Abstract

We demonstrate a tunable temporal photonic fractional-order differentiator based on a Mach–Zenhder interferometer (MZI) coupled microring. An MZI structure is designed to replace conventional coupling structure of straight waveguide and ring waveguide. When the refractive index of one arm of the MZI is adjusted by thermo-optic effect, the coupling coefficient between the straight waveguide and the microring can be changed and a tunable photonic differentiator is implemented. In the experiment, the device presents a tunable differentiation order range from 0.25 to 1.75, which is the largest tuning range of a tunable photonic differentiator using a single microring resonator to the best of our knowledge.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref] [PubMed]

2017 (2)

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photonics 2(9), 096104 (2017).
[Crossref]

W. Liu, W. Zhang, and J. Yao, “Silicon-Based Integrated Tunable Fractional Order Photonic Temporal Differentiators,” J. Lightwave Technol. 35(12), 2487– 2493 (2017).

2016 (2)

L. Poveda-Wong, A. Carrascosa, C. Cuadrado-Laborde, J. L. Cruz, and M. V. Andrés, “Experimental demonstration of fractional order differentiation using a long-period grating-based in-fiber modal interferometer,” Opt. Commun. 380, 35–40 (2016).
[Crossref]

T. Yang, S. Liao, L. Liu, and J. Dong, “Large-range tunable fractional-order differentiator based on cascaded microring resonators,” Front. Optoelectron. 9(3), 1–7 (2016).
[Crossref]

2015 (5)

2014 (3)

2013 (3)

2012 (2)

Y. Hu, L. Zhang, X. Xiao, Z. Li, Y. Li, T. Chu, Y. Su, Y. Yu, and J. Yu, “An ultra-high-speed photonic temporal differentiator using cascaded SOI microring resonators,” J. Opt. 14(6), 065501 (2012).
[Crossref]

H. Shahoei, J. Albert, and J. Yao, “Fractional Order Temporal Differentiator by Optically Pumping a Tilted Fiber Bragg Grating,” IEEE Photonics Technol. Lett. 24(9), 730–732 (2012).
[Crossref]

2011 (2)

J. Dong, B. Luo, Y. Zhang, D. Huang, and X. Zhang, “Reconfigurable photonic differentiators based on all-optical phase modulation and linear filtering,” Opt. Commun. 284(24), 5792–5797 (2011).
[Crossref]

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

2010 (2)

H. Shen, M. H. Khan, L. Fan, L. Zhao, Y. Xuan, J. Ouyang, L. T. Varghese, and M. Qi, “Eight-channel reconfigurable microring filters with tunable frequency, extinction ratio and bandwidth,” Opt. Express 18(17), 18067–18076 (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]

2009 (2)

2008 (2)

2007 (5)

2006 (1)

2005 (1)

J. Azaña and M. Kulishov, “All-fibre ultrafast optical differentiator based on π phase-shifted long-period grating,” Electron. Lett. 41(25), 1368–1369 (2005).
[Crossref]

2004 (1)

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

Albert, J.

H. Shahoei, J. Albert, and J. Yao, “Fractional Order Temporal Differentiator by Optically Pumping a Tilted Fiber Bragg Grating,” IEEE Photonics Technol. Lett. 24(9), 730–732 (2012).
[Crossref]

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

Andrés, M. V.

L. Poveda-Wong, A. Carrascosa, C. Cuadrado-Laborde, J. L. Cruz, and M. V. Andrés, “Experimental demonstration of fractional order differentiation using a long-period grating-based in-fiber modal interferometer,” Opt. Commun. 380, 35–40 (2016).
[Crossref]

C. Cuadrado-Laborde and M. V. Andrés, “In-fiber all-optical fractional differentiator,” Opt. Lett. 34(6), 833–835 (2009).
[Crossref] [PubMed]

Azaña, J.

Berger, N. K.

Cao, P.

Carrascosa, A.

L. Poveda-Wong, A. Carrascosa, C. Cuadrado-Laborde, J. L. Cruz, and M. V. Andrés, “Experimental demonstration of fractional order differentiation using a long-period grating-based in-fiber modal interferometer,” Opt. Commun. 380, 35–40 (2016).
[Crossref]

Chen, J.

Chen, L.

Chu, S. T.

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photonics 2(9), 096104 (2017).
[Crossref]

Chu, T.

Y. Hu, L. Zhang, X. Xiao, Z. Li, Y. Li, T. Chu, Y. Su, Y. Yu, and J. Yu, “An ultra-high-speed photonic temporal differentiator using cascaded SOI microring resonators,” J. Opt. 14(6), 065501 (2012).
[Crossref]

Cruz, J. L.

L. Poveda-Wong, A. Carrascosa, C. Cuadrado-Laborde, J. L. Cruz, and M. V. Andrés, “Experimental demonstration of fractional order differentiation using a long-period grating-based in-fiber modal interferometer,” Opt. Commun. 380, 35–40 (2016).
[Crossref]

Cuadrado-Laborde, C.

L. Poveda-Wong, A. Carrascosa, C. Cuadrado-Laborde, J. L. Cruz, and M. V. Andrés, “Experimental demonstration of fractional order differentiation using a long-period grating-based in-fiber modal interferometer,” Opt. Commun. 380, 35–40 (2016).
[Crossref]

C. Cuadrado-Laborde and M. V. Andrés, “In-fiber all-optical fractional differentiator,” Opt. Lett. 34(6), 833–835 (2009).
[Crossref] [PubMed]

C. Cuadrado-Laborde, “All-optical ultrafast fractional differentiator,” Opt. Quantum Electron. 40(13), 983–990 (2008).
[Crossref]

da Silva, J. A. N.

J. A. N. da Silva and M. L. R. de Campos, “Spectrally efficient UWB pulse shaping with application in orthogonal PSM,” IEEE Trans. Commun. 55(2), 313–322 (2007).
[Crossref]

de Campos, M. L. R.

J. A. N. da Silva and M. L. R. de Campos, “Spectrally efficient UWB pulse shaping with application in orthogonal PSM,” IEEE Trans. Commun. 55(2), 313–322 (2007).
[Crossref]

Dong, J.

T. Yang, S. Liao, L. Liu, and J. Dong, “Large-range tunable fractional-order differentiator based on cascaded microring resonators,” Front. Optoelectron. 9(3), 1–7 (2016).
[Crossref]

S. Yan, Y. Zhang, J. Dong, A. Zheng, S. Liao, H. Zhou, Z. Wu, J. Xia, and X. Zhang, “Operation bandwidth optimization of photonic differentiators,” Opt. Express 23(15), 18925–18936 (2015).
[Crossref] [PubMed]

A. Zheng, J. Dong, L. Zhou, X. Xiao, Q. Yang, X. Zhang, and J. Chen, “Fractional-order photonic differentiator using an on-chip microring resonator,” Opt. Lett. 39(21), 6355–6358 (2014).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

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, 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).
[Crossref] [PubMed]

J. Dong, B. Luo, Y. Zhang, D. Huang, and X. Zhang, “Reconfigurable photonic differentiators based on all-optical phase modulation and linear filtering,” Opt. Commun. 284(24), 5792–5797 (2011).
[Crossref]

J. Xu, X. Zhang, J. Dong, D. Liu, and D. Huang, “High-speed all-optical differentiator based on a semiconductor optical amplifier and an optical filter,” Opt. Lett. 32(13), 1872–1874 (2007).
[Crossref] [PubMed]

Dong, J. J.

Fan, L.

Farrell, G.

Fischer, B.

Gao, D.

Gao, D. S.

Hu, X.

Hu, Y.

Y. Hu, L. Zhang, X. Xiao, Z. Li, Y. Li, T. Chu, Y. Su, Y. Yu, and J. Yu, “An ultra-high-speed photonic temporal differentiator using cascaded SOI microring resonators,” J. Opt. 14(6), 065501 (2012).
[Crossref]

Huang, D.

Huang, T. L.

Jiang, X.

Jin, B.

B. Jin, J. Yuan, K. Wang, X. Sang, B. Yan, Q. Wu, F. Li, X. Zhou, G. Zhou, C. Yu, C. Lu, H. Yaw Tam, and P. K. A. Wai, “A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators,” Sci. Rep. 5(1), 14216 (2015).
[Crossref] [PubMed]

B. Jin, J. Yuan, C. Yu, X. Sang, Q. Wu, F. Li, K. Wang, B. Yan, G. Farrell, and P. K. A. Wai, “Tunable fractional-order photonic differentiator based on the inverse Raman scattering in a silicon microring resonator,” Opt. Express 23(9), 11141–11151 (2015).
[Crossref] [PubMed]

Kam, C.

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

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]

H. Shen, M. H. Khan, L. Fan, L. Zhao, Y. Xuan, J. Ouyang, L. T. Varghese, and M. Qi, “Eight-channel reconfigurable microring filters with tunable frequency, extinction ratio and bandwidth,” Opt. Express 18(17), 18067–18076 (2010).
[Crossref] [PubMed]

Kulishov, M.

Leaird, D. E.

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.

Levit, B.

Li, F.

Li, M.

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

Li, W.

Li, Y.

Y. Hu, L. Zhang, X. Xiao, Z. Li, Y. Li, T. Chu, Y. Su, Y. Yu, and J. Yu, “An ultra-high-speed photonic temporal differentiator using cascaded SOI microring resonators,” J. Opt. 14(6), 065501 (2012).
[Crossref]

Li, Z.

Y. Hu, L. Zhang, X. Xiao, Z. Li, Y. Li, T. Chu, Y. Su, Y. Yu, and J. Yu, “An ultra-high-speed photonic temporal differentiator using cascaded SOI microring resonators,” J. Opt. 14(6), 065501 (2012).
[Crossref]

Z. Li and C. Wu, “All-optical differentiator and high-speed pulse generation based on cross-polarization modulation in a semiconductor optical amplifier,” Opt. Lett. 34(6), 830–832 (2009).
[Crossref] [PubMed]

Liao, S.

Lipson, M.

Little, B. E.

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photonics 2(9), 096104 (2017).
[Crossref]

Liu, D.

Liu, F.

Liu, L.

T. Yang, S. Liao, L. Liu, and J. Dong, “Large-range tunable fractional-order differentiator based on cascaded microring resonators,” Front. Optoelectron. 9(3), 1–7 (2016).
[Crossref]

Liu, W.

Lu, C.

B. Jin, J. Yuan, K. Wang, X. Sang, B. Yan, Q. Wu, F. Li, X. Zhou, G. Zhou, C. Yu, C. Lu, H. Yaw Tam, and P. K. A. Wai, “A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators,” Sci. Rep. 5(1), 14216 (2015).
[Crossref] [PubMed]

Luo, B.

J. Dong, B. Luo, Y. Zhang, D. Huang, and X. Zhang, “Reconfigurable photonic differentiators based on all-optical phase modulation and linear filtering,” Opt. Commun. 284(24), 5792–5797 (2011).
[Crossref]

Mitchell, A.

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photonics 2(9), 096104 (2017).
[Crossref]

Morandotti, R.

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photonics 2(9), 096104 (2017).
[Crossref]

Moss, D. J.

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photonics 2(9), 096104 (2017).
[Crossref]

Ngo, N.

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

Nguyen, T. G.

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photonics 2(9), 096104 (2017).
[Crossref]

Ouyang, J.

Pan, T.

Park, Y.

Plant, D. V.

Poveda-Wong, L.

L. Poveda-Wong, A. Carrascosa, C. Cuadrado-Laborde, J. L. Cruz, and M. V. Andrés, “Experimental demonstration of fractional order differentiation using a long-period grating-based in-fiber modal interferometer,” Opt. Commun. 380, 35–40 (2016).
[Crossref]

Qi, M.

H. Shen, M. H. Khan, L. Fan, L. Zhao, Y. Xuan, J. Ouyang, L. T. Varghese, and M. Qi, “Eight-channel reconfigurable microring filters with tunable frequency, extinction ratio and bandwidth,” Opt. Express 18(17), 18067–18076 (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]

Qiang, L.

Qiu, C.

Qiu, M.

Sang, X.

B. Jin, J. Yuan, K. Wang, X. Sang, B. Yan, Q. Wu, F. Li, X. Zhou, G. Zhou, C. Yu, C. Lu, H. Yaw Tam, and P. K. A. Wai, “A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators,” Sci. Rep. 5(1), 14216 (2015).
[Crossref] [PubMed]

B. Jin, J. Yuan, C. Yu, X. Sang, Q. Wu, F. Li, K. Wang, B. Yan, G. Farrell, and P. K. A. Wai, “Tunable fractional-order photonic differentiator based on the inverse Raman scattering in a silicon microring resonator,” Opt. Express 23(9), 11141–11151 (2015).
[Crossref] [PubMed]

Schmid, J. H.

H. Shahoei, D. Xu, J. H. Schmid, and J. Yao, “Photonic Fractional-Order Differentiator Using an SOI Microring Resonator With an MMI Coupler,” IEEE Photonics Technol. Lett. 25(15), 1408–1411 (2013).
[Crossref]

Shahoei, H.

W. Zhang, W. Liu, W. Li, H. Shahoei, and J. Yao, “Independently Tunable Multichannel Fractional-Order Temporal Differentiator Based on a Silicon-Photonic Symmetric Mach–Zehnder Interferometer Incorporating Cascaded Microring Resonators,” J. Lightwave Technol. 33(2), 361–367 (2015).
[Crossref]

H. Shahoei, D. Xu, J. H. Schmid, and J. Yao, “Photonic Fractional-Order Differentiator Using an SOI Microring Resonator With an MMI Coupler,” IEEE Photonics Technol. Lett. 25(15), 1408–1411 (2013).
[Crossref]

H. Shahoei, J. Albert, and J. Yao, “Fractional Order Temporal Differentiator by Optically Pumping a Tilted Fiber Bragg Grating,” IEEE Photonics Technol. Lett. 24(9), 730–732 (2012).
[Crossref]

Shao, L.

M. Li, L. Shao, J. Albert, and J. Yao, “Continuously tunable photonic fractional temporal differentiator based on tilted fiber Bragg grating,” IEEE Photonics 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]

H. Shen, M. H. Khan, L. Fan, L. Zhao, Y. Xuan, J. Ouyang, L. T. Varghese, and M. Qi, “Eight-channel reconfigurable microring filters with tunable frequency, extinction ratio and bandwidth,” Opt. Express 18(17), 18067–18076 (2010).
[Crossref] [PubMed]

Sherwood-Droz, N.

Shoeiby, M.

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photonics 2(9), 096104 (2017).
[Crossref]

Slavík, R.

Su, Y.

Tjin, S.

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

Tremblay, C.

Varghese, L. T.

Wai, P. K. A.

B. Jin, J. Yuan, K. Wang, X. Sang, B. Yan, Q. Wu, F. Li, X. Zhou, G. Zhou, C. Yu, C. Lu, H. Yaw Tam, and P. K. A. Wai, “A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators,” Sci. Rep. 5(1), 14216 (2015).
[Crossref] [PubMed]

B. Jin, J. Yuan, C. Yu, X. Sang, Q. Wu, F. Li, K. Wang, B. Yan, G. Farrell, and P. K. A. Wai, “Tunable fractional-order photonic differentiator based on the inverse Raman scattering in a silicon microring resonator,” Opt. Express 23(9), 11141–11151 (2015).
[Crossref] [PubMed]

Wang, K.

B. Jin, J. Yuan, C. Yu, X. Sang, Q. Wu, F. Li, K. Wang, B. Yan, G. Farrell, and P. K. A. Wai, “Tunable fractional-order photonic differentiator based on the inverse Raman scattering in a silicon microring resonator,” Opt. Express 23(9), 11141–11151 (2015).
[Crossref] [PubMed]

B. Jin, J. Yuan, K. Wang, X. Sang, B. Yan, Q. Wu, F. Li, X. Zhou, G. Zhou, C. Yu, C. Lu, H. Yaw Tam, and P. K. A. Wai, “A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators,” Sci. Rep. 5(1), 14216 (2015).
[Crossref] [PubMed]

Wang, T.

Weiner, A. 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]

Wu, C.

Wu, J.

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photonics 2(9), 096104 (2017).
[Crossref]

J. Wu, P. Cao, X. Hu, X. Jiang, T. Pan, Y. Yang, C. Qiu, C. Tremblay, and Y. Su, “Compact tunable silicon photonic differential-equation solver for general linear time-invariant systems,” Opt. Express 22(21), 26254–26264 (2014).
[Crossref] [PubMed]

Wu, Q.

B. Jin, J. Yuan, K. Wang, X. Sang, B. Yan, Q. Wu, F. Li, X. Zhou, G. Zhou, C. Yu, C. Lu, H. Yaw Tam, and P. K. A. Wai, “A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators,” Sci. Rep. 5(1), 14216 (2015).
[Crossref] [PubMed]

B. Jin, J. Yuan, C. Yu, X. Sang, Q. Wu, F. Li, K. Wang, B. Yan, G. Farrell, and P. K. A. Wai, “Tunable fractional-order photonic differentiator based on the inverse Raman scattering in a silicon microring resonator,” Opt. Express 23(9), 11141–11151 (2015).
[Crossref] [PubMed]

Wu, Z.

Xia, J.

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.

Xu, D.

H. Shahoei, D. Xu, J. H. Schmid, and J. Yao, “Photonic Fractional-Order Differentiator Using an SOI Microring Resonator With an MMI Coupler,” IEEE Photonics Technol. Lett. 25(15), 1408–1411 (2013).
[Crossref]

Xu, J.

Xu, X.

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photonics 2(9), 096104 (2017).
[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]

H. Shen, M. H. Khan, L. Fan, L. Zhao, Y. Xuan, J. Ouyang, L. T. Varghese, and M. Qi, “Eight-channel reconfigurable microring filters with tunable frequency, extinction ratio and bandwidth,” Opt. Express 18(17), 18067–18076 (2010).
[Crossref] [PubMed]

Yan, B.

B. Jin, J. Yuan, K. Wang, X. Sang, B. Yan, Q. Wu, F. Li, X. Zhou, G. Zhou, C. Yu, C. Lu, H. Yaw Tam, and P. K. A. Wai, “A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators,” Sci. Rep. 5(1), 14216 (2015).
[Crossref] [PubMed]

B. Jin, J. Yuan, C. Yu, X. Sang, Q. Wu, F. Li, K. Wang, B. Yan, G. Farrell, and P. K. A. Wai, “Tunable fractional-order photonic differentiator based on the inverse Raman scattering in a silicon microring resonator,” Opt. Express 23(9), 11141–11151 (2015).
[Crossref] [PubMed]

Yan, S.

Yang, Q.

Yang, T.

T. Yang, S. Liao, L. Liu, and J. Dong, “Large-range tunable fractional-order differentiator based on cascaded microring resonators,” Front. Optoelectron. 9(3), 1–7 (2016).
[Crossref]

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).
[Crossref] [PubMed]

Yang, Y.

Yao, J.

W. Liu, W. Zhang, and J. Yao, “Silicon-Based Integrated Tunable Fractional Order Photonic Temporal Differentiators,” J. Lightwave Technol. 35(12), 2487– 2493 (2017).

W. Zhang, W. Liu, W. Li, H. Shahoei, and J. Yao, “Independently Tunable Multichannel Fractional-Order Temporal Differentiator Based on a Silicon-Photonic Symmetric Mach–Zehnder Interferometer Incorporating Cascaded Microring Resonators,” J. Lightwave Technol. 33(2), 361–367 (2015).
[Crossref]

H. Shahoei, D. Xu, J. H. Schmid, and J. Yao, “Photonic Fractional-Order Differentiator Using an SOI Microring Resonator With an MMI Coupler,” IEEE Photonics Technol. Lett. 25(15), 1408–1411 (2013).
[Crossref]

H. Shahoei, J. Albert, and J. Yao, “Fractional Order Temporal Differentiator by Optically Pumping a Tilted Fiber Bragg Grating,” IEEE Photonics Technol. Lett. 24(9), 730–732 (2012).
[Crossref]

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

Yaw Tam, H.

B. Jin, J. Yuan, K. Wang, X. Sang, B. Yan, Q. Wu, F. Li, X. Zhou, G. Zhou, C. Yu, C. Lu, H. Yaw Tam, and P. K. A. Wai, “A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators,” Sci. Rep. 5(1), 14216 (2015).
[Crossref] [PubMed]

Ye, T.

Yu, C.

B. Jin, J. Yuan, K. Wang, X. Sang, B. Yan, Q. Wu, F. Li, X. Zhou, G. Zhou, C. Yu, C. Lu, H. Yaw Tam, and P. K. A. Wai, “A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators,” Sci. Rep. 5(1), 14216 (2015).
[Crossref] [PubMed]

B. Jin, J. Yuan, C. Yu, X. Sang, Q. Wu, F. Li, K. Wang, B. Yan, G. Farrell, and P. K. A. Wai, “Tunable fractional-order photonic differentiator based on the inverse Raman scattering in a silicon microring resonator,” Opt. Express 23(9), 11141–11151 (2015).
[Crossref] [PubMed]

Yu, J.

Y. Hu, L. Zhang, X. Xiao, Z. Li, Y. Li, T. Chu, Y. Su, Y. Yu, and J. Yu, “An ultra-high-speed photonic temporal differentiator using cascaded SOI microring resonators,” J. Opt. 14(6), 065501 (2012).
[Crossref]

Yu, S.

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

Yu, Y.

Y. Hu, L. Zhang, X. Xiao, Z. Li, Y. Li, T. Chu, Y. Su, Y. Yu, and J. Yu, “An ultra-high-speed photonic temporal differentiator using cascaded SOI microring resonators,” J. Opt. 14(6), 065501 (2012).
[Crossref]

Yuan, J.

B. Jin, J. Yuan, K. Wang, X. Sang, B. Yan, Q. Wu, F. Li, X. Zhou, G. Zhou, C. Yu, C. Lu, H. Yaw Tam, and P. K. A. Wai, “A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators,” Sci. Rep. 5(1), 14216 (2015).
[Crossref] [PubMed]

B. Jin, J. Yuan, C. Yu, X. Sang, Q. Wu, F. Li, K. Wang, B. Yan, G. Farrell, and P. K. A. Wai, “Tunable fractional-order photonic differentiator based on the inverse Raman scattering in a silicon microring resonator,” Opt. Express 23(9), 11141–11151 (2015).
[Crossref] [PubMed]

Zhang, L.

Y. Hu, L. Zhang, X. Xiao, Z. Li, Y. Li, T. Chu, Y. Su, Y. Yu, and J. Yu, “An ultra-high-speed photonic temporal differentiator using cascaded SOI microring resonators,” J. Opt. 14(6), 065501 (2012).
[Crossref]

Zhang, W.

Zhang, X.

S. Yan, Y. Zhang, J. Dong, A. Zheng, S. Liao, H. Zhou, Z. Wu, J. Xia, and X. Zhang, “Operation bandwidth optimization of photonic differentiators,” Opt. Express 23(15), 18925–18936 (2015).
[Crossref] [PubMed]

A. Zheng, J. Dong, L. Zhou, X. Xiao, Q. Yang, X. Zhang, and J. Chen, “Fractional-order photonic differentiator using an on-chip microring resonator,” Opt. Lett. 39(21), 6355–6358 (2014).
[Crossref] [PubMed]

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).
[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).
[Crossref] [PubMed]

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, D. Huang, and X. Zhang, “Reconfigurable photonic differentiators based on all-optical phase modulation and linear filtering,” Opt. Commun. 284(24), 5792–5797 (2011).
[Crossref]

J. Xu, X. Zhang, J. Dong, D. Liu, and D. Huang, “High-speed all-optical differentiator based on a semiconductor optical amplifier and an optical filter,” Opt. Lett. 32(13), 1872–1874 (2007).
[Crossref] [PubMed]

Zhang, X. L.

Zhang, Y.

S. Yan, Y. Zhang, J. Dong, A. Zheng, S. Liao, H. Zhou, Z. Wu, J. Xia, and X. Zhang, “Operation bandwidth optimization of photonic differentiators,” Opt. Express 23(15), 18925–18936 (2015).
[Crossref] [PubMed]

J. Dong, B. Luo, Y. Zhang, D. Huang, and X. Zhang, “Reconfigurable photonic differentiators based on all-optical phase modulation and linear filtering,” Opt. Commun. 284(24), 5792–5797 (2011).
[Crossref]

Zhang, Z.

Zhao, L.

H. Shen, M. H. Khan, L. Fan, L. Zhao, Y. Xuan, J. Ouyang, L. T. Varghese, and M. Qi, “Eight-channel reconfigurable microring filters with tunable frequency, extinction ratio and bandwidth,” Opt. Express 18(17), 18067–18076 (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]

Zheng, A.

Zheng, A. L.

Zhou, G.

B. Jin, J. Yuan, K. Wang, X. Sang, B. Yan, Q. Wu, F. Li, X. Zhou, G. Zhou, C. Yu, C. Lu, H. Yaw Tam, and P. K. A. Wai, “A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators,” Sci. Rep. 5(1), 14216 (2015).
[Crossref] [PubMed]

Zhou, H.

Zhou, L.

Zhou, X.

B. Jin, J. Yuan, K. Wang, X. Sang, B. Yan, Q. Wu, F. Li, X. Zhou, G. Zhou, C. Yu, C. Lu, H. Yaw Tam, and P. K. A. Wai, “A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators,” Sci. Rep. 5(1), 14216 (2015).
[Crossref] [PubMed]

APL Photonics (1)

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photonics 2(9), 096104 (2017).
[Crossref]

Electron. Lett. (1)

J. Azaña and M. Kulishov, “All-fibre ultrafast optical differentiator based on π phase-shifted long-period grating,” Electron. Lett. 41(25), 1368–1369 (2005).
[Crossref]

Front. Optoelectron. (1)

T. Yang, S. Liao, L. Liu, and J. Dong, “Large-range tunable fractional-order differentiator based on cascaded microring resonators,” Front. Optoelectron. 9(3), 1–7 (2016).
[Crossref]

IEEE Photonics Technol. Lett. (3)

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

H. Shahoei, J. Albert, and J. Yao, “Fractional Order Temporal Differentiator by Optically Pumping a Tilted Fiber Bragg Grating,” IEEE Photonics Technol. Lett. 24(9), 730–732 (2012).
[Crossref]

H. Shahoei, D. Xu, J. H. Schmid, and J. Yao, “Photonic Fractional-Order Differentiator Using an SOI Microring Resonator With an MMI Coupler,” IEEE Photonics Technol. Lett. 25(15), 1408–1411 (2013).
[Crossref]

IEEE Trans. Commun. (1)

J. A. N. da Silva and M. L. R. de Campos, “Spectrally efficient UWB pulse shaping with application in orthogonal PSM,” IEEE Trans. Commun. 55(2), 313–322 (2007).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. (1)

Y. Hu, L. Zhang, X. Xiao, Z. Li, Y. Li, T. Chu, Y. Su, Y. Yu, and J. Yu, “An ultra-high-speed photonic temporal differentiator using cascaded SOI microring resonators,” J. Opt. 14(6), 065501 (2012).
[Crossref]

Nat. Photonics (1)

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. (3)

J. Dong, B. Luo, Y. Zhang, D. Huang, and X. Zhang, “Reconfigurable photonic differentiators based on all-optical phase modulation and linear filtering,” Opt. Commun. 284(24), 5792–5797 (2011).
[Crossref]

L. Poveda-Wong, A. Carrascosa, C. Cuadrado-Laborde, J. L. Cruz, and M. V. Andrés, “Experimental demonstration of fractional order differentiation using a long-period grating-based in-fiber modal interferometer,” Opt. Commun. 380, 35–40 (2016).
[Crossref]

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

Opt. Express (9)

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]

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]

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]

S. Yan, Y. Zhang, J. Dong, A. Zheng, S. Liao, H. Zhou, Z. Wu, J. Xia, and X. Zhang, “Operation bandwidth optimization of photonic differentiators,” Opt. Express 23(15), 18925–18936 (2015).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

J. Wu, P. Cao, X. Hu, X. Jiang, T. Pan, Y. Yang, C. Qiu, C. Tremblay, and Y. Su, “Compact tunable silicon photonic differential-equation solver for general linear time-invariant systems,” Opt. Express 22(21), 26254–26264 (2014).
[Crossref] [PubMed]

H. Shen, M. H. Khan, L. Fan, L. Zhao, Y. Xuan, J. Ouyang, L. T. Varghese, and M. Qi, “Eight-channel reconfigurable microring filters with tunable frequency, extinction ratio and bandwidth,” Opt. Express 18(17), 18067–18076 (2010).
[Crossref] [PubMed]

B. Jin, J. Yuan, C. Yu, X. Sang, Q. Wu, F. Li, K. Wang, B. Yan, G. Farrell, and P. K. A. Wai, “Tunable fractional-order photonic differentiator based on the inverse Raman scattering in a silicon microring resonator,” Opt. Express 23(9), 11141–11151 (2015).
[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).
[Crossref] [PubMed]

Opt. Lett. (8)

C. Cuadrado-Laborde and M. V. Andrés, “In-fiber all-optical fractional differentiator,” Opt. Lett. 34(6), 833–835 (2009).
[Crossref] [PubMed]

L. Chen, N. Sherwood-Droz, and M. Lipson, “Compact bandwidth-tunable microring resonators,” Opt. Lett. 32(22), 3361–3363 (2007).
[Crossref] [PubMed]

Z. Li and C. Wu, “All-optical differentiator and high-speed pulse generation based on cross-polarization modulation in a semiconductor optical amplifier,” Opt. Lett. 34(6), 830–832 (2009).
[Crossref] [PubMed]

J. Xu, X. Zhang, J. Dong, D. Liu, and D. Huang, “High-speed all-optical differentiator based on a semiconductor optical amplifier and an optical filter,” Opt. Lett. 32(13), 1872–1874 (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]

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]

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]

A. Zheng, J. Dong, L. Zhou, X. Xiao, Q. Yang, X. Zhang, and J. Chen, “Fractional-order photonic differentiator using an on-chip microring resonator,” Opt. Lett. 39(21), 6355–6358 (2014).
[Crossref] [PubMed]

Opt. Quantum Electron. (1)

C. Cuadrado-Laborde, “All-optical ultrafast fractional differentiator,” Opt. Quantum Electron. 40(13), 983–990 (2008).
[Crossref]

Sci. Rep. (1)

B. Jin, J. Yuan, K. Wang, X. Sang, B. Yan, Q. Wu, F. Li, X. Zhou, G. Zhou, C. Yu, C. Lu, H. Yaw Tam, and P. K. A. Wai, “A comprehensive theoretical model for on-chip microring-based photonic fractional differentiators,” Sci. Rep. 5(1), 14216 (2015).
[Crossref] [PubMed]

Other (1)

M. A. Popovic, T. Barwicz, F. Gan, M. S. Dahlem, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Transparent Wavelength Switching of Resonant Filters,” in Conference on Lasers and Electro-Optics (2007), paper CPDA2.

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Figures (9)

Fig. 1
Fig. 1 Schematics of (a) an add–drop MRR and (b) an MZI coupled microring resonator.
Fig. 2
Fig. 2 (a) Intensity transmission and (b) phase response of the MZI-MRR with varying values of Δφ.
Fig. 3
Fig. 3 (a) Magnitude response and (b) phase response of the MZI-MRR (dot lines) and the ideal first-order differentiator (solid lines). (c) Simulated the output response from the MZI-MRR (dot line) and the ideal first-order differentiator (solid line) of a 50 ps-pulsewidth Gaussian pulse. (d) Deviations of the simulated output response with different pulsewidth. (e) Deviations of the simulated output response with different differentiation order of a 50 ps-pulsewidth.
Fig. 4
Fig. 4 (a) Schematic concept diagram of the MZI-MRR. (b) Microscope image of the waveguides and rings after ICP etching. (c) Microscope image of fabricated MZI-MRR and (d) the zoom-in ring region.
Fig. 5
Fig. 5 Measured transmission spectra of the fabricated MZI-MRR at different heating powers applied to the heater above the arc-shaped waveguide.
Fig. 6
Fig. 6 Experimental setup for the fractional-order differentiator based on an MZI-MRR. TLD: Tunable laser diode. PC: Polarization controller. MZM: Mach-Zehnder modulator. EA: Electronic amplifier. BPG: Bit pattern generator. EDFA: Erbium doped fiber amplifier. OTDL: Optical tunable delay line. ATT: Attenuator. OC: Optical coupler.
Fig. 7
Fig. 7 (a) The experimental input pulse (blue dot line) and the simulated Gaussian pulse with a pulsewidth of 56 ps (red solid line). The measured differentiated output pulses at applied heating power of (b) 2.46 mW, (c) 3.12 mW, (d) 3.47 mW, (e) 3.92 mW, (f) 4.24 mW, (g) 4.65 mW, (h) 5 mW, (i) 5.54 mW, (j) 5.91 mW. Sim: simulation, Exp: experiment.
Fig. 8
Fig. 8 Averaged error of the fabricated MZI-MRR as a function of differentiation order N.
Fig. 9
Fig. 9 Measured spectra of the critical coupling MZI-MRR, the input Gaussian pulse with a pulsewidth of 56ps and the output pulse.

Equations (3)

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H( ω )= [ j( ω ω 0 ) ] N ,
t= E out E in = r 1 α r 2 e jϕ 1α r 1 r 2 e jϕ ,
κ 1 2 = κ 0 2 ( 1 κ 0 2 )×( t b + t r 2 t b t r cosφ ),

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