Abstract

We propose and demonstrate an optical arbitrary waveform generator and high-order photonic differentiator based on a four-tap finite impulse response (FIR) silicon-on-insulator (SOI) on-chip circuit. Based on amplitude and phase modulation of each tap controlled by thermal heaters, we obtain several typical waveforms such as triangular waveform, sawtooth waveform, square waveform and Gaussian waveform, etc., assisted by an optical frequency comb injection. Unlike other proposed schemes, our scheme does not require a spectral disperser which is difficult to fabricate on chip with high resolution. In addition, we demonstrate first-, second- and third-order differentiators based on the optical pulse shaper. Our scheme can switch the differentiator patterns from first- to third-order freely. In addition, our scheme has distinct advantages of compactness, capability for integration with electronics.

© 2015 Optical Society of America

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References

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2014 (4)

2013 (4)

2012 (3)

2011 (5)

M. Li, L. Y. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

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

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36(17), 3398–3400 (2011).
[Crossref] [PubMed]

K. A. Rutkowska, D. Duchesne, M. J. Strain, R. Morandotti, M. Sorel, and J. Azaña, “Ultrafast all-optical temporal differentiators based on CMOS-compatible integrated-waveguide Bragg gratings,” Opt. Express 19(20), 19514–19522 (2011).
[Crossref] [PubMed]

2010 (6)

A. Vega, D. E. Leaird, and A. M. Weiner, “High-speed direct space-to-time pulse shaping with 1 ns reconfiguration,” Opt. Lett. 35(10), 1554–1556 (2010).
[Crossref] [PubMed]

C. Wang and J. Yao, “Large time-bandwidth product microwave arbitrary waveform generation using a spatially discrete chirped fiber Bragg grating,” J. Lightwave Technol. 28(11), 1652–1660 (2010).
[Crossref]

N. N. Feng, P. Dong, D. Feng, W. Qian, H. Liang, D. C. Lee, J. B. Luff, A. Agarwal, T. Banwell, R. Menendez, P. Toliver, T. K. Woodward, and M. Asghari, “Thermally-efficient reconfigurable narrowband RF-photonic filter,” Opt. Express 18(24), 24648–24653 (2010).
[Crossref] [PubMed]

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. M. Kuo, J. W. Shi, H. C. Chiang, H. P. Chuang, H. K. Chiou, C. L. Pan, N. W. Chen, H. J. Tsai, and C. B. Huang, “Spectral power enhancement in a 100 GHz photonic millimeter-wave generator enabled by spectral line-by-line pulse shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[Crossref]

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

2009 (2)

2008 (4)

R. P. Scott, N. K. Fontaine, C. Yang, D. J. Geisler, K. Okamoto, J. P. Heritage, and S. J. Yoo, “Rapid updating of optical arbitrary waveforms via time-domain multiplexing,” Opt. Lett. 33(10), 1068–1070 (2008).
[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).
[Crossref] [PubMed]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

C. Wang and J. Yao, “Photonic generation of chirped millimeter-wave pulses based on nonlinear frequency-to-time mapping in a nonlinearly chirped fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 56(2), 542–553 (2008).
[Crossref]

2007 (4)

2006 (1)

2005 (1)

A. Monsterleet, S. Tonda-Goldstein, D. Dolfi, J. Huignard, P. Sapé, and J. Chazelas, “Optically generated arbitrary waveforms for radar applications,” Electron. Lett. 41(6), 332–334 (2005).
[Crossref]

2003 (1)

2001 (1)

G. Lenz, B. Eggleton, C. K. Madsen, and R. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37(4), 525–532 (2001).
[Crossref]

1999 (1)

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11(12), 1623–1625 (1999).
[Crossref]

1993 (1)

R. A. Soref, “Silicon-based optoelectronics,” Proc. IEEE 81(12), 1687–1706 (1993).
[Crossref]

Agarwal, A.

Ahn, T. J.

Aksyuk, V.

Albert, J.

M. Li, L. Y. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

Asghari, M.

Asghari, M. H.

Ayotte, N.

Azaña, J.

Banwell, T.

Bortnik, B.

Bruce, A.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11(12), 1623–1625 (1999).
[Crossref]

Cao, J.

Cappuzzo, M.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11(12), 1623–1625 (1999).
[Crossref]

Chazelas, J.

A. Monsterleet, S. Tonda-Goldstein, D. Dolfi, J. Huignard, P. Sapé, and J. Chazelas, “Optically generated arbitrary waveforms for radar applications,” Electron. Lett. 41(6), 332–334 (2005).
[Crossref]

Chen, L.

F. Ferdous, H. Miao, P. H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express 20(19), 21033–21043 (2012).
[Crossref] [PubMed]

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, N. W.

F. M. Kuo, J. W. Shi, H. C. Chiang, H. P. Chuang, H. K. Chiou, C. L. Pan, N. W. Chen, H. J. Tsai, and C. B. Huang, “Spectral power enhancement in a 100 GHz photonic millimeter-wave generator enabled by spectral line-by-line pulse shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[Crossref]

Chen, X.

Y. Dai, X. Chen, H. Ji, and S. Xie, “Optical arbitrary waveform generation based on sampled fiber Bragg gratings,” IEEE Photon. Technol. Lett. 19(23), 1916–1918 (2007).
[Crossref]

Chiang, H. C.

F. M. Kuo, J. W. Shi, H. C. Chiang, H. P. Chuang, H. K. Chiou, C. L. Pan, N. W. Chen, H. J. Tsai, and C. B. Huang, “Spectral power enhancement in a 100 GHz photonic millimeter-wave generator enabled by spectral line-by-line pulse shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[Crossref]

Chiou, H. K.

F. M. Kuo, J. W. Shi, H. C. Chiang, H. P. Chuang, H. K. Chiou, C. L. Pan, N. W. Chen, H. J. Tsai, and C. B. Huang, “Spectral power enhancement in a 100 GHz photonic millimeter-wave generator enabled by spectral line-by-line pulse shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[Crossref]

Chou, J.

Chuang, H. P.

F. M. Kuo, J. W. Shi, H. C. Chiang, H. P. Chuang, H. K. Chiou, C. L. Pan, N. W. Chen, H. J. Tsai, and C. B. Huang, “Spectral power enhancement in a 100 GHz photonic millimeter-wave generator enabled by spectral line-by-line pulse shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[Crossref]

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

Dai, Y.

Y. Dai, X. Chen, H. Ji, and S. Xie, “Optical arbitrary waveform generation based on sampled fiber Bragg gratings,” IEEE Photon. Technol. Lett. 19(23), 1916–1918 (2007).
[Crossref]

Dezfooliyan, A.

Ding, Y.

Dolfi, D.

A. Monsterleet, S. Tonda-Goldstein, D. Dolfi, J. Huignard, P. Sapé, and J. Chazelas, “Optically generated arbitrary waveforms for radar applications,” Electron. Lett. 41(6), 332–334 (2005).
[Crossref]

Dong, J.

Dong, P.

Doucet, S.

Duchesne, D.

Eggleton, B.

G. Lenz, B. Eggleton, C. K. Madsen, and R. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37(4), 525–532 (2001).
[Crossref]

Fang, X.

Feng, D.

Feng, N. N.

Ferdous, F.

F. Ferdous, H. Miao, P. H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express 20(19), 21033–21043 (2012).
[Crossref] [PubMed]

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]

Fetterman, H. R.

Fontaine, N. K.

Gaeta, A. L.

Gao, D.

Geisler, D. J.

Gomez, L.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11(12), 1623–1625 (1999).
[Crossref]

He, T.

Heritage, J. P.

Huang, C. B.

F. M. Kuo, J. W. Shi, H. C. Chiang, H. P. Chuang, H. K. Chiou, C. L. Pan, N. W. Chen, H. J. Tsai, and C. B. Huang, “Spectral power enhancement in a 100 GHz photonic millimeter-wave generator enabled by spectral line-by-line pulse shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[Crossref]

C. B. Huang, D. E. Leaird, and A. M. Weiner, “Time-multiplexed photonically enabled radio-frequency arbitrary waveform generation with 100 ps transitions,” Opt. Lett. 32(22), 3242–3244 (2007).
[Crossref] [PubMed]

Huang, D.

Huignard, J.

A. Monsterleet, S. Tonda-Goldstein, D. Dolfi, J. Huignard, P. Sapé, and J. Chazelas, “Optically generated arbitrary waveforms for radar applications,” Electron. Lett. 41(6), 332–334 (2005).
[Crossref]

Jalali, B.

Ji, H.

Y. Dai, X. Chen, H. Ji, and S. Xie, “Optical arbitrary waveform generation based on sampled fiber Bragg gratings,” IEEE Photon. Technol. Lett. 19(23), 1916–1918 (2007).
[Crossref]

Jiang, W.

Karalar, A.

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]

Kolner, B. H.

Kuo, F. M.

F. M. Kuo, J. W. Shi, H. C. Chiang, H. P. Chuang, H. K. Chiou, C. L. Pan, N. W. Chen, H. J. Tsai, and C. B. Huang, “Spectral power enhancement in a 100 GHz photonic millimeter-wave generator enabled by spectral line-by-line pulse shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[Crossref]

LaRochelle, S.

Leaird, D. E.

F. Ferdous, H. Miao, P. H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express 20(19), 21033–21043 (2012).
[Crossref] [PubMed]

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]

A. Vega, D. E. Leaird, and A. M. Weiner, “High-speed direct space-to-time pulse shaping with 1 ns reconfiguration,” Opt. Lett. 35(10), 1554–1556 (2010).
[Crossref] [PubMed]

C. B. Huang, D. E. Leaird, and A. M. Weiner, “Time-multiplexed photonically enabled radio-frequency arbitrary waveform generation with 100 ps transitions,” Opt. Lett. 32(22), 3242–3244 (2007).
[Crossref] [PubMed]

Lee, D. C.

Lei, L.

A. Zheng, J. Dong, L. Lei, T. Yang, and X. Zhang, “Diversity of photonic differentiators based on flexible demodulation of phase signals,” Chin. Phys. B. 23(3), 033201 (2014).
[Crossref]

J. Dong, A. Zheng, D. Gao, S. Liao, L. Lei, D. Huang, and X. Zhang, “High-order photonic differentiator employing on-chip cascaded microring resonators,” Opt. Lett. 38(5), 628–630 (2013).
[Crossref] [PubMed]

J. Dong, B. Luo, Y. Zhang, L. Lei, D. Huang, and X. Zhang, “All-optical temporal differentiator using a high resolution optical arbitrary waveform shaper,” Chin. Phys. Lett. 29(1), 014203 (2012).
[Crossref]

Lenz, G.

G. Lenz, B. Eggleton, C. K. Madsen, and R. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37(4), 525–532 (2001).
[Crossref]

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11(12), 1623–1625 (1999).
[Crossref]

Levy, J. S.

Li, C.

Li, M.

M. Li, L. Y. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

Li, S.

Liang, H.

Liao, S.

Lipson, M.

Luff, J. B.

Luo, B.

J. Dong, B. Luo, Y. Zhang, L. Lei, D. Huang, and X. Zhang, “All-optical temporal differentiator using a high resolution optical arbitrary waveform shaper,” Chin. Phys. Lett. 29(1), 014203 (2012).
[Crossref]

Madsen, C.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11(12), 1623–1625 (1999).
[Crossref]

Madsen, C. K.

G. Lenz, B. Eggleton, C. K. Madsen, and R. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37(4), 525–532 (2001).
[Crossref]

Menendez, R.

Miao, H.

F. Ferdous, H. Miao, P. H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express 20(19), 21033–21043 (2012).
[Crossref] [PubMed]

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]

Monsterleet, A.

A. Monsterleet, S. Tonda-Goldstein, D. Dolfi, J. Huignard, P. Sapé, and J. Chazelas, “Optically generated arbitrary waveforms for radar applications,” Electron. Lett. 41(6), 332–334 (2005).
[Crossref]

Morandotti, R.

O’Brien, J. L.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

Okamoto, K.

Okawachi, Y.

Ou, H.

Pan, C. L.

F. M. Kuo, J. W. Shi, H. C. Chiang, H. P. Chuang, H. K. Chiou, C. L. Pan, N. W. Chen, H. J. Tsai, and C. B. Huang, “Spectral power enhancement in a 100 GHz photonic millimeter-wave generator enabled by spectral line-by-line pulse shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[Crossref]

Paraschis, L.

Park, Y.

Peucheret, C.

Poberezhskiy, I. Y.

Politi, A.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

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]

Qian, W.

Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

Rutkowska, K. A.

Saha, K.

Sapé, P.

A. Monsterleet, S. Tonda-Goldstein, D. Dolfi, J. Huignard, P. Sapé, and J. Chazelas, “Optically generated arbitrary waveforms for radar applications,” Electron. Lett. 41(6), 332–334 (2005).
[Crossref]

Scott, R. P.

Scotti, R.

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11(12), 1623–1625 (1999).
[Crossref]

Shao, L. Y.

M. Li, L. Y. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

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]

Shi, J. W.

F. M. Kuo, J. W. Shi, H. C. Chiang, H. P. Chuang, H. K. Chiou, C. L. Pan, N. W. Chen, H. J. Tsai, and C. B. Huang, “Spectral power enhancement in a 100 GHz photonic millimeter-wave generator enabled by spectral line-by-line pulse shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[Crossref]

Slavík, R.

Slusher, R.

G. Lenz, B. Eggleton, C. K. Madsen, and R. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37(4), 525–532 (2001).
[Crossref]

Soref, R. A.

R. A. Soref, “Silicon-based optoelectronics,” Proc. IEEE 81(12), 1687–1706 (1993).
[Crossref]

Sorel, M.

Srinivasan, K.

F. Ferdous, H. Miao, P. H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express 20(19), 21033–21043 (2012).
[Crossref] [PubMed]

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]

Strain, M. J.

Toliver, P.

Tonda-Goldstein, S.

A. Monsterleet, S. Tonda-Goldstein, D. Dolfi, J. Huignard, P. Sapé, and J. Chazelas, “Optically generated arbitrary waveforms for radar applications,” Electron. Lett. 41(6), 332–334 (2005).
[Crossref]

Tsai, H. J.

F. M. Kuo, J. W. Shi, H. C. Chiang, H. P. Chuang, H. K. Chiou, C. L. Pan, N. W. Chen, H. J. Tsai, and C. B. Huang, “Spectral power enhancement in a 100 GHz photonic millimeter-wave generator enabled by spectral line-by-line pulse shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[Crossref]

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]

Vega, A.

Wang, C.

C. Wang and J. Yao, “Large time-bandwidth product microwave arbitrary waveform generation using a spatially discrete chirped fiber Bragg grating,” J. Lightwave Technol. 28(11), 1652–1660 (2010).
[Crossref]

C. Wang and J. Yao, “Photonic generation of chirped millimeter-wave pulses based on nonlinear frequency-to-time mapping in a nonlinearly chirped fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 56(2), 542–553 (2008).
[Crossref]

Wang, D. N.

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, P. H.

Weiner, A. M.

A. Dezfooliyan and A. M. Weiner, “Photonic synthesis of high fidelity microwave arbitrary waveforms using near field frequency to time mapping,” Opt. Express 21(19), 22974–22987 (2013).
[Crossref] [PubMed]

F. Ferdous, H. Miao, P. H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express 20(19), 21033–21043 (2012).
[Crossref] [PubMed]

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).
[Crossref]

A. Vega, D. E. Leaird, and A. M. Weiner, “High-speed direct space-to-time pulse shaping with 1 ns reconfiguration,” Opt. Lett. 35(10), 1554–1556 (2010).
[Crossref] [PubMed]

C. B. Huang, D. E. Leaird, and A. M. Weiner, “Time-multiplexed photonically enabled radio-frequency arbitrary waveform generation with 100 ps transitions,” Opt. Lett. 32(22), 3242–3244 (2007).
[Crossref] [PubMed]

Wen, Y. H.

Woodward, T. K.

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).
[Crossref]

Xiao, X.

Xie, S.

Y. Dai, X. Chen, H. Ji, and S. Xie, “Optical arbitrary waveform generation based on sampled fiber Bragg gratings,” IEEE Photon. Technol. Lett. 19(23), 1916–1918 (2007).
[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, C.

Yang, Q.

Yang, T.

Yao, J.

M. Li, L. Y. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

C. Wang and J. Yao, “Large time-bandwidth product microwave arbitrary waveform generation using a spatially discrete chirped fiber Bragg grating,” J. Lightwave Technol. 28(11), 1652–1660 (2010).
[Crossref]

J. Yao, “Photonics for ultrawideband communications,” IEEE Microw. Mag. 10(4), 82–95 (2009).
[Crossref]

C. Wang and J. Yao, “Photonic generation of chirped millimeter-wave pulses based on nonlinear frequency-to-time mapping in a nonlinearly chirped fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 56(2), 542–553 (2008).
[Crossref]

Yoo, S. J.

Yu, S.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

Yvind, K.

Zhang, A.

Zhang, X.

Zhang, Y.

J. Dong, B. Luo, Y. Zhang, L. Lei, D. Huang, and X. Zhang, “All-optical temporal differentiator using a high resolution optical arbitrary waveform shaper,” Chin. Phys. Lett. 29(1), 014203 (2012).
[Crossref]

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.

Chin. Phys. B. (1)

A. Zheng, J. Dong, L. Lei, T. Yang, and X. Zhang, “Diversity of photonic differentiators based on flexible demodulation of phase signals,” Chin. Phys. B. 23(3), 033201 (2014).
[Crossref]

Chin. Phys. Lett. (1)

J. Dong, B. Luo, Y. Zhang, L. Lei, D. Huang, and X. Zhang, “All-optical temporal differentiator using a high resolution optical arbitrary waveform shaper,” Chin. Phys. Lett. 29(1), 014203 (2012).
[Crossref]

Electron. Lett. (1)

A. Monsterleet, S. Tonda-Goldstein, D. Dolfi, J. Huignard, P. Sapé, and J. Chazelas, “Optically generated arbitrary waveforms for radar applications,” Electron. Lett. 41(6), 332–334 (2005).
[Crossref]

IEEE J. Quantum Electron. (1)

G. Lenz, B. Eggleton, C. K. Madsen, and R. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37(4), 525–532 (2001).
[Crossref]

IEEE Microw. Mag. (1)

J. Yao, “Photonics for ultrawideband communications,” IEEE Microw. Mag. 10(4), 82–95 (2009).
[Crossref]

IEEE Photon. J. (2)

F. M. Kuo, J. W. Shi, H. C. Chiang, H. P. Chuang, H. K. Chiou, C. L. Pan, N. W. Chen, H. J. Tsai, and C. B. Huang, “Spectral power enhancement in a 100 GHz photonic millimeter-wave generator enabled by spectral line-by-line pulse shaping,” IEEE Photon. J. 2(5), 719–727 (2010).
[Crossref]

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

IEEE Photon. Technol. Lett. (3)

M. Li, L. Y. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

Y. Dai, X. Chen, H. Ji, and S. Xie, “Optical arbitrary waveform generation based on sampled fiber Bragg gratings,” IEEE Photon. Technol. Lett. 19(23), 1916–1918 (2007).
[Crossref]

C. Madsen, G. Lenz, A. Bruce, M. Cappuzzo, L. Gomez, and R. Scotti, “Integrated all-pass filters for tunable dispersion and dispersion slope compensation,” IEEE Photon. Technol. Lett. 11(12), 1623–1625 (1999).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

C. Wang and J. Yao, “Photonic generation of chirped millimeter-wave pulses based on nonlinear frequency-to-time mapping in a nonlinearly chirped fiber Bragg grating,” IEEE Trans. Microw. Theory Tech. 56(2), 542–553 (2008).
[Crossref]

J. Lightwave Technol. (2)

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

Nat. Photonics (2)

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]

Opt. Commun. (1)

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

Opt. Express (11)

A. Zhang and C. Li, “Dynamic optical arbitrary waveform generation with amplitude controlled by interference of two FBG arrays,” Opt. Express 20(21), 23074–23081 (2012).
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F. Ferdous, H. Miao, P. H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express 20(19), 21033–21043 (2012).
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D. J. Geisler, N. K. Fontaine, T. He, R. P. Scott, L. Paraschis, J. P. Heritage, and S. J. Yoo, “Modulation-format agile, reconfigurable Tb/s transmitter based on optical arbitrary waveform generation,” Opt. Express 17(18), 15911–15925 (2009).
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A. Dezfooliyan and A. M. Weiner, “Photonic synthesis of high fidelity microwave arbitrary waveforms using near field frequency to time mapping,” Opt. Express 21(19), 22974–22987 (2013).
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S. Liao, Y. Ding, C. Peucheret, T. Yang, J. Dong, and X. Zhang, “Integrated programmable photonic filter on the silicon-on-insulator platform,” Opt. Express 22(26), 31993–31998 (2014).
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A. Zheng, T. Yang, X. Xiao, Q. Yang, X. Zhang, and J. Dong, “Tunable fractional-order differentiator using an electrically tuned silicon-on-isolator Mach-Zehnder interferometer,” Opt. Express 22(15), 18232–18237 (2014).
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K. A. Rutkowska, D. Duchesne, M. J. Strain, R. Morandotti, M. Sorel, and J. Azaña, “Ultrafast all-optical temporal differentiators based on CMOS-compatible integrated-waveguide Bragg gratings,” Opt. Express 19(20), 19514–19522 (2011).
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Opt. Lett. (8)

Y. Ding, H. Ou, and C. Peucheret, “Ultrahigh-efficiency apodized grating coupler using fully etched photonic crystals,” Opt. Lett. 38(15), 2732–2734 (2013).
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J. Dong, A. Zheng, D. Gao, S. Liao, L. Lei, D. Huang, and X. Zhang, “High-order photonic differentiator employing on-chip cascaded microring resonators,” Opt. Lett. 38(5), 628–630 (2013).
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Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36(17), 3398–3400 (2011).
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A. Vega, D. E. Leaird, and A. M. Weiner, “High-speed direct space-to-time pulse shaping with 1 ns reconfiguration,” Opt. Lett. 35(10), 1554–1556 (2010).
[Crossref] [PubMed]

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. Yoo, “32 phase× 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 (2007).
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W. Jiang, F. M. Soares, S. W. Seo, J. H. Baek, N. K. Fontaine, R. G. Broeke, J. Cao, J. Yan, K. Okamoto, and F. Olsson, “A monolithic InP-based photonic integrated circuit for optical arbitrary waveform generation, ” in National Fiber Optic Engineers Conference (Optical Society of America, 2008), p. JThA39.
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Figures (14)

Fig. 1
Fig. 1 Schematic diagram of the proposed on-chip pulse shaper.
Fig. 2
Fig. 2 Simulated waveforms (red solid line) of the pulse shaper and the ideal ones (blue dash line) of (a) square waveform (the amplitude array and phase array are [0.93, 1, 1, 0.94] and [0.305π, 0.013π, −0.015π, 0.23π], respectively), (b) isosceles triangular waveform (the amplitude array and phase array are [0.69, 1, 0.75, 0.114] and [-0.05π, −0.4π, −0.1π, −0.1π], respectively), (c) and (d) sawtooth waveforms (the amplitude array and phase array are [0.15, 0.46, 0.77, 1], [0.5π, −0.1π, −0.3π, 0.09π] and [1, 0.77, 0.46, 0.15], [0.09π, −0.3π, −0.1π, 0.5π], respectively), (e) and (f) Gaussian waveforms (the amplitude array and phase array are [0.2, 1, 0.5, 0], [0, 0, 0, 0] and [0.65, 1, 0.65, 0], [0.1π, 0, 0, 0], respectively).
Fig. 3
Fig. 3 Metallurgical microscopy image of the on-chip pulse shaper.
Fig. 4
Fig. 4 Experimental setup of the arbitrary waveform generation with employing the on-chip pulse shaper.
Fig. 5
Fig. 5 (a) Measured spectra of OFC (blue solid line) and input signal (red solid line), (b) measured waveforms of OFC (blue solid line) and input signal (red solid line).
Fig. 6
Fig. 6 Measured waveforms (blue solid line) of the pulse shaper and ideal ones (red dash line) of (a) square waveform, (b) isosceles triangular waveform, (c) and (d) sawtooth waveform, (e) and (f) Gaussian waveform, (g), (h) and (i) oblique triangular waveform, (j) flat-top waveform.
Fig. 7
Fig. 7 Measured spectra of input optical frequency comb and output waveforms of (a) square waveform, (b) isosceles triangular waveform, (c) and (d) sawtooth waveform, (e) and (f) Gaussian waveform, (g), (h) and (i) oblique triangular waveform, (j) flat-top waveform.
Fig. 8
Fig. 8 Simulated amplitude-frequency responses/ phase-frequency responses (blue solid line) of the pulse shaper and the ideal ones (red dash line) of different order differentiators, (a1) and (a2) amplitude-frequency and phase-frequency responses of first-order differentiator (the amplitude array and phase array are [0.0675, 1, 0.028, 1] and [-π, -π, π, −0.15π], respectively), (b1) and (b2) amplitude-frequency and phase-frequency responses of second-order differentiator (the amplitude array and phase array are [0.38, 0.746, 1, 0.38] and [-0.075π, 0.13π, 0.06π, −0.025π], respectively), (c1) and (c2) amplitude-frequency and phase-frequency responses of third-order differentiator (the amplitude array and phase array are [0.18, 0.624, 1, 0.48] and [0.04π, 0.08π, 0.01π, −0.03π], respectively).
Fig. 9
Fig. 9 Measured and ideal spectra of (a) first-, (b) second-, and (c) third-order differentiators.
Fig. 10
Fig. 10 Measured spectra of input pulse and output differentiation signals of (a) first-order, (b) second order, and (c) third-order.
Fig. 11
Fig. 11 Experimental results for different order differentiations, (a) input pulse, (b)-(d) temporal waveforms for first-, second- and third-order differentiations, respectively.
Fig. 12
Fig. 12 Output pulse broadening with the pulsewidth of the input signal.
Fig. 13
Fig. 13 Experimental setup of the different order differentiators with broader input pulse.
Fig. 14
Fig. 14 Experimental results for different order differentiations of broader input pulse, (a) input pulse, (b)-(d) temporal waveforms for first-, second- and third-order differentiations, respectively.

Equations (1)

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H 0 ( ω )= n=1 4 α n e j( nωτ+ ϕ n )

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