Abstract

We report the first realization of integrated, all-optical first- and higher-order photonic differentiators operating at terahertz (THz) processing speeds. This is accomplished in a Silicon-on-Insulator (SOI) CMOS-compatible platform using a simple integrated geometry based on (π-)phase-shifted Bragg gratings. Moreover, we achieve on-chip generation of sub-picosecond Hermite-Gaussian pulse waveforms, which are noteworthy for applications in next-generation optical telecommunications.

©2011 Optical Society of America

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    [Crossref]
  21. M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, “Modeling of photonic wire Bragg gratings,” Opt. Quantum Electron. 38(1-3), 133–148 (2006).
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    [Crossref]
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    [Crossref]
  29. C. Dorrer, N. Belabas, J.-P. Likforman, and M. Joffre, “Experimental implementation of Fourier-transform spectral interferometry and its application to study of spectrometers,” Appl. Phys. B 70, S99–S107 (2000).
    [Crossref]
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    [Crossref] [PubMed]

2010 (3)

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(3), 1–5 (2010).
[Crossref] [PubMed]

J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-Bragg grating devices,” IEEE Photon. J. 2(3), 359–386 (2010).
[Crossref]

M. J. Strain and M. Sorel, “Design and fabrication of integrated chirped Bragg gratings for on-chip dispersion control,” IEEE J. Quantum Electron. 46(5), 774–782 (2010).
[Crossref]

2009 (4)

2008 (6)

L. K. Oxenlowe, R. Slavik, M. Galili, H. C. M. Mulvad, A. T. Clausen, Y. Park, J. Azaña, and P. Jeppesen, “640 Gbit/s timing jitter tolerant data processing using a long-period fiber grating-based flat-top pulse shaper,” IEEE J. Sel. Top. Quantum Electron. 14(3), 566–572 (2008).
[Crossref]

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).
[Crossref] [PubMed]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[Crossref] [PubMed]

M. Vasilyev, Y. Su, and C. McKinstrie, “Nonlinear optical signal processing,” IEEE J. Sel. Top. Quantum Electron. 14(3), 527–528 (2008).
[Crossref]

M. H. Asghari and J. Azaña, “Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings,” Opt. Express 16(15), 11459–11469 (2008).
[Crossref] [PubMed]

M. H. Asghari and J. Azaña, “Proposal and analysis of a reconfigurable pulse shaping technique based on multi-arm optical differentiators,” Opt. Commun. 281(18), 4581–4588 (2008).
[Crossref]

2007 (3)

2006 (4)

M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, “Modeling of photonic wire Bragg gratings,” Opt. Quantum Electron. 38(1-3), 133–148 (2006).
[Crossref]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14(22), 10699–10707 (2006).
[Crossref] [PubMed]

C.-W. Hsue, L.-C. Tsai, and Y.-H. Tsai, “Time-constant control of microwave integrators using transmission lines,” IEEE Trans. Microw. Theory Tech. 54(3), 1043–1047 (2006).
[Crossref]

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-compatible integrated silicon photonics devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

2005 (3)

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17(12), 2613–2615 (2005).
[Crossref]

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, “Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset,” IEEE/OSA J. Lightwave Technol. 23(10), 3282–3289 (2005).
[Crossref]

M. Stratmann, T. Pagel, and F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95(14), 143902–1 (2005).
[Crossref] [PubMed]

2004 (2)

C.-W. Hsue, L.-C. Tsai, and K.-L. Chen, “Implementation of first-order and second-order microwave differentiators,” IEEE Trans. Microw. Theory Tech. 52(5), 1443–1448 (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]

2000 (1)

C. Dorrer, N. Belabas, J.-P. Likforman, and M. Joffre, “Experimental implementation of Fourier-transform spectral interferometry and its application to study of spectrometers,” Appl. Phys. B 70, S99–S107 (2000).
[Crossref]

1997 (1)

1989 (1)

Andrés, M. V.

Asghari, M. H.

M. H. Asghari and J. Azaña, “Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings,” Opt. Express 16(15), 11459–11469 (2008).
[Crossref] [PubMed]

M. H. Asghari and J. Azaña, “Proposal and analysis of a reconfigurable pulse shaping technique based on multi-arm optical differentiators,” Opt. Commun. 281(18), 4581–4588 (2008).
[Crossref]

Azaña, J.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(3), 1–5 (2010).
[Crossref] [PubMed]

J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-Bragg grating devices,” IEEE Photon. J. 2(3), 359–386 (2010).
[Crossref]

F. Li, Y. Park, and J. Azaña, “Linear characterization of optical pulses with durations ranging from the picosecond to the nanosecond regime using ultrafast photonic differentiation,” IEEE/OSA J. Lightwave Technol. 27(21), 4623–4633 (2009).
[Crossref]

M. H. Asghari and J. Azaña, “Proposal and analysis of a reconfigurable pulse shaping technique based on multi-arm optical differentiators,” Opt. Commun. 281(18), 4581–4588 (2008).
[Crossref]

M. H. Asghari and J. Azaña, “Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings,” Opt. Express 16(15), 11459–11469 (2008).
[Crossref] [PubMed]

L. K. Oxenlowe, R. Slavik, M. Galili, H. C. M. Mulvad, A. T. Clausen, Y. Park, J. Azaña, and P. Jeppesen, “640 Gbit/s timing jitter tolerant data processing using a long-period fiber grating-based flat-top pulse shaper,” IEEE J. Sel. Top. Quantum Electron. 14(3), 566–572 (2008).
[Crossref]

M. Kulishov and J. Azaña, “Design of high-order all-optical temporal differentiators based on multiple-phase-shifted fiber Bragg gratings,” Opt. Express 15(10), 6152–6166 (2007).
[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).
[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]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14(22), 10699–10707 (2006).
[Crossref] [PubMed]

Baets, R.

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17(12), 2613–2615 (2005).
[Crossref]

Barkai, A.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-compatible integrated silicon photonics devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Bassi, P.

M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, “Modeling of photonic wire Bragg gratings,” Opt. Quantum Electron. 38(1-3), 133–148 (2006).
[Crossref]

Belabas, N.

C. Dorrer, N. Belabas, J.-P. Likforman, and M. Joffre, “Experimental implementation of Fourier-transform spectral interferometry and its application to study of spectrometers,” Appl. Phys. B 70, S99–S107 (2000).
[Crossref]

Bellanca, G.

M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, “Modeling of photonic wire Bragg gratings,” Opt. Quantum Electron. 38(1-3), 133–148 (2006).
[Crossref]

Berger, N. K.

Bogaerts, W.

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17(12), 2613–2615 (2005).
[Crossref]

Chen, K.-L.

C.-W. Hsue, L.-C. Tsai, and K.-L. Chen, “Implementation of first-order and second-order microwave differentiators,” IEEE Trans. Microw. Theory Tech. 52(5), 1443–1448 (2004).
[Crossref]

Chong, H.

M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, “Modeling of photonic wire Bragg gratings,” Opt. Quantum Electron. 38(1-3), 133–148 (2006).
[Crossref]

Chu, S. T.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(3), 1–5 (2010).
[Crossref] [PubMed]

Clausen, A. T.

L. K. Oxenlowe, R. Slavik, M. Galili, H. C. M. Mulvad, A. T. Clausen, Y. Park, J. Azaña, and P. Jeppesen, “640 Gbit/s timing jitter tolerant data processing using a long-period fiber grating-based flat-top pulse shaper,” IEEE J. Sel. Top. Quantum Electron. 14(3), 566–572 (2008).
[Crossref]

Cohen, O.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-compatible integrated silicon photonics devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Cohen, R.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-compatible integrated silicon photonics devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Cuadrado-Laborde, C.

da Silva, H. J. A.

De La Rue, R. M.

M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, “Modeling of photonic wire Bragg gratings,” Opt. Quantum Electron. 38(1-3), 133–148 (2006).
[Crossref]

Dorrer, C.

C. Dorrer, N. Belabas, J.-P. Likforman, and M. Joffre, “Experimental implementation of Fourier-transform spectral interferometry and its application to study of spectrometers,” Appl. Phys. B 70, S99–S107 (2000).
[Crossref]

Dumon, P.

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17(12), 2613–2615 (2005).
[Crossref]

Ferrera, M.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(3), 1–5 (2010).
[Crossref] [PubMed]

Fischer, B.

Foster, M. A.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[Crossref] [PubMed]

Gaeta, A. L.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[Crossref] [PubMed]

Galili, M.

L. K. Oxenlowe, R. Slavik, M. Galili, H. C. M. Mulvad, A. T. Clausen, Y. Park, J. Azaña, and P. Jeppesen, “640 Gbit/s timing jitter tolerant data processing using a long-period fiber grating-based flat-top pulse shaper,” IEEE J. Sel. Top. Quantum Electron. 14(3), 566–572 (2008).
[Crossref]

Geraghty, D. F.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[Crossref] [PubMed]

Gnan, M.

M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, “Modeling of photonic wire Bragg gratings,” Opt. Quantum Electron. 38(1-3), 133–148 (2006).
[Crossref]

Hofstetter, D.

Hsue, C.-W.

C.-W. Hsue, L.-C. Tsai, and Y.-H. Tsai, “Time-constant control of microwave integrators using transmission lines,” IEEE Trans. Microw. Theory Tech. 54(3), 1043–1047 (2006).
[Crossref]

C.-W. Hsue, L.-C. Tsai, and K.-L. Chen, “Implementation of first-order and second-order microwave differentiators,” IEEE Trans. Microw. Theory Tech. 52(5), 1443–1448 (2004).
[Crossref]

Izhaky, N.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-compatible integrated silicon photonics devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Janner, D.

Jeppesen, P.

L. K. Oxenlowe, R. Slavik, M. Galili, H. C. M. Mulvad, A. T. Clausen, Y. Park, J. Azaña, and P. Jeppesen, “640 Gbit/s timing jitter tolerant data processing using a long-period fiber grating-based flat-top pulse shaper,” IEEE J. Sel. Top. Quantum Electron. 14(3), 566–572 (2008).
[Crossref]

Joffre, M.

C. Dorrer, N. Belabas, J.-P. Likforman, and M. Joffre, “Experimental implementation of Fourier-transform spectral interferometry and its application to study of spectrometers,” Appl. Phys. B 70, S99–S107 (2000).
[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]

Koehl, S.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-compatible integrated silicon photonics devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Kulishov, M.

Kumar, P. V.

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, “Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset,” IEEE/OSA J. Lightwave Technol. 23(10), 3282–3289 (2005).
[Crossref]

Levit, B.

Li, F.

F. Li, Y. Park, and J. Azaña, “Linear characterization of optical pulses with durations ranging from the picosecond to the nanosecond regime using ultrafast photonic differentiation,” IEEE/OSA J. Lightwave Technol. 27(21), 4623–4633 (2009).
[Crossref]

Li, M.

Li, Z.

Likforman, J.-P.

C. Dorrer, N. Belabas, J.-P. Likforman, and M. Joffre, “Experimental implementation of Fourier-transform spectral interferometry and its application to study of spectrometers,” Appl. Phys. B 70, S99–S107 (2000).
[Crossref]

Lipson, M.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[Crossref] [PubMed]

Little, B. E.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(3), 1–5 (2010).
[Crossref] [PubMed]

Liu, F.

McGeehan, J. E.

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, “Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset,” IEEE/OSA J. Lightwave Technol. 23(10), 3282–3289 (2005).
[Crossref]

McKinstrie, C.

M. Vasilyev, Y. Su, and C. McKinstrie, “Nonlinear optical signal processing,” IEEE J. Sel. Top. Quantum Electron. 14(3), 527–528 (2008).
[Crossref]

Mitschke, F.

M. Stratmann, T. Pagel, and F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95(14), 143902–1 (2005).
[Crossref] [PubMed]

Morandotti, R.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(3), 1–5 (2010).
[Crossref] [PubMed]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14(22), 10699–10707 (2006).
[Crossref] [PubMed]

Morse, M. T.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-compatible integrated silicon photonics devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Moss, D. J.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(3), 1–5 (2010).
[Crossref] [PubMed]

Mulvad, H. C. M.

L. K. Oxenlowe, R. Slavik, M. Galili, H. C. M. Mulvad, A. T. Clausen, Y. Park, J. Azaña, and P. Jeppesen, “640 Gbit/s timing jitter tolerant data processing using a long-period fiber grating-based flat-top pulse shaper,” IEEE J. Sel. Top. Quantum Electron. 14(3), 566–572 (2008).
[Crossref]

Nezam, S. M. R. M.

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, “Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset,” IEEE/OSA J. Lightwave Technol. 23(10), 3282–3289 (2005).
[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]

O’Reilly, J. J.

Omrani, R.

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, “Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset,” IEEE/OSA J. Lightwave Technol. 23(10), 3282–3289 (2005).
[Crossref]

Oxenlowe, L. K.

L. K. Oxenlowe, R. Slavik, M. Galili, H. C. M. Mulvad, A. T. Clausen, Y. Park, J. Azaña, and P. Jeppesen, “640 Gbit/s timing jitter tolerant data processing using a long-period fiber grating-based flat-top pulse shaper,” IEEE J. Sel. Top. Quantum Electron. 14(3), 566–572 (2008).
[Crossref]

Pagel, T.

M. Stratmann, T. Pagel, and F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95(14), 143902–1 (2005).
[Crossref] [PubMed]

Paniccia, M. J.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-compatible integrated silicon photonics devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Park, Y.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(3), 1–5 (2010).
[Crossref] [PubMed]

F. Li, Y. Park, and J. Azaña, “Linear characterization of optical pulses with durations ranging from the picosecond to the nanosecond regime using ultrafast photonic differentiation,” IEEE/OSA J. Lightwave Technol. 27(21), 4623–4633 (2009).
[Crossref]

L. K. Oxenlowe, R. Slavik, M. Galili, H. C. M. Mulvad, A. T. Clausen, Y. Park, J. Azaña, and P. Jeppesen, “640 Gbit/s timing jitter tolerant data processing using a long-period fiber grating-based flat-top pulse shaper,” IEEE J. Sel. Top. Quantum Electron. 14(3), 566–572 (2008).
[Crossref]

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]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14(22), 10699–10707 (2006).
[Crossref] [PubMed]

Plant, D. V.

Pruneri, V.

Qiang, L.

Qiu, M.

Razzari, L.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(3), 1–5 (2010).
[Crossref] [PubMed]

Roelkens, G.

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17(12), 2613–2615 (2005).
[Crossref]

Rubin, D.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-compatible integrated silicon photonics devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Saghari, P.

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, “Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset,” IEEE/OSA J. Lightwave Technol. 23(10), 3282–3289 (2005).
[Crossref]

Salem, R.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[Crossref] [PubMed]

Sarid, G.

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-compatible integrated silicon photonics devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

Slavik, R.

L. K. Oxenlowe, R. Slavik, M. Galili, H. C. M. Mulvad, A. T. Clausen, Y. Park, J. Azaña, and P. Jeppesen, “640 Gbit/s timing jitter tolerant data processing using a long-period fiber grating-based flat-top pulse shaper,” IEEE J. Sel. Top. Quantum Electron. 14(3), 566–572 (2008).
[Crossref]

Slavík, R.

Sorel, M.

M. J. Strain and M. Sorel, “Design and fabrication of integrated chirped Bragg gratings for on-chip dispersion control,” IEEE J. Quantum Electron. 46(5), 774–782 (2010).
[Crossref]

Strain, M. J.

M. J. Strain and M. Sorel, “Design and fabrication of integrated chirped Bragg gratings for on-chip dispersion control,” IEEE J. Quantum Electron. 46(5), 774–782 (2010).
[Crossref]

Stratmann, M.

M. Stratmann, T. Pagel, and F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95(14), 143902–1 (2005).
[Crossref] [PubMed]

Su, Y.

Thornton, R. L.

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]

Tsai, L.-C.

C.-W. Hsue, L.-C. Tsai, and Y.-H. Tsai, “Time-constant control of microwave integrators using transmission lines,” IEEE Trans. Microw. Theory Tech. 54(3), 1043–1047 (2006).
[Crossref]

C.-W. Hsue, L.-C. Tsai, and K.-L. Chen, “Implementation of first-order and second-order microwave differentiators,” IEEE Trans. Microw. Theory Tech. 52(5), 1443–1448 (2004).
[Crossref]

Tsai, Y.-H.

C.-W. Hsue, L.-C. Tsai, and Y.-H. Tsai, “Time-constant control of microwave integrators using transmission lines,” IEEE Trans. Microw. Theory Tech. 54(3), 1043–1047 (2006).
[Crossref]

Turner-Foster, A. C.

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[Crossref] [PubMed]

Van Thourhout, D.

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17(12), 2613–2615 (2005).
[Crossref]

Vasilyev, M.

M. Vasilyev, Y. Su, and C. McKinstrie, “Nonlinear optical signal processing,” IEEE J. Sel. Top. Quantum Electron. 14(3), 527–528 (2008).
[Crossref]

Wang, T.

Willner, A. E.

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, “Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset,” IEEE/OSA J. Lightwave Technol. 23(10), 3282–3289 (2005).
[Crossref]

Wu, C.

Yao, J. P.

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]

Zhang, Z.

Appl. Phys. B (1)

C. Dorrer, N. Belabas, J.-P. Likforman, and M. Joffre, “Experimental implementation of Fourier-transform spectral interferometry and its application to study of spectrometers,” Appl. Phys. B 70, S99–S107 (2000).
[Crossref]

IEEE J. Quantum Electron. (1)

M. J. Strain and M. Sorel, “Design and fabrication of integrated chirped Bragg gratings for on-chip dispersion control,” IEEE J. Quantum Electron. 46(5), 774–782 (2010).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (3)

L. K. Oxenlowe, R. Slavik, M. Galili, H. C. M. Mulvad, A. T. Clausen, Y. Park, J. Azaña, and P. Jeppesen, “640 Gbit/s timing jitter tolerant data processing using a long-period fiber grating-based flat-top pulse shaper,” IEEE J. Sel. Top. Quantum Electron. 14(3), 566–572 (2008).
[Crossref]

M. Vasilyev, Y. Su, and C. McKinstrie, “Nonlinear optical signal processing,” IEEE J. Sel. Top. Quantum Electron. 14(3), 527–528 (2008).
[Crossref]

N. Izhaky, M. T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, and M. J. Paniccia, “Development of CMOS-compatible integrated silicon photonics devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1688–1698 (2006).
[Crossref]

IEEE Photon. J. (1)

J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-Bragg grating devices,” IEEE Photon. J. 2(3), 359–386 (2010).
[Crossref]

IEEE Photon. Technol. Lett. (1)

G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, and R. Baets, “Efficient silicon-on-insulator fiber coupler fabricated using 248-nm-deep UV lithography,” IEEE Photon. Technol. Lett. 17(12), 2613–2615 (2005).
[Crossref]

IEEE Trans. Microw. Theory Tech. (2)

C.-W. Hsue, L.-C. Tsai, and K.-L. Chen, “Implementation of first-order and second-order microwave differentiators,” IEEE Trans. Microw. Theory Tech. 52(5), 1443–1448 (2004).
[Crossref]

C.-W. Hsue, L.-C. Tsai, and Y.-H. Tsai, “Time-constant control of microwave integrators using transmission lines,” IEEE Trans. Microw. Theory Tech. 54(3), 1043–1047 (2006).
[Crossref]

IEEE/OSA J. Lightwave Technol. (2)

F. Li, Y. Park, and J. Azaña, “Linear characterization of optical pulses with durations ranging from the picosecond to the nanosecond regime using ultrafast photonic differentiation,” IEEE/OSA J. Lightwave Technol. 27(21), 4623–4633 (2009).
[Crossref]

J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani, and P. V. Kumar, “Experimental demonstration of OCDMA transmission using a three-dimensional (time-wavelength-polarization) codeset,” IEEE/OSA J. Lightwave Technol. 23(10), 3282–3289 (2005).
[Crossref]

Nat. Commun. (1)

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(3), 1–5 (2010).
[Crossref] [PubMed]

Nature (1)

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456(7218), 81–84 (2008).
[Crossref] [PubMed]

Opt. Commun. (2)

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]

M. H. Asghari and J. Azaña, “Proposal and analysis of a reconfigurable pulse shaping technique based on multi-arm optical differentiators,” Opt. Commun. 281(18), 4581–4588 (2008).
[Crossref]

Opt. Express (6)

Opt. Lett. (5)

Opt. Quantum Electron. (1)

M. Gnan, G. Bellanca, H. Chong, P. Bassi, and R. M. De La Rue, “Modeling of photonic wire Bragg gratings,” Opt. Quantum Electron. 38(1-3), 133–148 (2006).
[Crossref]

Phys. Rev. Lett. (1)

M. Stratmann, T. Pagel, and F. Mitschke, “Experimental observation of temporal soliton molecules,” Phys. Rev. Lett. 95(14), 143902–1 (2005).
[Crossref] [PubMed]

Other (4)

R. Kashyap, Fiber Bragg gratings (second edition, Optics and Photonics Series, Academic Press, San Diego, 2009).

Photonic technologies, Nature Insight 424, No. 6950 (2003). http://www.nature.com/nature/insights/6950.html .

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., special issue on “Optical signal processing,” IEEE/OSA J. Lightwav.Technol. 24, 2484–2767 (2006).

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems (2nd edition, Prentice Hall, Upper Saddle River, NJ, USA, 1996).

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Figures (5)
Fig. 1
Fig. 1 General scheme of the Nth-order temporal differentiators based on multiple-phase-shifted Bragg gratings (with a constant period Λ). The grating coupling strength is determined by the recess depth d of the waveguide sidewall-etching.

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Fig. 2
Fig. 2 Amplitude reflectivity |r| and phase ϕr=arg(r) as a function of the optical frequency for first- (a-b) and second- (c-d) order differentiators, respectively. The reflection spectra were obtained using a transfer matrix method, for a grating period of Λ=316nm and a Bragg wavelength of 1550nm. The dashed lines represent linear and parabolic functions of the base-band frequency, respectively. The operational bandwidth ∆f of each proposed device is determined by the frequency region over which the solid and dashed curves agree. The subscript 'A' in the graphs above corresponds to the cases close to the optimal operation condition (i.e. 2κiLiA≈π), while the data indicated by the subscript 'B' were obtained by reducing the intensity reflectivity |r|2 from 1 to 0.7 out of the resonance notch. The optimal operation condition for κ1=500/cm is not presented, since the operational bandwidth is much narrower than the one described by ∆f 2A. Also, note that in all the simulated cases, a π-phase-jump at the resonance frequency is observed for the first-order differentiator (b), while the reflection phase is nearly linear over all the operation bandwidth of the second-order differentiator (i.e. with no phase shift at the resonance frequency) (d), as desired (for the sake of clarity, the phase filtering profile is shown only for the ideal condition cases).

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Fig. 3
Fig. 3 Schemes (a-b) and SEM images (c) of the π-phase-shifted Bragg-grating-based devices used for performing all-optical temporal differentiation. The coupling coefficient κ, and thus the operational bandwidth of the fabricated devices, can be adjusted by changing the recess depth d (as shown in panel (d)). The recess depth in (c) is 30nm (maximum in the fabricated set of devices).

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Fig. 4
Fig. 4 The experimentally obtained normalized intensity reflectivity (retrieved from transmission measurements) of a Bragg grating separated by a single π-phase shift (a) and of a Bragg grating composed of three segments separated by two π-phase shifts (b). The red lines represent the intensity reflectivities calculated theoretically for phase-shifted Bragg gratings with the specific parameters given in each panel.

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Fig. 5
Fig. 5 Results for the experimentally retrieved (normalized) intensity autocorrelations for the pulses under differentiation are shown in (a) and (d), respectively. The black traces represent direct measurements from the autocorrelator (Femtochrome FR-103xl) while the red autocorrelation traces are obtained via numerical calculations using the power spectra of the input pulses from the OSA. Experimental results obtained for the first- (b-c) and second- (e-f) order differentiators. Using the first order differentiator (with intensity reflectivity shown in Fig. 4a), the first-order differentiation of an input optical pulse (~4nm FWHM) is obtained (b). The derivative of an ideal 700fs Gaussian pulse is also shown in red (dashed line) for comparison. As expected, a phase shift of π is observed in the center of the differentiated signal (c). Similarly, a Bragg grating with intensity reflectivity presented in Fig. 4b, is used to obtain the second-order differentiation of the input pulse (~3nm FWHM) (e). The second-order derivative of a 1250fs Gaussian pulse is also shown. Two distinct phase shifts of ~π are observed in the differentiated signal (f).

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Equations (2)

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r 1st = 2 κ σ sin h 2 ( γ L ) κ 2 − σ ( σ cos h ( 2 γ L ) + i γ sin h ( 2 γ L ) ) and r 2nd = 4 κσ 2 ( 2 sin h ( 2γ L ) − sin h ( 4γ L ) ) iγσ 2 ( 1 − 4 cos h ( 4γ L ) ) + iγ ( 3 κ 2 + γ 2 ) + 4 σ ( 2 κ 2 sin h ( 2γ L ) − σ 2 sin h ( 4γ L ) ) ,
r 1st = 2 σ sin h 2 ( κ L ) κ and r 2nd = 4   i σ 2   sin h ( 2κ L )   sin h 2 ( κ L ) κ 2

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