Abstract

We report a type of programmable pulse shaping method based on cascaded frequency-detuned optical differentiators. By properly adjusting the central wavelength of each differentiator, a large variety of symmetric pulses can be generated from a transform-limited Gaussian-like pulse. We numerically and experimentally demonstrate the generation of flat-top, parabolic and triangular pulses with tunable pulse widths from a 20-ps Gaussian-like pulse, using no more than three cascaded differentiators. It can be found that as more differentiators are used, higher synthesized accuracy and larger tuning range of pulse widths can be obtained in general. Additionally, in our experiment, we design and fabricate thermally tunable delay interferometers on the silicon-on-insulator (SOI) platform to work as optical differentiators, which can help us realize the shaping system with small footprint (943μm × 395μm) and high stability.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (2)

J. Huh and J. Azaña, “In-fiber reconfigurable generation of arbitrary (asymmetric) picosecond temporal intensity waveforms by time-domain optical pulse shaping,” Opt. Lett. 41(4), 693–696 (2016).
[Crossref] [PubMed]

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

2015 (8)

T. L. Huang, A. L. Zheng, J. J. Dong, D. S. Gao, and X. L. Zhang, “Terahertz-bandwidth photonic temporal differentiator based on a silicon-on-isolator directional coupler,” Opt. Lett. 40(23), 5614–5617 (2015).
[Crossref] [PubMed]

H. P. Bazargani and J. Azaña, “Optical pulse shaping based on discrete space-to-time mapping in cascaded co-directional couplers,” Opt. Express 23(18), 23450–23461 (2015).
[Crossref] [PubMed]

H. P. Bazargani, M. Burla, and J. Azaña, “Experimental demonstration of sub-picosecond optical pulse shaping in silicon based on discrete space-to-time mapping,” Opt. Lett. 40(23), 5423–5426 (2015).
[Crossref] [PubMed]

K. Suzuki, G. Cong, K. Tanizawa, S.-H. Kim, K. Ikeda, S. Namiki, and H. Kawashima, “Ultra-high-extinction-ratio 2 × 2 silicon optical switch with variable splitter,” Opt. Express 23(7), 9086–9092 (2015).
[Crossref] [PubMed]

D. A. B. Miller, “Perfect optics with imperfect components,” Optica 2(8), 747–750 (2015).
[Crossref]

S. Liao, Y. Ding, J. Dong, T. Yang, X. Chen, D. Gao, and X. Zhang, “Arbitrary waveform generator and differentiator employing an integrated optical pulse shaper,” Opt. Express 23(9), 12161–12173 (2015).
[Crossref] [PubMed]

L. Lei, J. Huh, L. R. Cortés, R. Maram, B. Wetzel, D. Duchesne, R. Morandotti, and J. Azaña, “Observation of spectral self-imaging by nonlinear parabolic cross-phase modulation,” Opt. Lett. 40(22), 5403–5406 (2015).
[Crossref] [PubMed]

V. V. Lozovoy, G. Rasskazov, A. Ryabtsev, and M. Dantus, “Phase-only synthesis of ultrafast stretched square pulses,” Opt. Express 23(21), 27105–27112 (2015).
[Crossref] [PubMed]

2014 (4)

2013 (4)

2012 (2)

M. Li, P. Dumais, R. Ashrafi, H. P. Bazargani, J. Quelene, C. Callender, and J. Azana, “Ultrashort flat-top pulse generation using on-chip CMOS-compatible Mach–Zehnder interferometers,” IEEE Photonics Technol. Lett. 24(16), 1387–1389 (2012).
[Crossref]

M. Li, H.-S. Jeong, J. Azaña, and T.-J. Ahn, “25-terahertz-bandwidth all-optical temporal differentiator,” Opt. Express 20(27), 28273–28280 (2012).
[Crossref] [PubMed]

2011 (3)

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

A. M. Weiner, “Ultrafast optical pulse shaping: a tutorial review,” Opt. Commun. 284(15), 3669–3692 (2011).
[Crossref]

L. Xiang, D. Jianji, Y. Yuan, and Z. Xinliang, “A tunable microwave photonic filter based on an all-optical differentiator,” IEEE Photonics Technol. Lett. 23(5), 308–310 (2011).
[Crossref]

2010 (3)

A. M. Clarke, D. G. Williams, M. A. F. Roelens, and B. J. Eggleton, “Reconfigurable optical pulse generator employing a fourier-domain programmable optical processor,” J. Lightwave Technol. 28(1), 97–103 (2010).
[Crossref]

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

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

2009 (2)

2008 (3)

2007 (4)

Y. Park, M. H. Asghari, T.-J. Ahn, and J. Azaña, “Transform-limited picosecond pulse shaping based on temporal coherence synthesization,” Opt. Express 15(15), 9584–9599 (2007).
[Crossref] [PubMed]

F. Li, Y. Park, and J. Azaña, “Complete temporal pulse characterization based on phase reconstruction using optical ultrafast differentiation (PROUD),” Opt. Lett. 32(22), 3364–3366 (2007).
[Crossref] [PubMed]

R. Slavik, L. K. Oxenlowe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azana, and P. Jeppesen, “Demultiplexing of 320-Gb/s OTDM data using ultrashort flat-top pulses,” IEEE Photonics Technol. Lett. 19(22), 1855–1857 (2007).
[Crossref]

J. P. Heritage and A. M. Weiner, “Advances in spectral optical code-division multiple-access communications,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1351–1369 (2007).
[Crossref]

2006 (2)

2003 (1)

D. Goswami, “Optical pulse shaping approaches to coherent control,” Phys. Rep. 374(6), 385–481 (2003).
[Crossref]

1995 (1)

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19(3), 161–237 (1995).
[Crossref]

Ahn, T.-J.

Andrés, M. V.

Argyris, A.

Asghari, M. H.

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]

Y. Park, M. H. Asghari, T.-J. Ahn, and J. Azaña, “Transform-limited picosecond pulse shaping based on temporal coherence synthesization,” Opt. Express 15(15), 9584–9599 (2007).
[Crossref] [PubMed]

Ashrafi, R.

M. Li, P. Dumais, R. Ashrafi, H. P. Bazargani, J. Quelene, C. Callender, and J. Azana, “Ultrashort flat-top pulse generation using on-chip CMOS-compatible Mach–Zehnder interferometers,” IEEE Photonics Technol. Lett. 24(16), 1387–1389 (2012).
[Crossref]

Azana, J.

M. Li, P. Dumais, R. Ashrafi, H. P. Bazargani, J. Quelene, C. Callender, and J. Azana, “Ultrashort flat-top pulse generation using on-chip CMOS-compatible Mach–Zehnder interferometers,” IEEE Photonics Technol. Lett. 24(16), 1387–1389 (2012).
[Crossref]

R. Slavik, L. K. Oxenlowe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azana, and P. Jeppesen, “Demultiplexing of 320-Gb/s OTDM data using ultrashort flat-top pulses,” IEEE Photonics Technol. Lett. 19(22), 1855–1857 (2007).
[Crossref]

Azaña, J.

J. Huh and J. Azaña, “In-fiber reconfigurable generation of arbitrary (asymmetric) picosecond temporal intensity waveforms by time-domain optical pulse shaping,” Opt. Lett. 41(4), 693–696 (2016).
[Crossref] [PubMed]

H. P. Bazargani, M. Burla, and J. Azaña, “Experimental demonstration of sub-picosecond optical pulse shaping in silicon based on discrete space-to-time mapping,” Opt. Lett. 40(23), 5423–5426 (2015).
[Crossref] [PubMed]

H. P. Bazargani and J. Azaña, “Optical pulse shaping based on discrete space-to-time mapping in cascaded co-directional couplers,” Opt. Express 23(18), 23450–23461 (2015).
[Crossref] [PubMed]

L. Lei, J. Huh, L. R. Cortés, R. Maram, B. Wetzel, D. Duchesne, R. Morandotti, and J. Azaña, “Observation of spectral self-imaging by nonlinear parabolic cross-phase modulation,” Opt. Lett. 40(22), 5403–5406 (2015).
[Crossref] [PubMed]

M. Li, H.-S. Jeong, J. Azaña, and T.-J. Ahn, “25-terahertz-bandwidth all-optical temporal differentiator,” Opt. Express 20(27), 28273–28280 (2012).
[Crossref] [PubMed]

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

R. Slavík, Y. Park, M. Kulishov, and J. Azaña, “Terahertz-bandwidth high-order temporal differentiators based on phase-shifted long-period fiber gratings,” Opt. Lett. 34(20), 3116–3118 (2009).
[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]

Y. Park, M. H. Asghari, T.-J. Ahn, and J. Azaña, “Transform-limited picosecond pulse shaping based on temporal coherence synthesization,” Opt. Express 15(15), 9584–9599 (2007).
[Crossref] [PubMed]

F. Li, Y. Park, and J. Azaña, “Complete temporal pulse characterization based on phase reconstruction using optical ultrafast differentiation (PROUD),” Opt. Lett. 32(22), 3364–3366 (2007).
[Crossref] [PubMed]

Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings,” Opt. Express 14(26), 12670–12678 (2006).
[Crossref] [PubMed]

Bazargani, H. P.

Bhamber, R. S.

Bogris, A.

Boscolo, S.

Burla, M.

Callender, C.

M. Li, P. Dumais, R. Ashrafi, H. P. Bazargani, J. Quelene, C. Callender, and J. Azana, “Ultrashort flat-top pulse generation using on-chip CMOS-compatible Mach–Zehnder interferometers,” IEEE Photonics Technol. Lett. 24(16), 1387–1389 (2012).
[Crossref]

Cao, P.

L. Zhang, J. Wu, X. Yin, X. Sun, P. Cao, X. Jiang, and Y. Su, “A high-speed second-order photonic differentiator based on two-stage silicon self-coupled optical waveguide,” IEEE Photonics J. 6, 1–5 (2014).
[Crossref]

Chen, L.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Chen, X.

Clarke, A. M.

Coldren, L. A.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Cong, G.

Cortés, L. R.

Dantus, M.

Ding, Y.

Dong, J.

Dong, J. J.

Duchesne, D.

Dumais, P.

M. Li, P. Dumais, R. Ashrafi, H. P. Bazargani, J. Quelene, C. Callender, and J. Azana, “Ultrashort flat-top pulse generation using on-chip CMOS-compatible Mach–Zehnder interferometers,” IEEE Photonics Technol. Lett. 24(16), 1387–1389 (2012).
[Crossref]

Eggleton, B. J.

Ferdous, F.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Fesenko, V. I.

Finot, C.

Galili, M.

R. Slavik, L. K. Oxenlowe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azana, and P. Jeppesen, “Demultiplexing of 320-Gb/s OTDM data using ultrashort flat-top pulses,” IEEE Photonics Technol. Lett. 19(22), 1855–1857 (2007).
[Crossref]

Gao, D.

Gao, D. S.

Goswami, D.

D. Goswami, “Optical pulse shaping approaches to coherent control,” Phys. Rep. 374(6), 385–481 (2003).
[Crossref]

Guzzon, R. S.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Heritage, J. P.

J. P. Heritage and A. M. Weiner, “Advances in spectral optical code-division multiple-access communications,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1351–1369 (2007).
[Crossref]

Hu, S.

Huang, D.

Huang, T. L.

Huh, J.

Iakushev, S. O.

Ibsen, M.

Ikeda, K.

Jeong, H.-S.

Jeppesen, P.

R. Slavik, L. K. Oxenlowe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azana, and P. Jeppesen, “Demultiplexing of 320-Gb/s OTDM data using ultrashort flat-top pulses,” IEEE Photonics Technol. Lett. 19(22), 1855–1857 (2007).
[Crossref]

Jiang, X.

L. Zhang, J. Wu, X. Yin, X. Sun, P. Cao, X. Jiang, and Y. Su, “A high-speed second-order photonic differentiator based on two-stage silicon self-coupled optical waveguide,” IEEE Photonics J. 6, 1–5 (2014).
[Crossref]

Jianji, D.

L. Xiang, D. Jianji, Y. Yuan, and Z. Xinliang, “A tunable microwave photonic filter based on an all-optical differentiator,” IEEE Photonics Technol. Lett. 23(5), 308–310 (2011).
[Crossref]

Kawashima, H.

Kazanskiy, N. L.

Khan, M. H.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Khonina, S. N.

Kim, S.-H.

Kulishov, M.

Latkin, A. I.

Leaird, D. E.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Lei, L.

Li, F.

Li, M.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

M. Li, P. Dumais, R. Ashrafi, H. P. Bazargani, J. Quelene, C. Callender, and J. Azana, “Ultrashort flat-top pulse generation using on-chip CMOS-compatible Mach–Zehnder interferometers,” IEEE Photonics Technol. Lett. 24(16), 1387–1389 (2012).
[Crossref]

M. Li, H.-S. Jeong, J. Azaña, and T.-J. Ahn, “25-terahertz-bandwidth all-optical temporal differentiator,” Opt. Express 20(27), 28273–28280 (2012).
[Crossref] [PubMed]

Li, W.

Liao, S.

Liu, F.

Liu, J. G.

Liu, W.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Lozovoy, V. V.

Lu, M.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Maram, R.

Miao, H.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Miller, D. A. B.

Morandotti, R.

Mukasa, K.

Mulvad, H. C. H.

R. Slavik, L. K. Oxenlowe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azana, and P. Jeppesen, “Demultiplexing of 320-Gb/s OTDM data using ultrashort flat-top pulses,” IEEE Photonics Technol. Lett. 19(22), 1855–1857 (2007).
[Crossref]

Namiki, S.

Norberg, E. J.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Oxenlowe, L. K.

R. Slavik, L. K. Oxenlowe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azana, and P. Jeppesen, “Demultiplexing of 320-Gb/s OTDM data using ultrashort flat-top pulses,” IEEE Photonics Technol. Lett. 19(22), 1855–1857 (2007).
[Crossref]

Park, Y.

Parker, J. S.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Parmigiani, F.

Petropoulos, P.

Qi, M.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Qiang, L.

Qiu, M.

Quelene, J.

M. Li, P. Dumais, R. Ashrafi, H. P. Bazargani, J. Quelene, C. Callender, and J. Azana, “Ultrashort flat-top pulse generation using on-chip CMOS-compatible Mach–Zehnder interferometers,” IEEE Photonics Technol. Lett. 24(16), 1387–1389 (2012).
[Crossref]

Rasskazov, G.

Richardson, D. J.

Rochette, M.

Roelens, M. A.

Roelens, M. A. F.

Ryabtsev, A.

Salehiomran, A.

Sayinc, H.

Serafimovich, P. G.

Shen, H.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Shulika, O. V.

Slavik, R.

R. Slavik, L. K. Oxenlowe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azana, and P. Jeppesen, “Demultiplexing of 320-Gb/s OTDM data using ultrashort flat-top pulses,” IEEE Photonics Technol. Lett. 19(22), 1855–1857 (2007).
[Crossref]

Slavík, R.

Srinivasan, K.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Su, Y.

L. Zhang, J. Wu, X. Yin, X. Sun, P. Cao, X. Jiang, and Y. Su, “A high-speed second-order photonic differentiator based on two-stage silicon self-coupled optical waveguide,” IEEE Photonics J. 6, 1–5 (2014).
[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]

Sukhoivanov, I. A.

Sun, W. H.

Sun, X.

L. Zhang, J. Wu, X. Yin, X. Sun, P. Cao, X. Jiang, and Y. Su, “A high-speed second-order photonic differentiator based on two-stage silicon self-coupled optical waveguide,” IEEE Photonics J. 6, 1–5 (2014).
[Crossref]

Suzuki, K.

Syvridis, D.

Tan, S.

Tanizawa, K.

Turitsyn, S. K.

Varghese, L. T.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Velanas, P.

Wang, J.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Wang, T.

Wang, W. T.

Wang, W. Y.

Weiner, A. M.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

A. M. Weiner, “Ultrafast optical pulse shaping: a tutorial review,” Opt. Commun. 284(15), 3669–3692 (2011).
[Crossref]

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
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J. P. Heritage and A. M. Weiner, “Advances in spectral optical code-division multiple-access communications,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1351–1369 (2007).
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A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19(3), 161–237 (1995).
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Wetzel, B.

Williams, D. G.

Wu, J.

L. Zhang, J. Wu, X. Yin, X. Sun, P. Cao, X. Jiang, and Y. Su, “A high-speed second-order photonic differentiator based on two-stage silicon self-coupled optical waveguide,” IEEE Photonics J. 6, 1–5 (2014).
[Crossref]

Wu, Z.

Xiang, L.

L. Xiang, D. Jianji, Y. Yuan, and Z. Xinliang, “A tunable microwave photonic filter based on an all-optical differentiator,” IEEE Photonics Technol. Lett. 23(5), 308–310 (2011).
[Crossref]

Xiao, S.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
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Xinliang, Z.

L. Xiang, D. Jianji, Y. Yuan, and Z. Xinliang, “A tunable microwave photonic filter based on an all-optical differentiator,” IEEE Photonics Technol. Lett. 23(5), 308–310 (2011).
[Crossref]

Xuan, Y.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Yang, T.

Yao, J.

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

Ye, T.

Yin, X.

L. Zhang, J. Wu, X. Yin, X. Sun, P. Cao, X. Jiang, and Y. Su, “A high-speed second-order photonic differentiator based on two-stage silicon self-coupled optical waveguide,” IEEE Photonics J. 6, 1–5 (2014).
[Crossref]

Yuan, Y.

L. Xiang, D. Jianji, Y. Yuan, and Z. Xinliang, “A tunable microwave photonic filter based on an all-optical differentiator,” IEEE Photonics Technol. Lett. 23(5), 308–310 (2011).
[Crossref]

Zhang, L.

L. Zhang, J. Wu, X. Yin, X. Sun, P. Cao, X. Jiang, and Y. Su, “A high-speed second-order photonic differentiator based on two-stage silicon self-coupled optical waveguide,” IEEE Photonics J. 6, 1–5 (2014).
[Crossref]

Zhang, X.

Zhang, X. L.

Zhang, Z.

Zhao, L.

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

Zheng, A.

Zheng, A. L.

Zhu, N. H.

IEEE J. Sel. Top. Quantum Electron. (1)

J. P. Heritage and A. M. Weiner, “Advances in spectral optical code-division multiple-access communications,” IEEE J. Sel. Top. Quantum Electron. 13(5), 1351–1369 (2007).
[Crossref]

IEEE Photonics J. (2)

J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photonics J. 2(3), 359–386 (2010).
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L. Zhang, J. Wu, X. Yin, X. Sun, P. Cao, X. Jiang, and Y. Su, “A high-speed second-order photonic differentiator based on two-stage silicon self-coupled optical waveguide,” IEEE Photonics J. 6, 1–5 (2014).
[Crossref]

IEEE Photonics Technol. Lett. (3)

L. Xiang, D. Jianji, Y. Yuan, and Z. Xinliang, “A tunable microwave photonic filter based on an all-optical differentiator,” IEEE Photonics Technol. Lett. 23(5), 308–310 (2011).
[Crossref]

R. Slavik, L. K. Oxenlowe, M. Galili, H. C. H. Mulvad, Y. Park, J. Azana, and P. Jeppesen, “Demultiplexing of 320-Gb/s OTDM data using ultrashort flat-top pulses,” IEEE Photonics Technol. Lett. 19(22), 1855–1857 (2007).
[Crossref]

M. Li, P. Dumais, R. Ashrafi, H. P. Bazargani, J. Quelene, C. Callender, and J. Azana, “Ultrashort flat-top pulse generation using on-chip CMOS-compatible Mach–Zehnder interferometers,” IEEE Photonics Technol. Lett. 24(16), 1387–1389 (2012).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (1)

Nat. Photonics (3)

W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, M. Lu, L. A. Coldren, and J. Yao, “A fully reconfigurable photonic integrated signal processor,” Nat. Photonics 10(3), 190–195 (2016).
[Crossref]

M. H. Khan, H. Shen, Y. Xuan, L. Zhao, S. Xiao, D. E. Leaird, A. M. Weiner, and M. Qi, “Ultrabroad-bandwidth arbitrary radiofrequency waveform generation with a silicon photonic chip-based spectral shaper,” Nat. Photonics 4(2), 117–122 (2010).
[Crossref]

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Opt. Commun. (2)

A. M. Weiner, “Ultrafast optical pulse shaping: a tutorial review,” Opt. Commun. 284(15), 3669–3692 (2011).
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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).
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Opt. Express (12)

Y. Park, M. H. Asghari, T.-J. Ahn, and J. Azaña, “Transform-limited picosecond pulse shaping based on temporal coherence synthesization,” Opt. Express 15(15), 9584–9599 (2007).
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S. Tan, Z. Wu, L. Lei, S. Hu, J. Dong, and X. Zhang, “All-optical computation system for solving differential equations based on optical intensity differentiator,” Opt. Express 21(6), 7008–7013 (2013).
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Y. Park, M. Kulishov, R. Slavík, and J. Azaña, “Picosecond and sub-picosecond flat-top pulse generation using uniform long-period fiber gratings,” Opt. Express 14(26), 12670–12678 (2006).
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V. V. Lozovoy, G. Rasskazov, A. Ryabtsev, and M. Dantus, “Phase-only synthesis of ultrafast stretched square pulses,” Opt. Express 23(21), 27105–27112 (2015).
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M. Li, H.-S. Jeong, J. Azaña, and T.-J. Ahn, “25-terahertz-bandwidth all-optical temporal differentiator,” Opt. Express 20(27), 28273–28280 (2012).
[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).
[Crossref] [PubMed]

J. Dong, A. Zheng, D. Gao, L. Lei, D. Huang, and X. Zhang, “Compact, flexible and versatile photonic differentiator using silicon Mach-Zehnder interferometers,” Opt. Express 21(6), 7014–7024 (2013).
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S. Liao, Y. Ding, J. Dong, T. Yang, X. Chen, D. Gao, and X. Zhang, “Arbitrary waveform generator and differentiator employing an integrated optical pulse shaper,” Opt. Express 23(9), 12161–12173 (2015).
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F. Parmigiani, C. Finot, K. Mukasa, M. Ibsen, M. A. Roelens, P. Petropoulos, and D. J. Richardson, “Ultra-flat SPM-broadened spectra in a highly nonlinear fiber using parabolic pulses formed in a fiber Bragg grating,” Opt. Express 14(17), 7617–7622 (2006).
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Opt. Lett. (9)

H. P. Bazargani, M. Burla, and J. Azaña, “Experimental demonstration of sub-picosecond optical pulse shaping in silicon based on discrete space-to-time mapping,” Opt. Lett. 40(23), 5423–5426 (2015).
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Figures (12)

Fig. 1
Fig. 1 Working principle of the pulse shaper based on cascaded frequency-detuned differentiators. The green lines represent the transmission spectra of ideal differentiators and the blue arrows show the carrier wavelength of the input signal.
Fig. 2
Fig. 2 Simulation results (blue solid lines) using (a) one differentiator, (b) two differentiators or (c) three differentiators. The red dash lines represent the target pulses and green dot lines represent the weight functions. The frequency detunings are shown with blue texts.
Fig. 3
Fig. 3 Shaping errors for generating triangular, parabolic and flat-top pulses using one OD, two ODs or three ODs. The widths of triangular and parabolic pulses are defined with FWHM, while the widths of flat-top pulses refer to the durations of flat regions.
Fig. 4
Fig. 4 Shaping errors and energy efficiencies for generating triangular, parabolic and flat-top pulses using a 3rd-order shaping system with different working bandwidths.
Fig. 5
Fig. 5 Triangular pulses with FWHM of 15 ps, 30 ps and 60 ps generated respectively from the 10-ps, 20-ps and 40-ps Gaussian pulses.
Fig. 6
Fig. 6 (a) Schematic diagram and (b) micrograph of the on-chip pulse shaper based on cascaded differentiators.
Fig. 7
Fig. 7 (a) Transmission spectra of the fabricated DI (blue solid line) and an ideal differentiator (red dash line). (b) Measured transmission spectra of DI under different voltages.
Fig. 8
Fig. 8 Experimental setup of pulse shaper. TMLL: tunable mode locked laser; PC: polarization controller; EDFA: erbium-doped fiber amplifier; BPF: bandpass filter; OSA: optical spectrum analyzer; OSO: optical sampling oscilloscope; DUT: device under test.
Fig. 9
Fig. 9 Measured (a) waveform (blue solid line) and (b) spectrum of the input Gaussian pulse. The inset shows the measured waveform displayed on the OSO.
Fig. 10
Fig. 10 Measured (a-1), (b-1) waveforms (blue solid lines) compared with simulation results (red dash lines) and target pulses (green dot lines). (a-2), (b-2) Optical spectra of input signal (blue) and output signals (red), the green lines show the transmission spectra using one optical differentiator and the blue texts are the practical frequency shifts.
Fig. 11
Fig. 11 Measured (a-1)-(f-1) waveforms and (a-2)-(f-2) their corresponding spectra using two cascaded optical differentiators.
Fig. 12
Fig. 12 Measured (a-1)-(g-1) waveforms and (a-2)-(g-2) their corresponding spectra using three cascaded optical differentiators.

Equations (8)

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H ( ω ) = k = 1 N ( j a k [ ( ω ω 0 ) δ ω k ] ) = k = 1 N a k [ i = 0 N ( b i [ j ( ω ω 0 ) ] i ) ] ,
{ b N = 1 b N 1 = ( j ) m = 1 N δ ω m b N 2 = ( j ) 2 m 2 > m 1 1 N δ ω m 1 δ ω m 2 b N i = ( j ) i m i > > m 2 > m 1 1 N δ ω m 1 δ ω m 2 δ ω m i b 0 = ( j ) N m = 1 N δ ω m = ( j ) N δ ω 1 δ ω 2 δ ω N .
I c a l c ( t ) = ( k = 1 N a k ) 2 | i = 0 N ( b i i E i n ( t ) t i ) | 2 ,
I c a l c ( t ) = ( k = 1 N a k ) 2 [ | 0 2 x N ( b 2 x 2 x E i n ( t ) t 2 x ) | 2 e v e n t e r m s + | 2 2 y N + 1 ( b 2 y 1 2 y 1 E i n ( t ) t 2 y 1 ) | 2 o d d t e r m s ] .
I f l a t t o p ( t ) = { 1 , | t | ( 1 α ) T f / 2 1 4 ( 1 + cos ( π α T f ( | t | 1 α 2 T f ) ) ) 2 , 1 α 2 T f | t | 1 + α 2 T f 0 , o t h e r w i s e ,
I p a r a b o l i c ( t ) = { 1 2 ( t / T p ) 2 , | t | T p / 2 0 , o t h e r w i s e ,
I t r i a n g u l a r ( t ) = { ( 1 | t / T t | ) , | t | T t 0 , o t h e r w i s e ,
E r r o r = m | I t a r g ( t m ) I c a l c ( t m ) | 2 w ( t m ) | I t a r g ( t m ) | 2 w ( t m ) ,

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