Abstract

All-optical integrators are key devices for the realization of ultra-fast passive photonic networks, and, despite their broad applicability range (e.g., photonic bit counting, optical memory units, analogue computing, etc.), their realization in an integrated form is still a challenge. In this work, an all-optical integrator based on a silicon photonic phase-shifted Bragg grating is proposed and experimentally demonstrated, which shows a wide operation bandwidth of 750 GHz and integration time window of 9 ps. The integral operation for single pulse, in-phase pulses, and π-shifted pulses with different delays has been successfully achieved.

© 2017 Chinese Laser Press

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References

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  1. D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
    [Crossref]
  2. M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
    [Crossref]
  3. Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express 17, 12835–12848 (2009).
    [Crossref]
  4. 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, 18202–18214 (2008).
    [Crossref]
  5. M. H. Asghari, Y. Park, and J. Azaña, “Photonic temporal integration of broadband intensity waveforms over long operation time windows,” Opt. Lett. 36, 3557–3559 (2011).
    [Crossref]
  6. N. Huang, M. Li, R. Ashrafi, L. Wang, X. Wang, J. Azaña, and N. Zhu, “Active Fabry–Perot cavity for photonic temporal integrator with ultra-long operation time window,” Opt. Express 22, 3105–3116 (2014).
    [Crossref]
  7. X.-H. Jia, X.-L. Ji, C. Xu, Z.-N. Wang, and W.-L. Zhang, “Analysis of all-optical temporal integrator employing phased-shifted DFB-SOA,” Opt. Express 22, 28530–28536 (2014).
    [Crossref]
  8. W. Liu, M. Li, R. S. Guzzon, E. J. Norberg, J. S. Parker, L. A. Coldren, and J. Yao, “A photonic temporal integrator with an ultra-long integration time window based on an InP-InGaAsP integrated ring resonator,” J. Lightwave Technol. 32, 3654–3659 (2014).
    [Crossref]
  9. J. Azaña, “Proposal of a uniform fiber Bragg grating as an ultrafast all-optical integrator,” Opt. Lett. 33, 4–6 (2008).
    [Crossref]
  10. Y. Park, T.-J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16, 17817–17825 (2008).
    [Crossref]
  11. M. A. Preciado and M. A. Muriel, “Ultrafast all-optical integrator based on a fiber Bragg grating: proposal and design,” Opt. Lett. 33, 1348–1350 (2008).
    [Crossref]
  12. M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35, 1191–1193 (2010).
    [Crossref]
  13. M. H. Asghari, Y. Park, and J. Azaña, “New design for photonic temporal integration with combined high processing speed and long operation time window,” Opt. Express 19, 425–435 (2011).
    [Crossref]
  14. M. H. Asghari and J. Azaña, “Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings,” Opt. Express 16, 11459–11469 (2008).
    [Crossref]
  15. 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, 1–5 (2010).
    [Crossref]
  16. M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “All-optical 1st and 2nd order integration on a chip,” Opt. Express 19, 23153–23161 (2011).
    [Crossref]
  17. X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” in IEEE Photonic Society 24th Annual Meeting (2011), pp. 869–870.

2014 (3)

2011 (3)

2010 (2)

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, 1–5 (2010).
[Crossref]

M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35, 1191–1193 (2010).
[Crossref]

2009 (1)

2008 (5)

2004 (1)

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref]

1999 (1)

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[Crossref]

Ahn, T.-J.

Asghari, M. H.

Ashrafi, R.

Ayotte, N.

Azaña, J.

N. Huang, M. Li, R. Ashrafi, L. Wang, X. Wang, J. Azaña, and N. Zhu, “Active Fabry–Perot cavity for photonic temporal integrator with ultra-long operation time window,” Opt. Express 22, 3105–3116 (2014).
[Crossref]

M. H. Asghari, Y. Park, and J. Azaña, “Photonic temporal integration of broadband intensity waveforms over long operation time windows,” Opt. Lett. 36, 3557–3559 (2011).
[Crossref]

M. H. Asghari, Y. Park, and J. Azaña, “New design for photonic temporal integration with combined high processing speed and long operation time window,” Opt. Express 19, 425–435 (2011).
[Crossref]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “All-optical 1st and 2nd order integration on a chip,” Opt. Express 19, 23153–23161 (2011).
[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, 1–5 (2010).
[Crossref]

M. H. Asghari, C. Wang, J. Yao, and J. Azaña, “High-order passive photonic temporal integrators,” Opt. Lett. 35, 1191–1193 (2010).
[Crossref]

Y. Park, T.-J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16, 17817–17825 (2008).
[Crossref]

M. H. Asghari and J. Azaña, “Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings,” Opt. Express 16, 11459–11469 (2008).
[Crossref]

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

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, 18202–18214 (2008).
[Crossref]

Binsma, H.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref]

Blow, K. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[Crossref]

Chrostowski, L.

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” in IEEE Photonic Society 24th Annual Meeting (2011), pp. 869–870.

Chu, S. T.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “All-optical 1st and 2nd order integration on a chip,” Opt. Express 19, 23153–23161 (2011).
[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, 1–5 (2010).
[Crossref]

Coldren, L. A.

Cotter, D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[Crossref]

Dai, Y.

de Vries, T.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref]

den Besten, J. H.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref]

Ding, Y.

Dorren, H. J. S.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref]

Doucet, S.

Ellis, A. D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[Crossref]

Ferrera, M.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “All-optical 1st and 2nd order integration on a chip,” Opt. Express 19, 23153–23161 (2011).
[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, 1–5 (2010).
[Crossref]

Grist, S.

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” in IEEE Photonic Society 24th Annual Meeting (2011), pp. 869–870.

Guzzon, R. S.

Hill, M. T.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref]

Huang, D.

Huang, N.

Jaeger, N. A. F.

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” in IEEE Photonic Society 24th Annual Meeting (2011), pp. 869–870.

Ji, X.-L.

Jia, X.-H.

Kelly, A. E.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[Crossref]

Khoe, G.-D.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref]

LaRochelle, S.

Leijtens, X. J. M.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref]

Li, M.

Little, B. E.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “All-optical 1st and 2nd order integration on a chip,” Opt. Express 19, 23153–23161 (2011).
[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, 1–5 (2010).
[Crossref]

Liu, W.

Manning, R. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[Crossref]

Morandotti, R.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “All-optical 1st and 2nd order integration on a chip,” Opt. Express 19, 23153–23161 (2011).
[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, 1–5 (2010).
[Crossref]

Moss, D. J.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “All-optical 1st and 2nd order integration on a chip,” Opt. Express 19, 23153–23161 (2011).
[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, 1–5 (2010).
[Crossref]

Muriel, M. A.

Nesset, D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[Crossref]

Norberg, E. J.

Oei, Y.-S.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref]

Park, Y.

Parker, J. S.

Phillips, I. D.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[Crossref]

Poustie, A. J.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[Crossref]

Preciado, M. A.

Razzari, L.

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “All-optical 1st and 2nd order integration on a chip,” Opt. Express 19, 23153–23161 (2011).
[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, 1–5 (2010).
[Crossref]

Rogers, D. C.

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[Crossref]

Shi, W.

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” in IEEE Photonic Society 24th Annual Meeting (2011), pp. 869–870.

Slavík, R.

Smalbrugge, B.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref]

Smit, M. K.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref]

Wang, C.

Wang, L.

Wang, X.

N. Huang, M. Li, R. Ashrafi, L. Wang, X. Wang, J. Azaña, and N. Zhu, “Active Fabry–Perot cavity for photonic temporal integrator with ultra-long operation time window,” Opt. Express 22, 3105–3116 (2014).
[Crossref]

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” in IEEE Photonic Society 24th Annual Meeting (2011), pp. 869–870.

Wang, Z.-N.

Xu, C.

Yao, J.

Yun, H.

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” in IEEE Photonic Society 24th Annual Meeting (2011), pp. 869–870.

Zhang, W.-L.

Zhang, X.

Zhu, N.

J. Lightwave Technol. (1)

Nat. Commun. (1)

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, 1–5 (2010).
[Crossref]

Nature (1)

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref]

Opt. Express (8)

M. H. Asghari and J. Azaña, “Design of all-optical high-order temporal integrators based on multiple-phase-shifted Bragg gratings,” Opt. Express 16, 11459–11469 (2008).
[Crossref]

Y. Park, T.-J. Ahn, Y. Dai, J. Yao, and J. Azaña, “All-optical temporal integration of ultrafast pulse waveforms,” Opt. Express 16, 17817–17825 (2008).
[Crossref]

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, 18202–18214 (2008).
[Crossref]

Y. Ding, X. Zhang, X. Zhang, and D. Huang, “Active microring optical integrator associated with electroabsorption modulators for high speed low light power loadable and erasable optical memory unit,” Opt. Express 17, 12835–12848 (2009).
[Crossref]

X.-H. Jia, X.-L. Ji, C. Xu, Z.-N. Wang, and W.-L. Zhang, “Analysis of all-optical temporal integrator employing phased-shifted DFB-SOA,” Opt. Express 22, 28530–28536 (2014).
[Crossref]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaña, “All-optical 1st and 2nd order integration on a chip,” Opt. Express 19, 23153–23161 (2011).
[Crossref]

N. Huang, M. Li, R. Ashrafi, L. Wang, X. Wang, J. Azaña, and N. Zhu, “Active Fabry–Perot cavity for photonic temporal integrator with ultra-long operation time window,” Opt. Express 22, 3105–3116 (2014).
[Crossref]

M. H. Asghari, Y. Park, and J. Azaña, “New design for photonic temporal integration with combined high processing speed and long operation time window,” Opt. Express 19, 425–435 (2011).
[Crossref]

Opt. Lett. (4)

Science (1)

D. Cotter, R. J. Manning, K. J. Blow, A. D. Ellis, A. E. Kelly, D. Nesset, I. D. Phillips, A. J. Poustie, and D. C. Rogers, “Nonlinear optics for high-speed digital information processing,” Science 286, 1523–1528 (1999).
[Crossref]

Other (1)

X. Wang, W. Shi, S. Grist, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Narrow-band transmission filter using phase-shifted Bragg gratings in SOI waveguide,” in IEEE Photonic Society 24th Annual Meeting (2011), pp. 869–870.

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Figures (6)

Fig. 1.
Fig. 1. Schematic of a photonic temporal integrator based on a PS-BG. Single pulse, in-phase pulses, and π-shifted pulses are integrated and used for data processing, photonic bit counting, and optical memory units, respectively.
Fig. 2.
Fig. 2. (a) Schematic of the silicon PS-BG. (b) SEM image of the uniform grating. (c) SEM image of the phase-shift region. (d) SEM image of the photonic crystal coupling grating.
Fig. 3.
Fig. 3. Measured spectral response of the fabricated PS-BG with different parameters. (a) N=200, different ΔW of 20, 30, and 40 nm. (b) ΔW=20  nm, different N of 200, 300, and 400.
Fig. 4.
Fig. 4. Experimental setup for optical integral. First, the optical pulse is emitted by an MLL and then reshaped by the interferometer. The interferometer has two arms for the time delay adjustment and phase adjustment. After waveform shaping, the signal is emitted into the chip and detected by the oscilloscope.
Fig. 5.
Fig. 5. (a) Normalized spectral response of the fabricated PS-BG. (b) Measured spectrum of the MLL.
Fig. 6.
Fig. 6. Experimental result of the optical integration. (a), (c), (e), (g), (i): Fitted input waveforms of the single pulse, in-phase pulses, and π-shifted pulses with different time delay (9 and 14 ps). (b), (d), (f), (h), (j): Measured (blue dots) and fitted (red line) output waveforms of the PS-BG.

Equations (4)

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

H(ω)=1j(ωω0),
hint(t)=u(t)={0fort<01fort0.
Haprx(ω)=Ajω+τ1,
haprx(t)=Aexp(t/τ)u(t),

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