K. Y. Yun, P. A. Beerel, V. Vakilotojar, A. E. Dooply, and J. Arceo, “The design and verification of a high-performance low-control-overhead asynchronous differential equation solver,” IEEE Trans. VLIS Syst. 6(4), 643–655 (1998).

[Crossref]

R. Ashrafi and J. Azaña, “Terahertz bandwidth all-optical Hilbert transformers based on long-period gratings,” Opt. Lett. 37(13), 2604–2606 (2012).

[Crossref]
[PubMed]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29), 29 (2010).

[PubMed]

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. J. Ahn, S. LaRochelle, and J. Azaña, “Photonic temporal integrator for all-optical computing,” Opt. Express 16(22), 18202–18214 (2008).

[Crossref]
[PubMed]

J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett. 33(1), 4–6 (2008).

[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]

K. Y. Yun, P. A. Beerel, V. Vakilotojar, A. E. Dooply, and J. Arceo, “The design and verification of a high-performance low-control-overhead asynchronous differential equation solver,” IEEE Trans. VLIS Syst. 6(4), 643–655 (1998).

[Crossref]

J. Wu, P. Cao, X. Hu, T. Wang, M. Xu, X. Jiang, F. Li, L. Zhou, and Y. Su, “Nested configuration of silicon microring resonator with multiple coupling regimes,” IEEE Photon. Technol. Lett. 25(6), 580–583 (2013).

[Crossref]

T. Yang, J. Dong, L. Lu, L. Zhou, A. Zheng, X. Zhang, and J. Chen, “All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator,” Sci. Rep. 4, 5581 (2014).

[PubMed]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29), 29 (2010).

[PubMed]

T. Yang, J. Dong, L. Lu, L. Zhou, A. Zheng, X. Zhang, and J. Chen, “All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator,” Sci. Rep. 4, 5581 (2014).

[PubMed]

S. Tan, Z. Wu, L. Lei, S. Hu, J. Dong, and X. Zhang, “All-optical computing system for solving differential equations based on optical intensity differentiator,” Opt. Express 21(6), 7008–7013 (2013).

[Crossref]

S. Tan, L. Xiang, J. Zou, Q. Zhang, Z. Wu, Y. Yu, J. Dong, and X. Zhang, “High-order all-optical differential equation solver based on microring resonators,” Opt. Lett. 38(19), 3735–3738 (2013).

[Crossref]
[PubMed]

K. Y. Yun, P. A. Beerel, V. Vakilotojar, A. E. Dooply, and J. Arceo, “The design and verification of a high-performance low-control-overhead asynchronous differential equation solver,” IEEE Trans. VLIS Syst. 6(4), 643–655 (1998).

[Crossref]

P. J. Winzer and R. J. Essiambre, “Advanced optical modulation formats,” Proc. IEEE 94(5), 952–985 (2006).

[Crossref]

C. Manolatou, M. Khan, S. Fan, P. 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]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29), 29 (2010).

[PubMed]

C. Manolatou, M. Khan, S. Fan, P. 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]

J. Wu, P. Cao, X. Hu, T. Wang, M. Xu, X. Jiang, F. Li, L. Zhou, and Y. Su, “Nested configuration of silicon microring resonator with multiple coupling regimes,” IEEE Photon. Technol. Lett. 25(6), 580–583 (2013).

[Crossref]

J. Wu, P. Cao, X. Hu, T. Wang, M. Xu, X. Jiang, F. Li, L. Zhou, and Y. Su, “Nested configuration of silicon microring resonator with multiple coupling regimes,” IEEE Photon. Technol. Lett. 25(6), 580–583 (2013).

[Crossref]

C. Manolatou, M. Khan, S. Fan, P. 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]

C. Manolatou, M. Khan, S. Fan, P. 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]

J. Wu, P. Cao, X. Hu, T. Wang, M. Xu, X. Jiang, F. Li, L. Zhou, and Y. Su, “Nested configuration of silicon microring resonator with multiple coupling regimes,” IEEE Photon. Technol. Lett. 25(6), 580–583 (2013).

[Crossref]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29), 29 (2010).

[PubMed]

T. Yang, J. Dong, L. Lu, L. Zhou, A. Zheng, X. Zhang, and J. Chen, “All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator,” Sci. Rep. 4, 5581 (2014).

[PubMed]

C. Manolatou, M. Khan, S. Fan, P. 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]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29), 29 (2010).

[PubMed]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29), 29 (2010).

[PubMed]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29), 29 (2010).

[PubMed]

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. J. Ahn, S. LaRochelle, and J. Azaña, “Photonic temporal integrator for all-optical computing,” Opt. Express 16(22), 18202–18214 (2008).

[Crossref]
[PubMed]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29), 29 (2010).

[PubMed]

J. Wu, P. Cao, X. Hu, T. Wang, M. Xu, X. Jiang, F. Li, L. Zhou, and Y. Su, “Nested configuration of silicon microring resonator with multiple coupling regimes,” IEEE Photon. Technol. Lett. 25(6), 580–583 (2013).

[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]

S. Tan, Z. Wu, L. Lei, S. Hu, J. Dong, and X. Zhang, “All-optical computing system for solving differential equations based on optical intensity differentiator,” Opt. Express 21(6), 7008–7013 (2013).

[Crossref]

S. Tan, L. Xiang, J. Zou, Q. Zhang, Z. Wu, Y. Yu, J. Dong, and X. Zhang, “High-order all-optical differential equation solver based on microring resonators,” Opt. Lett. 38(19), 3735–3738 (2013).

[Crossref]
[PubMed]

K. Y. Yun, P. A. Beerel, V. Vakilotojar, A. E. Dooply, and J. Arceo, “The design and verification of a high-performance low-control-overhead asynchronous differential equation solver,” IEEE Trans. VLIS Syst. 6(4), 643–655 (1998).

[Crossref]

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

[Crossref]

C. Manolatou, M. Khan, S. Fan, P. 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]

J. Wu, P. Cao, X. Hu, T. Wang, M. Xu, X. Jiang, F. Li, L. Zhou, and Y. Su, “Nested configuration of silicon microring resonator with multiple coupling regimes,” IEEE Photon. Technol. Lett. 25(6), 580–583 (2013).

[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]

P. J. Winzer and R. J. Essiambre, “Advanced optical modulation formats,” Proc. IEEE 94(5), 952–985 (2006).

[Crossref]

J. Wu, P. Cao, X. Hu, T. Wang, M. Xu, X. Jiang, F. Li, L. Zhou, and Y. Su, “Nested configuration of silicon microring resonator with multiple coupling regimes,” IEEE Photon. Technol. Lett. 25(6), 580–583 (2013).

[Crossref]

S. Tan, L. Xiang, J. Zou, Q. Zhang, Z. Wu, Y. Yu, J. Dong, and X. Zhang, “High-order all-optical differential equation solver based on microring resonators,” Opt. Lett. 38(19), 3735–3738 (2013).

[Crossref]
[PubMed]

S. Tan, Z. Wu, L. Lei, S. Hu, J. Dong, and X. Zhang, “All-optical computing system for solving differential equations based on optical intensity differentiator,” Opt. Express 21(6), 7008–7013 (2013).

[Crossref]

S. Tan, L. Xiang, J. Zou, Q. Zhang, Z. Wu, Y. Yu, J. Dong, and X. Zhang, “High-order all-optical differential equation solver based on microring resonators,” Opt. Lett. 38(19), 3735–3738 (2013).

[Crossref]
[PubMed]

J. Wu, P. Cao, X. Hu, T. Wang, M. Xu, X. Jiang, F. Li, L. Zhou, and Y. Su, “Nested configuration of silicon microring resonator with multiple coupling regimes,” IEEE Photon. Technol. Lett. 25(6), 580–583 (2013).

[Crossref]

T. Yang, J. Dong, L. Lu, L. Zhou, A. Zheng, X. Zhang, and J. Chen, “All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator,” Sci. Rep. 4, 5581 (2014).

[PubMed]

S. Tan, L. Xiang, J. Zou, Q. Zhang, Z. Wu, Y. Yu, J. Dong, and X. Zhang, “High-order all-optical differential equation solver based on microring resonators,” Opt. Lett. 38(19), 3735–3738 (2013).

[Crossref]
[PubMed]

K. Y. Yun, P. A. Beerel, V. Vakilotojar, A. E. Dooply, and J. Arceo, “The design and verification of a high-performance low-control-overhead asynchronous differential equation solver,” IEEE Trans. VLIS Syst. 6(4), 643–655 (1998).

[Crossref]

S. Tan, L. Xiang, J. Zou, Q. Zhang, Z. Wu, Y. Yu, J. Dong, and X. Zhang, “High-order all-optical differential equation solver based on microring resonators,” Opt. Lett. 38(19), 3735–3738 (2013).

[Crossref]
[PubMed]

T. Yang, J. Dong, L. Lu, L. Zhou, A. Zheng, X. Zhang, and J. Chen, “All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator,” Sci. Rep. 4, 5581 (2014).

[PubMed]

S. Tan, L. Xiang, J. Zou, Q. Zhang, Z. Wu, Y. Yu, J. Dong, and X. Zhang, “High-order all-optical differential equation solver based on microring resonators,” Opt. Lett. 38(19), 3735–3738 (2013).

[Crossref]
[PubMed]

S. Tan, Z. Wu, L. Lei, S. Hu, J. Dong, and X. Zhang, “All-optical computing system for solving differential equations based on optical intensity differentiator,” Opt. Express 21(6), 7008–7013 (2013).

[Crossref]

T. Yang, J. Dong, L. Lu, L. Zhou, A. Zheng, X. Zhang, and J. Chen, “All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator,” Sci. Rep. 4, 5581 (2014).

[PubMed]

T. Yang, J. Dong, L. Lu, L. Zhou, A. Zheng, X. Zhang, and J. Chen, “All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator,” Sci. Rep. 4, 5581 (2014).

[PubMed]

J. Wu, P. Cao, X. Hu, T. Wang, M. Xu, X. Jiang, F. Li, L. Zhou, and Y. Su, “Nested configuration of silicon microring resonator with multiple coupling regimes,” IEEE Photon. Technol. Lett. 25(6), 580–583 (2013).

[Crossref]

S. Tan, L. Xiang, J. Zou, Q. Zhang, Z. Wu, Y. Yu, J. Dong, and X. Zhang, “High-order all-optical differential equation solver based on microring resonators,” Opt. Lett. 38(19), 3735–3738 (2013).

[Crossref]
[PubMed]

C. Manolatou, M. Khan, S. Fan, P. 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]

J. Wu, P. Cao, X. Hu, T. Wang, M. Xu, X. Jiang, F. Li, L. Zhou, and Y. Su, “Nested configuration of silicon microring resonator with multiple coupling regimes,” IEEE Photon. Technol. Lett. 25(6), 580–583 (2013).

[Crossref]

K. Y. Yun, P. A. Beerel, V. Vakilotojar, A. E. Dooply, and J. Arceo, “The design and verification of a high-performance low-control-overhead asynchronous differential equation solver,” IEEE Trans. VLIS Syst. 6(4), 643–655 (1998).

[Crossref]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1(29), 29 (2010).

[PubMed]

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

[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]

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T. J. Ahn, S. LaRochelle, and J. Azaña, “Photonic temporal integrator for all-optical computing,” Opt. Express 16(22), 18202–18214 (2008).

[Crossref]
[PubMed]

L. Zhuang, M. R. Khan, W. Beeker, A. Leinse, R. Heideman, and C. Roeloffzen, “Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter,” Opt. Express 20(24), 26499–26510 (2012).

[Crossref]
[PubMed]

S. Tan, Z. Wu, L. Lei, S. Hu, J. Dong, and X. Zhang, “All-optical computing system for solving differential equations based on optical intensity differentiator,” Opt. Express 21(6), 7008–7013 (2013).

[Crossref]

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]

N. Quoc Ngo, “Design of an optical temporal integrator based on a phase-shifted fiber Bragg grating in transmission,” Opt. Lett. 32(20), 3020–3022 (2007).

[Crossref]
[PubMed]

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

[Crossref]
[PubMed]

J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett. 33(1), 4–6 (2008).

[Crossref]
[PubMed]

S. Tan, L. Xiang, J. Zou, Q. Zhang, Z. Wu, Y. Yu, J. Dong, and X. Zhang, “High-order all-optical differential equation solver based on microring resonators,” Opt. Lett. 38(19), 3735–3738 (2013).

[Crossref]
[PubMed]

R. Ashrafi and J. Azaña, “Terahertz bandwidth all-optical Hilbert transformers based on long-period gratings,” Opt. Lett. 37(13), 2604–2606 (2012).

[Crossref]
[PubMed]

P. J. Winzer and R. J. Essiambre, “Advanced optical modulation formats,” Proc. IEEE 94(5), 952–985 (2006).

[Crossref]

T. Yang, J. Dong, L. Lu, L. Zhou, A. Zheng, X. Zhang, and J. Chen, “All-optical differential equation solver with constant-coefficient tunable based on a single microring resonator,” Sci. Rep. 4, 5581 (2014).

[PubMed]

A. V. Oppenheim, A. S. Willsky, and S. Hamid, Signals and Systems (Prentice-Hall, 1996), Chap. 4.

G. F. Simmons, Differential Equations With Applications and Historical Notes (McGraw-Hill, 1991), Chap. 1.

A. V. Oppenheim, A. S. Willsky, and S. Hamid, Signals and Systems (Prentice-Hall, 1996), Chap. 2.