnitude response and a controllable bandwidth; 2) the temporal differentiator can be designed and fabricated with an arbitrary differentiation order that is realized in a single FBG; 3) the required maximum index modulation of the FBG-based differentiator is largely decreased by using a Gaussian windowing function. The use of the proposed technique to design temporal differentiators with a differentiation order up to the fourth and with a bandwidth up to 500 GHz is studied. A proof-of-concept experiment is then carried out. A first- and a second-order temporal differentiator with a bandwidth of 25 GHz are experimentally demonstrated.

© 2009 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  22. M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31(17), 1488–1489 (1995).
    [CrossRef]

2009

2008

2007

2006

2005

2004

H. Li, T. Kumagai, K. Ogusu, and Y. Sheng, “Advanced design of a multichannel fiber Bragg grating based on a layer-peeling method,” J. Opt. Soc. Am. B 21, 1929–1938 (2004).
[CrossRef]

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230(1-3), 115–129 (2004).
[CrossRef]

2003

L. Venema, “Photonics Technologies,” Nature Insight 424, 809 (2003).
[CrossRef]

S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003).
[CrossRef]

2001

J. Skaar, L. Wang, and T. Erdogen, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37(2), 165–173 (2001).
[CrossRef]

1999

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35(8), 1105–1115 (1999).
[CrossRef]

1995

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31(17), 1488–1489 (1995).
[CrossRef]

Ahn, T. J.

Asghari, M. H.

M. H. Asghari and J. Azaña, “On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber bragg gratings,” J. Lightwave Technol. (to be published).

Ayotte, N.

Azaña, J.

L. M. Rivas, S. Boudreau, Y. Park, R. Slavík, S. Larochelle, A. Carballar, and J. Azaña, “Experimental demonstration of ultrafast all-fiber high-order photonic temporal differentiators,” Opt. Lett. 34(12), 1792–1794 (2009).
[CrossRef] [PubMed]

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. J. Ahn, S. LaRochelle, and J. Azaña, “Photonic temporal integrator for all-optical computing,” Opt. Express 16(22), 18202–18214 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-22-18202 .
[CrossRef] [PubMed]

N. K. Berger, B. Levit, B. Fischer, M. Kulishov, D. V. Plant, and J. Azaña, “Temporal differentiation of optical signals using a phase-shifted fiber Bragg grating,” Opt. Express 15(2), 371–381 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-2-371 .
[CrossRef] [PubMed]

R. Slavík, Y. Park, and J. Azaña, “Tunable dispersion-tolerant picosecond flat-top waveform generation using an optical differentiator,” Opt. Express 15(11), 6717–6726 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-11-6717 .
[CrossRef] [PubMed]

Y. Park, J. Azaña, and R. Slavík, “Ultrafast all-optical first- and higher-order differentiators based on interferometers,” Opt. Lett. 32(6), 710–712 (2007).
[CrossRef] [PubMed]

L.-M. Rivas, K. Singh, A. Carballar, and J. Azaña, “Arbitrary-order ultra-broadband all-optical differentiators based on fiber Bragg gratings,” IEEE Photon. Technol. Lett. 19(16), 1209–1211 (2007).
[CrossRef]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14(22), 10699–10707 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-22-10699 .
[CrossRef] [PubMed]

M. Kulishov and J. Azaña, “Long-period fiber gratings as ultrafast optical differentiators,” Opt. Lett. 30(20), 2700–2702 (2005).
[CrossRef] [PubMed]

M. H. Asghari and J. Azaña, “On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber bragg gratings,” J. Lightwave Technol. (to be published).

Barcelos, S.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31(17), 1488–1489 (1995).
[CrossRef]

Berger, N. K.

Bernier, M.

Blais, S.

Boudreau, S.

Carballar, A.

L. M. Rivas, S. Boudreau, Y. Park, R. Slavík, S. Larochelle, A. Carballar, and J. Azaña, “Experimental demonstration of ultrafast all-fiber high-order photonic temporal differentiators,” Opt. Lett. 34(12), 1792–1794 (2009).
[CrossRef] [PubMed]

L.-M. Rivas, K. Singh, A. Carballar, and J. Azaña, “Arbitrary-order ultra-broadband all-optical differentiators based on fiber Bragg gratings,” IEEE Photon. Technol. Lett. 19(16), 1209–1211 (2007).
[CrossRef]

Cole, M. J.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31(17), 1488–1489 (1995).
[CrossRef]

Dong, J.

Doucet, S.

Erdogen, T.

J. Skaar, L. Wang, and T. Erdogen, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37(2), 165–173 (2001).
[CrossRef]

Feced, R.

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35(8), 1105–1115 (1999).
[CrossRef]

Fischer, B.

Huang, D.

James, S. W.

S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003).
[CrossRef]

Kam, C. H.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230(1-3), 115–129 (2004).
[CrossRef]

Kulishov, M.

Kumagai, T.

Laming, R. I.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31(17), 1488–1489 (1995).
[CrossRef]

Larochelle, S.

Levit, B.

Li, H.

Liu, D.

Liu, F.

Loh, W. H.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31(17), 1488–1489 (1995).
[CrossRef]

Morandotti, R.

Muriel, M. A.

M. A. Preciado and M. A. Muriel, “Design of an ultrafast all-optical differentiator based on a fiber Bragg grating in transmission,” Opt. Lett. 33(21), 2458–2460 (2008).
[CrossRef] [PubMed]

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35(8), 1105–1115 (1999).
[CrossRef]

Ngo, N. Q.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230(1-3), 115–129 (2004).
[CrossRef]

Ogusu, K.

Park, Y.

Plant, D. V.

Preciado, M. A.

Qiang, L.

Qiu, M.

Rivas, L. M.

Rivas, L.-M.

L.-M. Rivas, K. Singh, A. Carballar, and J. Azaña, “Arbitrary-order ultra-broadband all-optical differentiators based on fiber Bragg gratings,” IEEE Photon. Technol. Lett. 19(16), 1209–1211 (2007).
[CrossRef]

Sheng, Y.

Singh, K.

L.-M. Rivas, K. Singh, A. Carballar, and J. Azaña, “Arbitrary-order ultra-broadband all-optical differentiators based on fiber Bragg gratings,” IEEE Photon. Technol. Lett. 19(16), 1209–1211 (2007).
[CrossRef]

Skaar, J.

J. Skaar, L. Wang, and T. Erdogen, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37(2), 165–173 (2001).
[CrossRef]

Slavík, R.

Su, Y.

Tatam, R. P.

S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003).
[CrossRef]

Tjin, S. C.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230(1-3), 115–129 (2004).
[CrossRef]

Vallée, R.

Venema, L.

L. Venema, “Photonics Technologies,” Nature Insight 424, 809 (2003).
[CrossRef]

Wang, L.

J. Skaar, L. Wang, and T. Erdogen, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37(2), 165–173 (2001).
[CrossRef]

Wang, Q.

Wang, T.

Xu, J.

Yao, J.

Ye, T.

Yu, S. F.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230(1-3), 115–129 (2004).
[CrossRef]

Zeng, F.

Zervas, M. N.

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35(8), 1105–1115 (1999).
[CrossRef]

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31(17), 1488–1489 (1995).
[CrossRef]

Zhang, X.

Zhang, Z.

Electron. Lett.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett. 31(17), 1488–1489 (1995).
[CrossRef]

IEEE J. Quantum Electron.

R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35(8), 1105–1115 (1999).
[CrossRef]

J. Skaar, L. Wang, and T. Erdogen, “On the synthesis of fiber Bragg grating by layer peeling,” IEEE J. Quantum Electron. 37(2), 165–173 (2001).
[CrossRef]

IEEE Photon. Technol. Lett.

L.-M. Rivas, K. Singh, A. Carballar, and J. Azaña, “Arbitrary-order ultra-broadband all-optical differentiators based on fiber Bragg gratings,” IEEE Photon. Technol. Lett. 19(16), 1209–1211 (2007).
[CrossRef]

J. Lightwave Technol.

M. H. Asghari and J. Azaña, “On the design of efficient and accurate arbitrary-order temporal optical integrators using fiber bragg gratings,” J. Lightwave Technol. (to be published).

J. Opt. Soc. Am. B

Meas. Sci. Technol.

S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003).
[CrossRef]

Nature Insight

L. Venema, “Photonics Technologies,” Nature Insight 424, 809 (2003).
[CrossRef]

Opt. Commun.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230(1-3), 115–129 (2004).
[CrossRef]

Opt. Express

N. K. Berger, B. Levit, B. Fischer, M. Kulishov, D. V. Plant, and J. Azaña, “Temporal differentiation of optical signals using a phase-shifted fiber Bragg grating,” Opt. Express 15(2), 371–381 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-2-371 .
[CrossRef] [PubMed]

F. Liu, T. Wang, L. Qiang, T. Ye, Z. Zhang, M. Qiu, and Y. Su, “Compact optical temporal differentiator based on silicon microring resonator,” Opt. Express 16(20), 15880–15886 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15880 .
[CrossRef] [PubMed]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14(22), 10699–10707 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-22-10699 .
[CrossRef] [PubMed]

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. J. Ahn, S. LaRochelle, and J. Azaña, “Photonic temporal integrator for all-optical computing,” Opt. Express 16(22), 18202–18214 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-22-18202 .
[CrossRef] [PubMed]

M. Bernier, Y. Sheng, and R. Vallée, “Ultrabroadband fiber Bragg gratings written with a highly chirped phase mask and infrared femtosecond pulses,” Opt. Express 17(5), 3285–3290 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-5-3285 .
[CrossRef] [PubMed]

R. Slavík, Y. Park, and J. Azaña, “Tunable dispersion-tolerant picosecond flat-top waveform generation using an optical differentiator,” Opt. Express 15(11), 6717–6726 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-11-6717 .
[CrossRef] [PubMed]

Opt. Lett.

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Figures (10)

Fig. 1
Fig. 1

(a) The high-order Gaussian spectrum Rg(ω) and the reflection spectra Rd(ω) used to implement the first-order and the second-order differentiation; (b) The formed target reflection magnitude and phase responses of the first-order and the second-order differentiator.

Fig. 2
Fig. 2

Index modulation profiles of the synthesized FBGs for the implementation of (a) the first-order differentiator, (b) the second-order differentiator, (c) the third-order differentiator and (d) the fourth-order differentiator based on the reflection spectra with Gaussian apodization in Fig. 1(b). Index modulation profiles for (e) the first-order differentiator and (f) for the second-order differentiator which are synthesized from the reflection spectrum without Gaussian apodization [see Fig. 1(a)].

Fig. 3
Fig. 3

Reflection magnitude and phase responses of the synthesized FBGs for (a) the first-order differentiator, (b) the second-order differentiator, (c) the third-order differentiator, and (d) the fourth-order differentiator.

Fig. 4
Fig. 4

Output pulse obtained from an input Gaussian pulse with a bandwidth of 500 GHz applied to (a) the first-order differentiator; (b) the second-order differentiator; (c) the third-order differentiator, and (d) the fourth-order differentiator.

Fig. 5
Fig. 5

Experimental setup. TLS, tunable laser source; PC, polarization controller; EO IM, electro-optic intensity modulator; OC, optical circulator; EDFA, erbium-doped fiber amplifier; PD, photodetector; SC, sampling oscilloscope; BERT, bit error rate tester.

Fig. 6
Fig. 6

Index modulation of the designed 25 GHz (a) first-order differentiator and (b) second-order differentiator.

Fig. 7
Fig. 7

Simulated (solid line) and measured (dashed line) reflection spectra for (a) the first-order differentiator and (b) the second-order differentiator. The insets show the phase responses of the differentiators.

Fig. 8
Fig. 8

Input and output pulses for the first-order temporal differentiator. (a) Simulated and measured input pulses; (b) Simulated and measured output pulses.

Fig. 9
Fig. 9

Input and output pulse of the second-order temporal differentiator. (a) Simulated and measured input pulses; (b) Simulated and measured output pulses.

Fig. 10
Fig. 10

Estimated processing error as a function of the input pulse bandwidth for the fabricated second-order differentiator. RMS: root mean square.

Equations (4)

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

r(ω)=[j(ω-ω0)]NE(ω-ω0).
rg(ω)=Rg(ω)=Aexp(ω2n/σ2n),
rd(ω)=Rd(ω)exp[jϕ(ω)],
r(ω)=rg(ω)rd(ω)=Rg(ω)Rd(ω)exp[jϕ(ω)],

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