Abstract

We propose and experimentally demonstrate a temporal differentiator in optical field based on a silicon microring resonator with a radius of 40 µm. The microring resonator operates near the critical coupling region, and can take the first order derivative of the optical field. It features compact size thus is suitable for integration with silicon-on-insulator (SOI) based optical and electronic devices. The performance of this optical differentiator is tested using signals with typical shapes such as Gaussian, sinusoidal and square-like pulses at data rates of 10 Gb/s and 5 Gb/s.

©2008 Optical Society of America

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References

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  1. 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, 371–381 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-2-371.
    [Crossref] [PubMed]
  2. J. Xu, X. Zhang, J. Dong, D. Liu, and D. Huang, “All-optical differentiator based on cross-gain modulation in semiconductor optical amplifier,” Opt. Lett. 32, 3029–3031 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-20-3029.
    [Crossref] [PubMed]
  3. N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, “A new theoretical basis of higher-derivative optical differentiators,” Opt. Commun. 230, 115–129 (2004).
    [Crossref]
  4. Z. Li, S. Zhang, J. M. Vazquez, Y. Liu, G. D. Khoe, H. J. S. Dorren, and D. Lenstra, “Ultrafast optical differentiators based on asymmetric Mach-Zehnder interferometer,” presented at the Symposium of the IEEE/LEOS, Benelux Chapter (2006).
  5. G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, “Optical delay lines based on optical filters,” IEEE J. Quantum Electron. 37, 525–532 (2001).
    [Crossref]
  6. G. S. Pandian and F. E. Seraji, “Optical pulse response of a fiber ring resonator,” IEE Proceedings-J,  138, 235–239 (1991).
  7. L. Li, X. Zhang, P. Sun, and L. Chen, “Microring resonator-coupled Mach-Zehnder interferometer as trigger pulse generator, optical differentiator and integrator,” Fundamental Problems of Optoelectronics and Microelectronics III, Proceedings of the SPIE,  6595, 659513-1–659513-8 (2007).
  8. R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14, 10699–10707 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10699.
    [Crossref] [PubMed]
  9. Q. Xu, V. R. Almeida, and M. Lipson, “Micrometer-scale all-optical wavelength converter on silicon,” Opt. Lett. 30, 2733–2735 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-20-2733.
    [Crossref] [PubMed]
  10. Z. Zhang, M. Dainese, L. Wosinski, and M. Qiu, “Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling,” Opt. Express 16, 4621–4630 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-7-4621.
    [Crossref] [PubMed]
  11. S. Scheerlinck, J. Schrauwen, F. Van Laere, D. Taillaert, D. Van Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9639–9644 (2007), http://www.opticsinfobase.org/viewmedia.cfm?uri=oe-15-15-9625&seq=0.
    [Crossref]
  12. F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” IEEE J. Sel. Top. Quantum Electron.  14, 706–712 (2008).
    [Crossref]
  13. A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996), ch. 4.
  14. G. Roelkens, D. Vermenlen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency SOI fiber-to-waveguide grating couplers fabricated using CMOS technology,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2008), paper IME3, http://www.opticsinfobase.org/abstract.cfm?URI=IPNRA-2008- IME3.

2008 (2)

Z. Zhang, M. Dainese, L. Wosinski, and M. Qiu, “Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling,” Opt. Express 16, 4621–4630 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-7-4621.
[Crossref] [PubMed]

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” IEEE J. Sel. Top. Quantum Electron.  14, 706–712 (2008).
[Crossref]

2007 (4)

S. Scheerlinck, J. Schrauwen, F. Van Laere, D. Taillaert, D. Van Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9639–9644 (2007), http://www.opticsinfobase.org/viewmedia.cfm?uri=oe-15-15-9625&seq=0.
[Crossref]

L. Li, X. Zhang, P. Sun, and L. Chen, “Microring resonator-coupled Mach-Zehnder interferometer as trigger pulse generator, optical differentiator and integrator,” Fundamental Problems of Optoelectronics and Microelectronics III, Proceedings of the SPIE,  6595, 659513-1–659513-8 (2007).

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, 371–381 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-2-371.
[Crossref] [PubMed]

J. Xu, X. Zhang, J. Dong, D. Liu, and D. Huang, “All-optical differentiator based on cross-gain modulation in semiconductor optical amplifier,” Opt. Lett. 32, 3029–3031 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-20-3029.
[Crossref] [PubMed]

2006 (2)

Z. Li, S. Zhang, J. M. Vazquez, Y. Liu, G. D. Khoe, H. J. S. Dorren, and D. Lenstra, “Ultrafast optical differentiators based on asymmetric Mach-Zehnder interferometer,” presented at the Symposium of the IEEE/LEOS, Benelux Chapter (2006).

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, “Ultrafast all-optical differentiators,” Opt. Express 14, 10699–10707 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-22-10699.
[Crossref] [PubMed]

2005 (1)

2004 (1)

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

2001 (1)

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

1991 (1)

G. S. Pandian and F. E. Seraji, “Optical pulse response of a fiber ring resonator,” IEE Proceedings-J,  138, 235–239 (1991).

Almeida, V. R.

Azaña, J.

Baets, R.

S. Scheerlinck, J. Schrauwen, F. Van Laere, D. Taillaert, D. Van Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9639–9644 (2007), http://www.opticsinfobase.org/viewmedia.cfm?uri=oe-15-15-9625&seq=0.
[Crossref]

G. Roelkens, D. Vermenlen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency SOI fiber-to-waveguide grating couplers fabricated using CMOS technology,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2008), paper IME3, http://www.opticsinfobase.org/abstract.cfm?URI=IPNRA-2008- IME3.

Berger, N. K.

Brision, S.

G. Roelkens, D. Vermenlen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency SOI fiber-to-waveguide grating couplers fabricated using CMOS technology,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2008), paper IME3, http://www.opticsinfobase.org/abstract.cfm?URI=IPNRA-2008- IME3.

Chen, L.

L. Li, X. Zhang, P. Sun, and L. Chen, “Microring resonator-coupled Mach-Zehnder interferometer as trigger pulse generator, optical differentiator and integrator,” Fundamental Problems of Optoelectronics and Microelectronics III, Proceedings of the SPIE,  6595, 659513-1–659513-8 (2007).

Dainese, M.

Dong, J.

Dorren, H. J. S.

Z. Li, S. Zhang, J. M. Vazquez, Y. Liu, G. D. Khoe, H. J. S. Dorren, and D. Lenstra, “Ultrafast optical differentiators based on asymmetric Mach-Zehnder interferometer,” presented at the Symposium of the IEEE/LEOS, Benelux Chapter (2006).

Eggleton, B. J.

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

Fedeli, J.-M.

G. Roelkens, D. Vermenlen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency SOI fiber-to-waveguide grating couplers fabricated using CMOS technology,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2008), paper IME3, http://www.opticsinfobase.org/abstract.cfm?URI=IPNRA-2008- IME3.

Fischer, B.

Gautier, P.

G. Roelkens, D. Vermenlen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency SOI fiber-to-waveguide grating couplers fabricated using CMOS technology,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2008), paper IME3, http://www.opticsinfobase.org/abstract.cfm?URI=IPNRA-2008- IME3.

Huang, D.

Kam, C. H.

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

Khoe, G. D.

Z. Li, S. Zhang, J. M. Vazquez, Y. Liu, G. D. Khoe, H. J. S. Dorren, and D. Lenstra, “Ultrafast optical differentiators based on asymmetric Mach-Zehnder interferometer,” presented at the Symposium of the IEEE/LEOS, Benelux Chapter (2006).

Kulishov, M.

Lenstra, D.

Z. Li, S. Zhang, J. M. Vazquez, Y. Liu, G. D. Khoe, H. J. S. Dorren, and D. Lenstra, “Ultrafast optical differentiators based on asymmetric Mach-Zehnder interferometer,” presented at the Symposium of the IEEE/LEOS, Benelux Chapter (2006).

Lenz, G.

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

Levit, B.

Li, L.

L. Li, X. Zhang, P. Sun, and L. Chen, “Microring resonator-coupled Mach-Zehnder interferometer as trigger pulse generator, optical differentiator and integrator,” Fundamental Problems of Optoelectronics and Microelectronics III, Proceedings of the SPIE,  6595, 659513-1–659513-8 (2007).

Li, Q.

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” IEEE J. Sel. Top. Quantum Electron.  14, 706–712 (2008).
[Crossref]

Li, Z.

Z. Li, S. Zhang, J. M. Vazquez, Y. Liu, G. D. Khoe, H. J. S. Dorren, and D. Lenstra, “Ultrafast optical differentiators based on asymmetric Mach-Zehnder interferometer,” presented at the Symposium of the IEEE/LEOS, Benelux Chapter (2006).

Lipson, M.

Liu, D.

Liu, F.

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” IEEE J. Sel. Top. Quantum Electron.  14, 706–712 (2008).
[Crossref]

Liu, Y.

Z. Li, S. Zhang, J. M. Vazquez, Y. Liu, G. D. Khoe, H. J. S. Dorren, and D. Lenstra, “Ultrafast optical differentiators based on asymmetric Mach-Zehnder interferometer,” presented at the Symposium of the IEEE/LEOS, Benelux Chapter (2006).

Lyan, P.

G. Roelkens, D. Vermenlen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency SOI fiber-to-waveguide grating couplers fabricated using CMOS technology,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2008), paper IME3, http://www.opticsinfobase.org/abstract.cfm?URI=IPNRA-2008- IME3.

Madsen, C. K.

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

Morandotti, R.

Nawab, S. H.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996), ch. 4.

Ngo, N. Q.

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

Oppenheim, A. V.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996), ch. 4.

Pandian, G. S.

G. S. Pandian and F. E. Seraji, “Optical pulse response of a fiber ring resonator,” IEE Proceedings-J,  138, 235–239 (1991).

Park, Y.

Plant, D. V.

Qiu, M.

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” IEEE J. Sel. Top. Quantum Electron.  14, 706–712 (2008).
[Crossref]

Z. Zhang, M. Dainese, L. Wosinski, and M. Qiu, “Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling,” Opt. Express 16, 4621–4630 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-7-4621.
[Crossref] [PubMed]

Roelkens, G.

G. Roelkens, D. Vermenlen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency SOI fiber-to-waveguide grating couplers fabricated using CMOS technology,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2008), paper IME3, http://www.opticsinfobase.org/abstract.cfm?URI=IPNRA-2008- IME3.

Scheerlinck, S.

S. Scheerlinck, J. Schrauwen, F. Van Laere, D. Taillaert, D. Van Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9639–9644 (2007), http://www.opticsinfobase.org/viewmedia.cfm?uri=oe-15-15-9625&seq=0.
[Crossref]

Schrauwen, J.

S. Scheerlinck, J. Schrauwen, F. Van Laere, D. Taillaert, D. Van Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9639–9644 (2007), http://www.opticsinfobase.org/viewmedia.cfm?uri=oe-15-15-9625&seq=0.
[Crossref]

Seraji, F. E.

G. S. Pandian and F. E. Seraji, “Optical pulse response of a fiber ring resonator,” IEE Proceedings-J,  138, 235–239 (1991).

Slavík, R.

Slusher, R. E.

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

Su, Y.

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” IEEE J. Sel. Top. Quantum Electron.  14, 706–712 (2008).
[Crossref]

Sun, P.

L. Li, X. Zhang, P. Sun, and L. Chen, “Microring resonator-coupled Mach-Zehnder interferometer as trigger pulse generator, optical differentiator and integrator,” Fundamental Problems of Optoelectronics and Microelectronics III, Proceedings of the SPIE,  6595, 659513-1–659513-8 (2007).

Taillaert, D.

S. Scheerlinck, J. Schrauwen, F. Van Laere, D. Taillaert, D. Van Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9639–9644 (2007), http://www.opticsinfobase.org/viewmedia.cfm?uri=oe-15-15-9625&seq=0.
[Crossref]

Tjin, S. C.

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

Van Laere, F.

S. Scheerlinck, J. Schrauwen, F. Van Laere, D. Taillaert, D. Van Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9639–9644 (2007), http://www.opticsinfobase.org/viewmedia.cfm?uri=oe-15-15-9625&seq=0.
[Crossref]

Van Thourhout, D.

S. Scheerlinck, J. Schrauwen, F. Van Laere, D. Taillaert, D. Van Thourhout, and R. Baets, “Efficient, broadband and compact metal grating couplers for silicon-on-insulator waveguides,” Opt. Express 15, 9639–9644 (2007), http://www.opticsinfobase.org/viewmedia.cfm?uri=oe-15-15-9625&seq=0.
[Crossref]

G. Roelkens, D. Vermenlen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency SOI fiber-to-waveguide grating couplers fabricated using CMOS technology,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2008), paper IME3, http://www.opticsinfobase.org/abstract.cfm?URI=IPNRA-2008- IME3.

Vazquez, J. M.

Z. Li, S. Zhang, J. M. Vazquez, Y. Liu, G. D. Khoe, H. J. S. Dorren, and D. Lenstra, “Ultrafast optical differentiators based on asymmetric Mach-Zehnder interferometer,” presented at the Symposium of the IEEE/LEOS, Benelux Chapter (2006).

Vermenlen, D.

G. Roelkens, D. Vermenlen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency SOI fiber-to-waveguide grating couplers fabricated using CMOS technology,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2008), paper IME3, http://www.opticsinfobase.org/abstract.cfm?URI=IPNRA-2008- IME3.

Willsky, A. S.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996), ch. 4.

Wosinski, L.

Xu, J.

Xu, Q.

Yu, S. F.

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

Zhang, S.

Z. Li, S. Zhang, J. M. Vazquez, Y. Liu, G. D. Khoe, H. J. S. Dorren, and D. Lenstra, “Ultrafast optical differentiators based on asymmetric Mach-Zehnder interferometer,” presented at the Symposium of the IEEE/LEOS, Benelux Chapter (2006).

Zhang, X.

J. Xu, X. Zhang, J. Dong, D. Liu, and D. Huang, “All-optical differentiator based on cross-gain modulation in semiconductor optical amplifier,” Opt. Lett. 32, 3029–3031 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-20-3029.
[Crossref] [PubMed]

L. Li, X. Zhang, P. Sun, and L. Chen, “Microring resonator-coupled Mach-Zehnder interferometer as trigger pulse generator, optical differentiator and integrator,” Fundamental Problems of Optoelectronics and Microelectronics III, Proceedings of the SPIE,  6595, 659513-1–659513-8 (2007).

Zhang, Z.

Z. Zhang, M. Dainese, L. Wosinski, and M. Qiu, “Resonance-splitting and enhanced notch depth in SOI ring resonators with mutual mode coupling,” Opt. Express 16, 4621–4630 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-7-4621.
[Crossref] [PubMed]

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” IEEE J. Sel. Top. Quantum Electron.  14, 706–712 (2008).
[Crossref]

Fundamental Problems of Optoelectronics and Microelectronics III, Proceedings of the SPIE (1)

L. Li, X. Zhang, P. Sun, and L. Chen, “Microring resonator-coupled Mach-Zehnder interferometer as trigger pulse generator, optical differentiator and integrator,” Fundamental Problems of Optoelectronics and Microelectronics III, Proceedings of the SPIE,  6595, 659513-1–659513-8 (2007).

IEE Proceedings-J (1)

G. S. Pandian and F. E. Seraji, “Optical pulse response of a fiber ring resonator,” IEE Proceedings-J,  138, 235–239 (1991).

IEEE J. Quantum Electron. (1)

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

IEEE J. Sel. Top. Quantum Electron (1)

F. Liu, Q. Li, Z. Zhang, M. Qiu, and Y. Su, “Optically tunable delay line in silicon microring resonator based on thermal nonlinear effect,” IEEE J. Sel. Top. Quantum Electron.  14, 706–712 (2008).
[Crossref]

Opt. Commun. (1)

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

Opt. Express (4)

Opt. Lett. (2)

presented at the Symposium of the IEEE/LEOS, Benelux Chapter (1)

Z. Li, S. Zhang, J. M. Vazquez, Y. Liu, G. D. Khoe, H. J. S. Dorren, and D. Lenstra, “Ultrafast optical differentiators based on asymmetric Mach-Zehnder interferometer,” presented at the Symposium of the IEEE/LEOS, Benelux Chapter (2006).

Other (2)

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996), ch. 4.

G. Roelkens, D. Vermenlen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency SOI fiber-to-waveguide grating couplers fabricated using CMOS technology,” in Integrated Photonics and Nanophotonics Research and Applications, OSA Technical Digest (CD) (Optical Society of America, 2008), paper IME3, http://www.opticsinfobase.org/abstract.cfm?URI=IPNRA-2008- IME3.

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Figures (9)
Fig. 1.
Fig. 1. Schematic of a microring resonator

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Fig. 2.
Fig. 2. Transmission and phase response of microring resonator operating (a) at the critical coupling, (b) close to the critical coupling region.

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Fig. 3.
Fig. 3. (a) SEM photo of the microring resonator, (b) zoom-in view of the coupling region.

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Fig. 4.
Fig. 4. Measured (solid) and fitted (dashed) spectrum of the resonance at 1554.46 nm.

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Fig. 5.
Fig. 5. Experimental setup for testing the performance of the microring-resonator based optical differentiator. BPF: bandpass filter.

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Fig. 6.
Fig. 6. Picture of the vertical coupling system.

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Fig. 7.
Fig. 7. (a-i) 10-Gb/s and (a-iii) 5-Gb/s input Gaussian-like pulses; (a-ii) 10-Gb/s and (a-iv) 5-Gb/s output OS-HG pulses; (b-i) 10-Gb/s and (b-iii) 5-Gb/s input sinusoidal-like pulses; (b-ii) 10-Gb/s and (b-iv) 5-Gb/s output sinusoidal-like pulse; 10-Gb/s (c-i) single ‘1’ and (c-iii) single ‘0’ input square pulse; differentiation results of 10-Gb/s (c-ii) single ‘1’ and (c-iv) single ‘0’ square pulse.

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Fig. 8.
Fig. 8. Theoretical (dashed) and experimental (solid) trances of the differentiation of 10-Gb/s input (a) Gaussian-like, (b) sinusoidal-like, (c) square signals, respectively

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Fig. 9.
Fig. 9. Waveforms after mixing with the CW light for (a), (b) Gaussian-like pulses; (c), (d) sinusoidal-like pulses before and after differentiation at the data rate of 10 Gb/s, respectively.

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Equations (3)

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T ( ω ) = s 0 s i = j ( ω − ω 0 ) + 1 τ i − 1 τ e j ( ω − ω 0 ) + 1 τ i + 1 τ e
T ( ω ) = j τ ( ω − ω 0 ) + 1 τ i − 1 τ e 1 τ i + 1 τ e
T ( ω ) = j τ ( ω − ω 0 )

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