Abstract

A novel photonic fractional-order temporal differentiator is proposed based on the inverse Raman scattering (IRS) in the side-coupled silicon microring resonator. By controlling the power of the pump light-wave, the intracavity loss is adjusted and the coupling state of the microring resonator can be changed, so the continuously tunable differentiation order is achieved. The influences of input pulse width on the differentiation order and the output deviation are discussed. Due to the narrow bandwidth of IRS in silicon, the intracavity loss can be adjusted on a specific resonance while keeping the adjacent resonances undisturbed. It can be expected that the proposed scheme has the potential to realize different differentiation orders simultaneously at different resonant wavelengths.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Widely tunable fractional-order photonic differentiator using a Mach–Zenhder interferometer coupled microring resonator

Mian Liu, Yuhe Zhao, Xu Wang, Xinliang Zhang, Shengqian Gao, Jianji Dong, and Xinlun Cai
Opt. Express 25(26) 33305-33314 (2017)

Tunable fractional-order differentiator using an electrically tuned silicon-on-isolator Mach-Zehnder interferometer

Aoling Zheng, Ting Yang, Xi Xiao, Qi Yang, Xinliang Zhang, and Jianji Dong
Opt. Express 22(15) 18232-18237 (2014)

Fractional-order photonic differentiator using an on-chip microring resonator

Aoling Zheng, Jianji Dong, Linjie Zhou, Xi Xiao, Qi Yang, Xinliang Zhang, and Jianping Chen
Opt. Lett. 39(21) 6355-6358 (2014)

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. J. Yao, F. Zeng, and Q. Wang, “Photonic generation of ultra-wideband signals,” J. Lightwave Technol. 25(11), 3219–3235 (2007).
    [Crossref]
  3. 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]
  4. J. Silva and M. Campos, “Spectrally efficient UWB pulse shaping with application in orthogonal PSM,” IEEE Trans. Commun. 55(2), 313–322 (2007).
    [Crossref]
  5. 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]
  6. 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]
  7. J. Dong, A. Zheng, Y. Zhang, J. Xia, S. Tan, T. Yang, and X. Zhang, “Photonic Hilbert transformer employing on-chip photonic crystal nanocavity,” J. Lightwave Technol. 32(20), 3704–3709 (2014).
    [Crossref]
  8. W. Zhang, W. Li, and J. Yao, “Optical differentiator based on an integrated sidewall phase-shifted Bragg grating,” IEEE Photon. Technol. Lett. 26(23), 2383–2386 (2014).
    [Crossref]
  9. H. Zhang, M. Tang, Y. Xie, S. Fu, D. Liu, and P. P. Shum, “Programmable wavelength-tunable second-order optical temporal differentiator based on a linearly chirped fiber Bragg grating and a digital thermal controller,” Opt. Lett. 39(7), 2004–2007 (2014).
    [Crossref] [PubMed]
  10. J. Dong, Y. Yu, Y. Zhang, B. Luo, T. Yang, and X. Zhang, “Arbitrary-order bandwidth-tunable temporal differentiator using a programmable optical pulse shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
    [Crossref]
  11. 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]
  12. 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]
  13. 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]
  14. 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]
  15. G. Zhou, L. Zhang, F. Li, X. Hu, T. Wang, Q. Li, M. Qiu, and Y. Su, “All-optical temporal differentiation of ultra-high-speed picosecond pulses based on compact silicon microring resonator,” Electron. Lett. 47(14), 814–816 (2011).
    [Crossref]
  16. C. Cuadrado-Laborde and M. V. Andrés, “In-fiber all-optical fractional differentiator,” Opt. Lett. 34(6), 833–835 (2009).
    [Crossref] [PubMed]
  17. 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]
  18. H. Shahoei, J. Albert, and J. Yao, “Tunable fractional order temporal differentiator by optically pumping a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 24(9), 730–732 (2012).
    [Crossref]
  19. H. Shahoei, D.-X. Xu, J. H. Schmid, and J. Yao, “Photonic fractional-order differentiator using an SOI microring resonator with an MMI coupler,” IEEE Photon. Technol. Lett. 25(15), 1408–1411 (2013).
    [Crossref]
  20. 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]
  21. 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]
  22. D. R. Solli, P. Koonath, and B. Jalali, “Inverse Raman scattering in silicon: a free-carrier enhanced effect,” Phys. Rev. A 79(5), 053853 (2009).
    [Crossref]
  23. Y. Xiong and W. N. Ye, “All-optical switching of a single wavelength in a silicon-based ring-assisted Mach-Zehnder interferometer,” Appl. Opt. 51(32), 7788–7793 (2012).
    [Crossref] [PubMed]
  24. Y. H. Wen, O. Kuzucu, T. Hou, M. Lipson, and A. L. Gaeta, “All-optical switching of a single resonance in silicon ring resonators,” Opt. Lett. 36(8), 1413–1415 (2011).
    [Crossref] [PubMed]
  25. Y. H. Wen, O. Kuzucu, M. Fridman, A. L. Gaeta, L.-W. Luo, and M. Lipson, “All-optical control of an individual resonance in a silicon microresonator,” Phys. Rev. Lett. 108(22), 223907 (2012).
    [Crossref] [PubMed]
  26. W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
    [Crossref]
  27. S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photonics Rev. 6(2), 145–177 (2012).
    [Crossref]
  28. J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
    [Crossref]
  29. M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron. 16(1), 216–225 (2010).
    [Crossref]
  30. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. 16(1), 200–215 (2010).
    [Crossref]
  31. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express 15(25), 16604–16644 (2007).
    [Crossref] [PubMed]
  32. X. Sang and O. Boyraz, “Gain and noise characteristics of high-bit-rate silicon parametric amplifiers,” Opt. Express 16(17), 13122–13132 (2008).
    [Crossref] [PubMed]
  33. A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18(4), 3582–3591 (2010).
    [Crossref] [PubMed]
  34. Y. Vlasov and S. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
    [Crossref] [PubMed]

2014 (5)

2013 (3)

2012 (6)

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]

Y. H. Wen, O. Kuzucu, M. Fridman, A. L. Gaeta, L.-W. Luo, and M. Lipson, “All-optical control of an individual resonance in a silicon microresonator,” Phys. Rev. Lett. 108(22), 223907 (2012).
[Crossref] [PubMed]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photonics Rev. 6(2), 145–177 (2012).
[Crossref]

H. Shahoei, J. Albert, and J. Yao, “Tunable fractional order temporal differentiator by optically pumping a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 24(9), 730–732 (2012).
[Crossref]

Y. Xiong and W. N. Ye, “All-optical switching of a single wavelength in a silicon-based ring-assisted Mach-Zehnder interferometer,” Appl. Opt. 51(32), 7788–7793 (2012).
[Crossref] [PubMed]

2011 (4)

Y. H. Wen, O. Kuzucu, T. Hou, M. Lipson, and A. L. Gaeta, “All-optical switching of a single resonance in silicon ring resonators,” Opt. Lett. 36(8), 1413–1415 (2011).
[Crossref] [PubMed]

G. Zhou, L. Zhang, F. Li, X. Hu, T. Wang, Q. Li, M. Qiu, and Y. Su, “All-optical temporal differentiation of ultra-high-speed picosecond pulses based on compact silicon microring resonator,” Electron. Lett. 47(14), 814–816 (2011).
[Crossref]

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]

J. Dong, Y. Yu, Y. Zhang, B. Luo, T. Yang, and X. Zhang, “Arbitrary-order bandwidth-tunable temporal differentiator using a programmable optical pulse shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
[Crossref]

2010 (3)

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron. 16(1), 216–225 (2010).
[Crossref]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. 16(1), 200–215 (2010).
[Crossref]

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18(4), 3582–3591 (2010).
[Crossref] [PubMed]

2009 (3)

2008 (2)

2007 (4)

2006 (1)

2004 (3)

Y. Vlasov and S. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
[Crossref] [PubMed]

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[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]

Agrawal, G. P.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. 16(1), 200–215 (2010).
[Crossref]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express 15(25), 16604–16644 (2007).
[Crossref] [PubMed]

Albert, J.

H. Shahoei, J. Albert, and J. Yao, “Tunable fractional order temporal differentiator by optically pumping a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 24(9), 730–732 (2012).
[Crossref]

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]

Andrés, M. V.

Azaña, J.

Baets, R.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Bienstman, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Bogaerts, W.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Boyd, R. W.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[Crossref]

Boyraz, O.

Brinkmeyer, E.

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron. 16(1), 216–225 (2010).
[Crossref]

Cai, H.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photonics Rev. 6(2), 145–177 (2012).
[Crossref]

Campos, M.

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

Chen, H.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photonics Rev. 6(2), 145–177 (2012).
[Crossref]

Chen, J.

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]

Claes, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Cuadrado-Laborde, C.

De Heyn, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

De Vos, K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Dong, J.

Dumon, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Feng, S.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photonics Rev. 6(2), 145–177 (2012).
[Crossref]

Foster, M. A.

Fridman, M.

Y. H. Wen, O. Kuzucu, M. Fridman, A. L. Gaeta, L.-W. Luo, and M. Lipson, “All-optical control of an individual resonance in a silicon microresonator,” Phys. Rev. Lett. 108(22), 223907 (2012).
[Crossref] [PubMed]

Fu, S.

Gaeta, A. L.

Gao, D.

Heebner, J. E.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[Crossref]

Hou, T.

Hu, X.

G. Zhou, L. Zhang, F. Li, X. Hu, T. Wang, Q. Li, M. Qiu, and Y. Su, “All-optical temporal differentiation of ultra-high-speed picosecond pulses based on compact silicon microring resonator,” Electron. Lett. 47(14), 814–816 (2011).
[Crossref]

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.

Jackson, D. J.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[Crossref]

Jalali, B.

D. R. Solli, P. Koonath, and B. Jalali, “Inverse Raman scattering in silicon: a free-carrier enhanced effect,” Phys. Rev. A 79(5), 053853 (2009).
[Crossref]

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]

Koonath, P.

D. R. Solli, P. Koonath, and B. Jalali, “Inverse Raman scattering in silicon: a free-carrier enhanced effect,” Phys. Rev. A 79(5), 053853 (2009).
[Crossref]

Krause, M.

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron. 16(1), 216–225 (2010).
[Crossref]

Kulishov, M.

Kumar Selvaraja, S.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Kuzucu, O.

Y. H. Wen, O. Kuzucu, M. Fridman, A. L. Gaeta, L.-W. Luo, and M. Lipson, “All-optical control of an individual resonance in a silicon microresonator,” Phys. Rev. Lett. 108(22), 223907 (2012).
[Crossref] [PubMed]

Y. H. Wen, O. Kuzucu, T. Hou, M. Lipson, and A. L. Gaeta, “All-optical switching of a single resonance in silicon ring resonators,” Opt. Lett. 36(8), 1413–1415 (2011).
[Crossref] [PubMed]

Lei, L.

Lei, T.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photonics Rev. 6(2), 145–177 (2012).
[Crossref]

Levy, J. S.

Li, F.

G. Zhou, L. Zhang, F. Li, X. Hu, T. Wang, Q. Li, M. Qiu, and Y. Su, “All-optical temporal differentiation of ultra-high-speed picosecond pulses based on compact silicon microring resonator,” Electron. Lett. 47(14), 814–816 (2011).
[Crossref]

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]

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, Q.

G. Zhou, L. Zhang, F. Li, X. Hu, T. Wang, Q. Li, M. Qiu, and Y. Su, “All-optical temporal differentiation of ultra-high-speed picosecond pulses based on compact silicon microring resonator,” Electron. Lett. 47(14), 814–816 (2011).
[Crossref]

Li, W.

W. Zhang, W. Li, and J. Yao, “Optical differentiator based on an integrated sidewall phase-shifted Bragg grating,” IEEE Photon. Technol. Lett. 26(23), 2383–2386 (2014).
[Crossref]

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]

Liao, S.

Lin, Q.

Lipson, M.

Liu, D.

Liu, F.

Luo, B.

J. Dong, Y. Yu, Y. Zhang, B. Luo, T. Yang, and X. Zhang, “Arbitrary-order bandwidth-tunable temporal differentiator using a programmable optical pulse shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
[Crossref]

Luo, L.-W.

Y. H. Wen, O. Kuzucu, M. Fridman, A. L. Gaeta, L.-W. Luo, and M. Lipson, “All-optical control of an individual resonance in a silicon microresonator,” Phys. Rev. Lett. 108(22), 223907 (2012).
[Crossref] [PubMed]

Luo, X.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photonics Rev. 6(2), 145–177 (2012).
[Crossref]

McNab, S.

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]

Painter, O. J.

Park, Y.

Poitras, C. B.

Poon, A.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photonics Rev. 6(2), 145–177 (2012).
[Crossref]

Premaratne, M.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. 16(1), 200–215 (2010).
[Crossref]

Qiang, L.

Qiu, M.

G. Zhou, L. Zhang, F. Li, X. Hu, T. Wang, Q. Li, M. Qiu, and Y. Su, “All-optical temporal differentiation of ultra-high-speed picosecond pulses based on compact silicon microring resonator,” Electron. Lett. 47(14), 814–816 (2011).
[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]

Renner, H.

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron. 16(1), 216–225 (2010).
[Crossref]

Rukhlenko, I. D.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. 16(1), 200–215 (2010).
[Crossref]

Salem, R.

Sang, X.

Schmid, J. H.

H. Shahoei, D.-X. Xu, J. H. Schmid, and J. Yao, “Photonic fractional-order differentiator using an SOI microring resonator with an MMI coupler,” IEEE Photon. Technol. Lett. 25(15), 1408–1411 (2013).
[Crossref]

Schweinsberg, A.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[Crossref]

Shahoei, H.

H. Shahoei, D.-X. Xu, J. H. Schmid, and J. Yao, “Photonic fractional-order differentiator using an SOI microring resonator with an MMI coupler,” IEEE Photon. Technol. Lett. 25(15), 1408–1411 (2013).
[Crossref]

H. Shahoei, J. Albert, and J. Yao, “Tunable fractional order temporal differentiator by optically pumping a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 24(9), 730–732 (2012).
[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]

Shum, P. P.

Silva, J.

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

Slavík, R.

Solli, D. R.

D. R. Solli, P. Koonath, and B. Jalali, “Inverse Raman scattering in silicon: a free-carrier enhanced effect,” Phys. Rev. A 79(5), 053853 (2009).
[Crossref]

Su, 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]

G. Zhou, L. Zhang, F. Li, X. Hu, T. Wang, Q. Li, M. Qiu, and Y. Su, “All-optical temporal differentiation of ultra-high-speed picosecond pulses based on compact silicon microring resonator,” Electron. Lett. 47(14), 814–816 (2011).
[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]

Tan, S.

Tang, M.

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]

Turner-Foster, A. C.

Van Thourhout, D.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Van Vaerenbergh, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Vlasov, Y.

Wang, Q.

Wang, T.

G. Zhou, L. Zhang, F. Li, X. Hu, T. Wang, Q. Li, M. Qiu, and Y. Su, “All-optical temporal differentiation of ultra-high-speed picosecond pulses based on compact silicon microring resonator,” Electron. Lett. 47(14), 814–816 (2011).
[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]

Wen, Y. H.

Y. H. Wen, O. Kuzucu, M. Fridman, A. L. Gaeta, L.-W. Luo, and M. Lipson, “All-optical control of an individual resonance in a silicon microresonator,” Phys. Rev. Lett. 108(22), 223907 (2012).
[Crossref] [PubMed]

Y. H. Wen, O. Kuzucu, T. Hou, M. Lipson, and A. L. Gaeta, “All-optical switching of a single resonance in silicon ring resonators,” Opt. Lett. 36(8), 1413–1415 (2011).
[Crossref] [PubMed]

Wong, V.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[Crossref]

Xia, J.

Xiao, X.

Xie, Y.

Xiong, Y.

Xu, D.-X.

H. Shahoei, D.-X. Xu, J. H. Schmid, and J. Yao, “Photonic fractional-order differentiator using an SOI microring resonator with an MMI coupler,” IEEE Photon. Technol. Lett. 25(15), 1408–1411 (2013).
[Crossref]

Yang, Q.

Yang, T.

Yao, J.

W. Zhang, W. Li, and J. Yao, “Optical differentiator based on an integrated sidewall phase-shifted Bragg grating,” IEEE Photon. Technol. Lett. 26(23), 2383–2386 (2014).
[Crossref]

H. Shahoei, D.-X. Xu, J. H. Schmid, and J. Yao, “Photonic fractional-order differentiator using an SOI microring resonator with an MMI coupler,” IEEE Photon. Technol. Lett. 25(15), 1408–1411 (2013).
[Crossref]

H. Shahoei, J. Albert, and J. Yao, “Tunable fractional order temporal differentiator by optically pumping a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 24(9), 730–732 (2012).
[Crossref]

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]

J. Yao, F. Zeng, and Q. Wang, “Photonic generation of ultra-wideband signals,” J. Lightwave Technol. 25(11), 3219–3235 (2007).
[Crossref]

Ye, T.

Ye, W. N.

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]

J. Dong, Y. Yu, Y. Zhang, B. Luo, T. Yang, and X. Zhang, “Arbitrary-order bandwidth-tunable temporal differentiator using a programmable optical pulse shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
[Crossref]

Zeng, F.

Zhang, H.

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]

G. Zhou, L. Zhang, F. Li, X. Hu, T. Wang, Q. Li, M. Qiu, and Y. Su, “All-optical temporal differentiation of ultra-high-speed picosecond pulses based on compact silicon microring resonator,” Electron. Lett. 47(14), 814–816 (2011).
[Crossref]

Zhang, W.

W. Zhang, W. Li, and J. Yao, “Optical differentiator based on an integrated sidewall phase-shifted Bragg grating,” IEEE Photon. Technol. Lett. 26(23), 2383–2386 (2014).
[Crossref]

Zhang, X.

Zhang, Y.

J. Dong, A. Zheng, Y. Zhang, J. Xia, S. Tan, T. Yang, and X. Zhang, “Photonic Hilbert transformer employing on-chip photonic crystal nanocavity,” J. Lightwave Technol. 32(20), 3704–3709 (2014).
[Crossref]

J. Dong, Y. Yu, Y. Zhang, B. Luo, T. Yang, and X. Zhang, “Arbitrary-order bandwidth-tunable temporal differentiator using a programmable optical pulse shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
[Crossref]

Zhang, Z.

Zheng, A.

Zhou, G.

G. Zhou, L. Zhang, F. Li, X. Hu, T. Wang, Q. Li, M. Qiu, and Y. Su, “All-optical temporal differentiation of ultra-high-speed picosecond pulses based on compact silicon microring resonator,” Electron. Lett. 47(14), 814–816 (2011).
[Crossref]

Zhou, L.

Appl. Opt. (1)

Electron. Lett. (1)

G. Zhou, L. Zhang, F. Li, X. Hu, T. Wang, Q. Li, M. Qiu, and Y. Su, “All-optical temporal differentiation of ultra-high-speed picosecond pulses based on compact silicon microring resonator,” Electron. Lett. 47(14), 814–816 (2011).
[Crossref]

IEEE J. Quantum Electron. (1)

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40(6), 726–730 (2004).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron. 16(1), 216–225 (2010).
[Crossref]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. 16(1), 200–215 (2010).
[Crossref]

IEEE Photon. J. (1)

J. Dong, Y. Yu, Y. Zhang, B. Luo, T. Yang, and X. Zhang, “Arbitrary-order bandwidth-tunable temporal differentiator using a programmable optical pulse shaper,” IEEE Photon. J. 3(6), 996–1003 (2011).
[Crossref]

IEEE Photon. Technol. Lett. (4)

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]

H. Shahoei, J. Albert, and J. Yao, “Tunable fractional order temporal differentiator by optically pumping a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 24(9), 730–732 (2012).
[Crossref]

H. Shahoei, D.-X. Xu, J. H. Schmid, and J. Yao, “Photonic fractional-order differentiator using an SOI microring resonator with an MMI coupler,” IEEE Photon. Technol. Lett. 25(15), 1408–1411 (2013).
[Crossref]

W. Zhang, W. Li, and J. Yao, “Optical differentiator based on an integrated sidewall phase-shifted Bragg grating,” IEEE Photon. Technol. Lett. 26(23), 2383–2386 (2014).
[Crossref]

IEEE Trans. Commun. (1)

J. Silva and M. 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]

Laser Photonics Rev. (2)

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photonics Rev. 6(2), 145–177 (2012).
[Crossref]

Opt. Commun. (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]

Opt. Express (8)

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]

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).
[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]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express 15(25), 16604–16644 (2007).
[Crossref] [PubMed]

X. Sang and O. Boyraz, “Gain and noise characteristics of high-bit-rate silicon parametric amplifiers,” Opt. Express 16(17), 13122–13132 (2008).
[Crossref] [PubMed]

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18(4), 3582–3591 (2010).
[Crossref] [PubMed]

Y. Vlasov and S. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
[Crossref] [PubMed]

Opt. Lett. (7)

Phys. Rev. A (1)

D. R. Solli, P. Koonath, and B. Jalali, “Inverse Raman scattering in silicon: a free-carrier enhanced effect,” Phys. Rev. A 79(5), 053853 (2009).
[Crossref]

Phys. Rev. Lett. (1)

Y. H. Wen, O. Kuzucu, M. Fridman, A. L. Gaeta, L.-W. Luo, and M. Lipson, “All-optical control of an individual resonance in a silicon microresonator,” Phys. Rev. Lett. 108(22), 223907 (2012).
[Crossref] [PubMed]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1 Schematic illustration of the fractional-order temporal differentiator realized by the IRS effect in the side-coupled microring resonator.
Fig. 2
Fig. 2 (a) Intensity transmission and (b) phase response for the microring resonator with r=0.83 and varying values of τ .
Fig. 3
Fig. 3 τ and intracavity loss at (a) 1439.5 nm and (b) 1442.3 nm as functions of the pump light power. The dashed lines depict the intracavity loss induced by all the mechanisms except IRS, and the solid lines include all the optical losses in the resonator.
Fig. 4
Fig. 4 Comparisons between the outputs of the proposed differentiator and the time-reversed ideal differentiator with (a) n=0.4 , (b) n=0.7 , (c) n=1 , (d) n=1.2 , and (e) n=1.5 . The FWHM of the input Gaussian pulse is 50 ps.
Fig. 5
Fig. 5 Differentiation order as function of the pump power and the input pulse width. To indicate the coupling state of the microring resonator, the correspondence of the pump power and the round-trip amplitude transmission coefficient is also presented.
Fig. 6
Fig. 6 Output of the proposed differentiator for various input pulse widths with (a) τ=0.834 , (b) τ=0.83 , and (c) τ=0.816 .
Fig. 7
Fig. 7 Effects of the differentiation order and the input pulse width on the average deviation in the proposed differentiator.
Fig. 8
Fig. 8 Output of the proposed differentiator when the signal wavelength is shifted to 1439.51 nm. The differentiation order is n=0.5 , n=1 , and n=1.5 , respectively.
Fig. 9
Fig. 9 The 1.23-order differentiated pulse at 1439.5 nm and the 0.49-order differentiated pulse at 1442.3 nm, where the 50 mW and 70 mW pump light-waves are launched at 1556.1 nm and 1559.2 nm simultaneously. The FWHM of the input Gaussian pulses is 50 ps.

Equations (5)

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

H n (ν)= (i2πν) n ={ |2πν | n exp(inπ/2) ν>0 |2πν | n exp(inπ/2) ν<0 ,
T= | E 2 E 1 | 2 = τ 2 2rτcosϕ+ r 2 12rτcosϕ+ r 2 τ 2 ,
Φ=arg( E 2 E 1 ) =π+ϕ+arctan( rsinϕ τrcosϕ )+arctan( rτsinϕ 1rτcosϕ ),
α R (ω,I)= g R Γ R 2 (ω ω a ) 2 /4 π 2 + Γ R 2 I,
D ave = 1 T T | P MR (t) P i (t) |dt ,

Metrics