Abstract

We theoretically investigate the operation bandwidth limitation of the photonic differentiator including the upper limitation, which is restrained by the device operation bandwidth and the lower limitation, which is restrained by the energy efficiency (EE) and detecting noise level. Taking the silicon photonic crystal L3 nano-cavity (PCN) as an example, for the first time, we experimentally demonstrate that the lower limitation of the operation bandwidth does exist and differentiators with different bandwidths have significantly different acceptable pulse width range of input signals, which are consistent to the theoretical prediction. Furthermore, we put forward a novel photonic differentiator scheme employing cascaded PCNs with different Q factors, which is likely to expand the operation bandwidth range of photonic differentiator dramatically.

© 2015 Optical Society of America

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References

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2014 (1)

2013 (5)

N. L. Kazanskiy, P. G. Serafimovich, and S. N. Khonina, “Use of photonic crystal cavities for temporal differentiation of optical signals,” Opt. Lett. 38(7), 1149–1151 (2013).
[Crossref] [PubMed]

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

M. Heuck, S. Combrié, G. Lehoucq, S. Malaguti, G. Bellanca, S. Trillo, P. T. Kristensen, J. Mørk, J. Reithmaier, and A. De Rossi, “Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity,” Appl. Phys. Lett. 103(18), 181120 (2013).
[Crossref]

T. Yang, J. Dong, S. Liao, D. Huang, and X. Zhang, “Comparison analysis of optical frequency comb generation with nonlinear effects in highly nonlinear fibers,” Opt. Express 21(7), 8508–8520 (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]

2012 (3)

2011 (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 Photonics 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 Photonics J. 3(6), 996–1003 (2011).
[Crossref]

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 (1)

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

2009 (4)

2008 (2)

J. Dong, X. Zhang, S. Fu, J. Xu, P. Shum, and D. Huang, “Ultrafast all-optical signal processing based on single semiconductor optical amplifier and optical filtering,” IEEE J. Sel. Top. Quantum Electron. 14(3), 770–778 (2008).
[Crossref]

F. Liu, T. Wang, L. Qiang, T. Ye, Z. Zhang, M. Qiu, and Y. Su, “Compact optical temporal differentiator based on silicon microring resonator,” Opt. Express 16(20), 15880–15886 (2008).
[Crossref] [PubMed]

2007 (1)

L. M. Rivas, K. Singh, A. Carballar, and J. Azana, “Arbitrary-order ultrabroadband all-optical differentiators based on fiber Bragg gratings,” IEEE Photonics Technol. Lett. 19(16), 1209–1211 (2007).
[Crossref]

2006 (3)

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

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

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

2005 (2)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13(4), 1202–1214 (2005).
[Crossref] [PubMed]

J. Azana 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 (2)

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]

T. Carmon, L. Yang, and K. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
[Crossref] [PubMed]

2003 (1)

L. Venema, “Photonic technologies,” Nature 424(6950), 809 (2003).
[Crossref]

1999 (1)

C. Manolatou, M. Khan, S. Fan, P. R. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

1994 (1)

H. M. Kwon, “Optical orthogonal code-division multiple-access system. I. APD noise and thermal noise,” IEEE Trans. Commun. 42(7), 2470–2479 (1994).
[Crossref]

Ahn, T.-J.

Akahane, Y.

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 Photonics Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

Asano, T.

Ashrafi, R.

Ayre, M.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Azana, J.

L. M. Rivas, K. Singh, A. Carballar, and J. Azana, “Arbitrary-order ultrabroadband all-optical differentiators based on fiber Bragg gratings,” IEEE Photonics Technol. Lett. 19(16), 1209–1211 (2007).
[Crossref]

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

Azaña, J.

Baets, R.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Bellanca, G.

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

M. Heuck, S. Combrié, G. Lehoucq, S. Malaguti, G. Bellanca, S. Trillo, P. T. Kristensen, J. Mørk, J. Reithmaier, and A. De Rossi, “Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity,” Appl. Phys. Lett. 103(18), 181120 (2013).
[Crossref]

Bienstman, P.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Bogaerts, W.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Bramerie, L.

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

Carballar, A.

L. M. Rivas, K. Singh, A. Carballar, and J. Azana, “Arbitrary-order ultrabroadband all-optical differentiators based on fiber Bragg gratings,” IEEE Photonics Technol. Lett. 19(16), 1209–1211 (2007).
[Crossref]

Carmon, T.

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]

Combrié, S.

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

M. Heuck, S. Combrié, G. Lehoucq, S. Malaguti, G. Bellanca, S. Trillo, P. T. Kristensen, J. Mørk, J. Reithmaier, and A. De Rossi, “Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity,” Appl. Phys. Lett. 103(18), 181120 (2013).
[Crossref]

De Rossi, A.

M. Heuck, S. Combrié, G. Lehoucq, S. Malaguti, G. Bellanca, S. Trillo, P. T. Kristensen, J. Mørk, J. Reithmaier, and A. De Rossi, “Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity,” Appl. Phys. Lett. 103(18), 181120 (2013).
[Crossref]

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

Dong, J.

Duchesne, D.

Fan, S.

C. Manolatou, M. Khan, S. Fan, P. R. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Fu, S.

J. Dong, X. Zhang, S. Fu, J. Xu, P. Shum, and D. Huang, “Ultrafast all-optical signal processing based on single semiconductor optical amplifier and optical filtering,” IEEE J. Sel. Top. Quantum Electron. 14(3), 770–778 (2008).
[Crossref]

Gao, D.

Gay, M.

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

Haus, H.

C. Manolatou, M. Khan, S. Fan, P. R. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Heuck, M.

M. Heuck, S. Combrié, G. Lehoucq, S. Malaguti, G. Bellanca, S. Trillo, P. T. Kristensen, J. Mørk, J. Reithmaier, and A. De Rossi, “Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity,” Appl. Phys. Lett. 103(18), 181120 (2013).
[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.

Janner, D.

Jeong, H.-S.

Joannopoulos, J.

C. Manolatou, M. Khan, S. Fan, P. R. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[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]

Kazanskiy, N. L.

Khan, M.

C. Manolatou, M. Khan, S. Fan, P. R. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Khonina, S. N.

Krcmarík, D.

Kristensen, P. T.

M. Heuck, S. Combrié, G. Lehoucq, S. Malaguti, G. Bellanca, S. Trillo, P. T. Kristensen, J. Mørk, J. Reithmaier, and A. De Rossi, “Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity,” Appl. Phys. Lett. 103(18), 181120 (2013).
[Crossref]

Kulishov, M.

Kwon, H. M.

H. M. Kwon, “Optical orthogonal code-division multiple-access system. I. APD noise and thermal noise,” IEEE Trans. Commun. 42(7), 2470–2479 (1994).
[Crossref]

Lehoucq, G.

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

M. Heuck, S. Combrié, G. Lehoucq, S. Malaguti, G. Bellanca, S. Trillo, P. T. Kristensen, J. Mørk, J. Reithmaier, and A. De Rossi, “Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity,” Appl. Phys. Lett. 103(18), 181120 (2013).
[Crossref]

Lei, L.

Lenglé, K.

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

Li, M.

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.

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 Photonics J. 3(6), 996–1003 (2011).
[Crossref]

Malaguti, S.

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

M. Heuck, S. Combrié, G. Lehoucq, S. Malaguti, G. Bellanca, S. Trillo, P. T. Kristensen, J. Mørk, J. Reithmaier, and A. De Rossi, “Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity,” Appl. Phys. Lett. 103(18), 181120 (2013).
[Crossref]

Manolatou, C.

C. Manolatou, M. Khan, S. Fan, P. R. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Morandotti, R.

Mørk, J.

M. Heuck, S. Combrié, G. Lehoucq, S. Malaguti, G. Bellanca, S. Trillo, P. T. Kristensen, J. Mørk, J. Reithmaier, and A. De Rossi, “Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity,” Appl. Phys. Lett. 103(18), 181120 (2013).
[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. N.

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

Noda, S.

Park, Y.

Pruneri, V.

Qiang, L.

Qiu, M.

Reithmaier, J.

M. Heuck, S. Combrié, G. Lehoucq, S. Malaguti, G. Bellanca, S. Trillo, P. T. Kristensen, J. Mørk, J. Reithmaier, and A. De Rossi, “Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity,” Appl. Phys. Lett. 103(18), 181120 (2013).
[Crossref]

Rivas, L. M.

L. M. Rivas, K. Singh, A. Carballar, and J. Azana, “Arbitrary-order ultrabroadband all-optical differentiators based on fiber Bragg gratings,” IEEE Photonics Technol. Lett. 19(16), 1209–1211 (2007).
[Crossref]

Rutkowska, K. A.

Serafimovich, P. G.

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 Photonics Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

Shum, P.

J. Dong, X. Zhang, S. Fu, J. Xu, P. Shum, and D. Huang, “Ultrafast all-optical signal processing based on single semiconductor optical amplifier and optical filtering,” IEEE J. Sel. Top. Quantum Electron. 14(3), 770–778 (2008).
[Crossref]

Simon, J.-C.

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

Singh, K.

L. M. Rivas, K. Singh, A. Carballar, and J. Azana, “Arbitrary-order ultrabroadband all-optical differentiators based on fiber Bragg gratings,” IEEE Photonics Technol. Lett. 19(16), 1209–1211 (2007).
[Crossref]

Slavík, R.

Song, B.-S.

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R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

Sorel, M.

Strain, M. J.

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]

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]

Taillaert, D.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Tan, S.

Thual, M.

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

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]

Trillo, S.

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

M. Heuck, S. Combrié, G. Lehoucq, S. Malaguti, G. Bellanca, S. Trillo, P. T. Kristensen, J. Mørk, J. Reithmaier, and A. De Rossi, “Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity,” Appl. Phys. Lett. 103(18), 181120 (2013).
[Crossref]

Vahala, K.

Van Laere, F.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Van Thourhout, D.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Venema, L.

L. Venema, “Photonic technologies,” Nature 424(6950), 809 (2003).
[Crossref]

Villeneuve, P. R.

C. Manolatou, M. Khan, S. Fan, P. R. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

Wang, T.

Wu, C.

Xia, J.

Xiao, X.

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]

Xu, J.

J. Dong, X. Zhang, S. Fu, J. Xu, P. Shum, and D. Huang, “Ultrafast all-optical signal processing based on single semiconductor optical amplifier and optical filtering,” IEEE J. Sel. Top. Quantum Electron. 14(3), 770–778 (2008).
[Crossref]

Yang, L.

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 Photonics Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

M. Li, D. Janner, J. Yao, and V. Pruneri, “Arbitrary-order all-fiber temporal differentiator based on a fiber Bragg grating: design and experimental demonstration,” Opt. Express 17(22), 19798–19807 (2009).
[Crossref] [PubMed]

Ye, T.

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 Photonics J. 3(6), 996–1003 (2011).
[Crossref]

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, 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 Photonics J. 3(6), 996–1003 (2011).
[Crossref]

Zhang, Z.

Zheng, A.

Appl. Phys. Lett. (1)

M. Heuck, S. Combrié, G. Lehoucq, S. Malaguti, G. Bellanca, S. Trillo, P. T. Kristensen, J. Mørk, J. Reithmaier, and A. De Rossi, “Heterodyne pump probe measurements of nonlinear dynamics in an indium phosphide photonic crystal cavity,” Appl. Phys. Lett. 103(18), 181120 (2013).
[Crossref]

Electron. Lett. (1)

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

IEEE J. Quantum Electron. (1)

C. Manolatou, M. Khan, S. Fan, P. R. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999).
[Crossref]

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

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

J. Dong, X. Zhang, S. Fu, J. Xu, P. Shum, and D. Huang, “Ultrafast all-optical signal processing based on single semiconductor optical amplifier and optical filtering,” IEEE J. Sel. Top. Quantum Electron. 14(3), 770–778 (2008).
[Crossref]

IEEE Photonics J. (2)

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 Photonics J. 3(6), 996–1003 (2011).
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J. Azaña, “Ultrafast analog all-optical signal processors based on fiber-grating devices,” IEEE Photonics J. 2(3), 359–386 (2010).
[Crossref]

IEEE Photonics 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 Photonics Technol. Lett. 23(4), 251–253 (2011).
[Crossref]

T. N. Nguyen, M. Gay, K. Lenglé, L. Bramerie, M. Thual, J.-C. Simon, S. Malaguti, G. Bellanca, S. Trillo, S. Combrié, G. Lehoucq, and A. De Rossi, “100-Gb/s wavelength division demultiplexing using a photonic crystal four-channel drop filter,” IEEE Photonics Technol. Lett. 25(9), 813–816 (2013).
[Crossref]

L. M. Rivas, K. Singh, A. Carballar, and J. Azana, “Arbitrary-order ultrabroadband all-optical differentiators based on fiber Bragg gratings,” IEEE Photonics Technol. Lett. 19(16), 1209–1211 (2007).
[Crossref]

IEEE Trans. Commun. (1)

H. M. Kwon, “Optical orthogonal code-division multiple-access system. I. APD noise and thermal noise,” IEEE Trans. Commun. 42(7), 2470–2479 (1994).
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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]

Jpn. J. Appl. Phys. (1)

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[Crossref]

Nature (1)

L. Venema, “Photonic technologies,” Nature 424(6950), 809 (2003).
[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 (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).
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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]

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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R. Ashrafi and J. Azaña, “Figure of merit for photonic differentiators,” Opt. Express 20(3), 2626–2639 (2012).
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M. Li, H.-S. Jeong, J. Azaña, and T.-J. Ahn, “25-terahertz-bandwidth all-optical temporal differentiator,” Opt. Express 20(27), 28273–28280 (2012).
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R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14(22), 10699–10707 (2006).
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M. Li, D. Janner, J. Yao, and V. Pruneri, “Arbitrary-order all-fiber temporal differentiator based on a fiber Bragg grating: design and experimental demonstration,” Opt. Express 17(22), 19798–19807 (2009).
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T. Yang, J. Dong, S. Liao, D. Huang, and X. Zhang, “Comparison analysis of optical frequency comb generation with nonlinear effects in highly nonlinear fibers,” Opt. Express 21(7), 8508–8520 (2013).
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Figures (10)

Fig. 1
Fig. 1 Theoretical calculation of photonic differentiators. (a) The cross-correlation coefficient. (b) The energy efficiency.
Fig. 2
Fig. 2 Cross-correlation Coefficient calculation results with noise under different BW of the DIFF. (a) BW = 50 GHz. (b) BW = 100 GHz. (c) BW = 250 GHz.
Fig. 3
Fig. 3 Maximum acceptable pulse width as a function of NEP under different BWs of DIFFs. (a) BW = 50 GHz. (b) BW = 100 GHz. (c) BW = 250 GHz.
Fig. 4
Fig. 4 (a) Scanning electron microscope of the PCN. (b)-(d) Zoom in region of three different nano-cavities with different Q factors. (e)-(g) Measured transmission spectra of three PCNs, respectively.
Fig. 5
Fig. 5 Experiment setup for photonic differentiation employing the PCN.
Fig. 6
Fig. 6 Time domain and spectrum measurement results of LS DIFF. (a)-(c). Input temporal waveforms. (d)-(f). Output temporal waveforms. (g)-(i): Measured spectra.
Fig. 7
Fig. 7 Time domain and spectrum measurement results of MS DIFF. (a)-(c). Input temporal waveforms. (d)-(f). Output temporal waveforms. (g)-(i). Measured spectra.
Fig. 8
Fig. 8 Time domain and spectrum measurement results of HS DIFF. (a)-(d). Input temporal waveforms. (e)-(h): Output temporal waveforms. (i)-(l). Measured spectra.
Fig. 9
Fig. 9 (a). C c for different DIFFs with different BW and (b) its zoom in. (c). EE for different DIFFs with different BW.
Fig. 10
Fig. 10 Schematic of the proposed differentiator with broader bandwidth.

Tables (1)

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Table 1 OIPW for DIFFs with different BWs

Equations (5)

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

H ( f ) = j 2 π ( f f 0 )
H ( f ) = { j 2 π ( f f 0 ) ( | f f 0 | B W / 2 ) j 2 π ( B W / 2 ) ( f f 0 > B W / 2 ) j 2 π ( B W / 2 ) ( f f 0 < B W / 2 )
C c = + P o u t ( t ) P i d e a l ( t ) d t ( + P o u t 2 ( t ) d t ) ( + P i d e a l 2 ( t ) d t )
E E = + P o u t ( t ) d t + P i n ( t ) d t
H cavity ( f ) = e j 2 β d j 2 π ( f f 0 ) + 1 / τ v j 2 π ( f f 0 ) + 1 / τ v + 1 / τ in

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