Abstract

We propose and numerically validate a new design concept for on-chip optical pulse shaping based on discrete space-to-time mapping in cascaded co-directional couplers. We show that under weak-coupling conditions, the amplitude and phase of the discrete complex apodization profile of the device can be directly mapped into its temporal impulse response. In this scheme, the amplitude and phase of the apodization profile can be controlled by tuning the coupling strength and relative time delay between the couplers, respectively. The proposed concept enables direct synthesis of the target temporal waveforms over a very broad range of time-resolution, from the femtosecond to the sub-nanosecond regime, using readily feasible integrated waveguide technologies. Moreover, the device offers compactness and the potential for reconfigurability.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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  1. P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photonics Technol. Lett. 14(2), 227–229 (2002).
    [Crossref]
  2. F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
    [Crossref]
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    [Crossref] [PubMed]
  4. J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. 8(3), 478–491 (1990).
    [Crossref]
  5. A. M. Weiner, Ultrafast optics, (John Wiley & sons, 2011).
  6. N. K. Fontaine, D. J. Geisler, R. P. Scott, T. He, J. P. Heritage, and S. J. B. Yoo, “Demonstration of high-fidelity dynamic optical arbitrary waveform generation,” Opt. Express 18(22), 22988–22995 (2010).
    [Crossref] [PubMed]
  7. R. P. Scott, N. K. Fontaine, J. P. Heritage, and S. J. B. Yoo, “Dynamic optical arbitrary waveform generation and measurement,” Opt. Express 18(18), 18655–18670 (2010).
    [Crossref] [PubMed]
  8. B. Muralidharan, V. Balakrishnan, and A. M. Weiner, “Design of double-passed arrayed-waveguide gratings for the generation of flat-topped femtosecond pulse trains,” J. Lightwave Technol. 24(1), 586–597 (2006).
    [Crossref]
  9. L.-M. Rivas, M. J. Strain, D. Duchesne, A. Carballar, M. Sorel, R. Morandotti, and J. Azaña, “Picosecond linear optical pulse shapers based on integrated waveguide Bragg gratings,” Opt. Lett. 33(21), 2425–2427 (2008).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  17. K. Jinguji and M. Kawachi, “Synthesis of Coherent Two-Port Lattice-Form Optical Delay-Line Circuit,” J. Lightwave Technol. 13(1), 73–82 (1995).
    [Crossref]
  18. B. Guan, S. S. Djordjevic, N. K. Fontaine, L. Zhou, S. Ibrahim, R. P. Scott, D. J. Geisler, Zh. Ding, and S. J. Ben Yoo, “CMOS compatible reconfigurable silicon photonic lattice filters using cascaded unit cells for RF-photonic processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202110 (2014).
  19. A. D. Simard, G. Beaudin, V. Aimez, Y. Painchaud, and S. Larochelle, “Characterization and reduction of spectral distortions in Silicon-on-Insulator integrated Bragg gratings,” Opt. Express 21(20), 23145–23159 (2013).
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    [Crossref]
  21. L. Chrostowski and M. Hochberg, Silicon Photonics Design Book-from Devices to Systems, (Cambridge University press, 2011).
  22. H. Pishvai Bazargani, J. Azaña, L. Chrostowski, and J. Flueckiger, “Microring resonator design with improved quality factors using quarter Bezier curves,” in Conference on Lasers and Electro-Optics: Science and Innovations, (OSA, 2015), paper JTu5A.
    [Crossref]

2015 (1)

2014 (1)

B. Guan, S. S. Djordjevic, N. K. Fontaine, L. Zhou, S. Ibrahim, R. P. Scott, D. J. Geisler, Zh. Ding, and S. J. Ben Yoo, “CMOS compatible reconfigurable silicon photonic lattice filters using cascaded unit cells for RF-photonic processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202110 (2014).

2013 (2)

2011 (2)

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

W. Bogaerts and S. K. Selvaraja, “Compact Single-Mode Silicon Hybrid Rib/Strip Waveguide With Adiabatic Bends,” IEEE Photonics J. 3(3), 422–432 (2011).
[Crossref]

2010 (3)

2008 (1)

2006 (1)

2002 (2)

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photonics Technol. Lett. 14(2), 227–229 (2002).
[Crossref]

J. Azaña and L. R. Chen, “Synthesis of temporal optical waveforms by fiber Bragg gratings: a new approach based on space-to-frequency-to-time mapping,” J. Opt. Soc. Am. B 19(11), 2758–2769 (2002).
[Crossref]

1995 (2)

F. Khaleghi, M. Kavehrad, and C. Barnard, “Tunable Coherent Optical Transversal EDFA Gain Equalization,” J. Lightwave Technol. 13(4), 581–587 (1995).
[Crossref]

K. Jinguji and M. Kawachi, “Synthesis of Coherent Two-Port Lattice-Form Optical Delay-Line Circuit,” J. Lightwave Technol. 13(1), 73–82 (1995).
[Crossref]

1994 (1)

K. Takiguchi, K. Okamoto, S. Suzuki, and Y. Ohmori, “Planar Lightwave Circuit Optical Dispersion Equalizer,” IEEE Photonics Technol. Lett. 6(1), 86–88 (1994).
[Crossref]

1990 (1)

J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. 8(3), 478–491 (1990).
[Crossref]

1976 (1)

H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55(1), 109–126 (1976).
[Crossref]

1975 (1)

H. Kogelnik, “An introduction to integrated optics,” IEEE Trans. Microw. Theory Tech. 23(1), 2–16 (1975).
[Crossref]

Aimez, V.

Ashrafi, R.

Azaña, J.

Balakrishnan, V.

Barnard, C.

F. Khaleghi, M. Kavehrad, and C. Barnard, “Tunable Coherent Optical Transversal EDFA Gain Equalization,” J. Lightwave Technol. 13(4), 581–587 (1995).
[Crossref]

Beaudin, G.

Belhadj, N.

Ben Yoo, S. J.

B. Guan, S. S. Djordjevic, N. K. Fontaine, L. Zhou, S. Ibrahim, R. P. Scott, D. J. Geisler, Zh. Ding, and S. J. Ben Yoo, “CMOS compatible reconfigurable silicon photonic lattice filters using cascaded unit cells for RF-photonic processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202110 (2014).

Bogaerts, W.

W. Bogaerts and S. K. Selvaraja, “Compact Single-Mode Silicon Hybrid Rib/Strip Waveguide With Adiabatic Bends,” IEEE Photonics J. 3(3), 422–432 (2011).
[Crossref]

Carballar, A.

Chen, L.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Chen, L. R.

Chen, X.

Dastmalchi, M.

Ding, Y.

Ding, Zh.

B. Guan, S. S. Djordjevic, N. K. Fontaine, L. Zhou, S. Ibrahim, R. P. Scott, D. J. Geisler, Zh. Ding, and S. J. Ben Yoo, “CMOS compatible reconfigurable silicon photonic lattice filters using cascaded unit cells for RF-photonic processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202110 (2014).

Djordjevic, S. S.

B. Guan, S. S. Djordjevic, N. K. Fontaine, L. Zhou, S. Ibrahim, R. P. Scott, D. J. Geisler, Zh. Ding, and S. J. Ben Yoo, “CMOS compatible reconfigurable silicon photonic lattice filters using cascaded unit cells for RF-photonic processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202110 (2014).

Dong, J.

Doylend, J. K.

Duchesne, D.

Ferdous, F.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Fontaine, N. K.

B. Guan, S. S. Djordjevic, N. K. Fontaine, L. Zhou, S. Ibrahim, R. P. Scott, D. J. Geisler, Zh. Ding, and S. J. Ben Yoo, “CMOS compatible reconfigurable silicon photonic lattice filters using cascaded unit cells for RF-photonic processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202110 (2014).

R. P. Scott, N. K. Fontaine, J. P. Heritage, and S. J. B. Yoo, “Dynamic optical arbitrary waveform generation and measurement,” Opt. Express 18(18), 18655–18670 (2010).
[Crossref] [PubMed]

N. K. Fontaine, D. J. Geisler, R. P. Scott, T. He, J. P. Heritage, and S. J. B. Yoo, “Demonstration of high-fidelity dynamic optical arbitrary waveform generation,” Opt. Express 18(22), 22988–22995 (2010).
[Crossref] [PubMed]

Gao, D.

Geisler, D. J.

B. Guan, S. S. Djordjevic, N. K. Fontaine, L. Zhou, S. Ibrahim, R. P. Scott, D. J. Geisler, Zh. Ding, and S. J. Ben Yoo, “CMOS compatible reconfigurable silicon photonic lattice filters using cascaded unit cells for RF-photonic processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202110 (2014).

N. K. Fontaine, D. J. Geisler, R. P. Scott, T. He, J. P. Heritage, and S. J. B. Yoo, “Demonstration of high-fidelity dynamic optical arbitrary waveform generation,” Opt. Express 18(22), 22988–22995 (2010).
[Crossref] [PubMed]

Guan, B.

B. Guan, S. S. Djordjevic, N. K. Fontaine, L. Zhou, S. Ibrahim, R. P. Scott, D. J. Geisler, Zh. Ding, and S. J. Ben Yoo, “CMOS compatible reconfigurable silicon photonic lattice filters using cascaded unit cells for RF-photonic processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202110 (2014).

He, T.

Heritage, J. P.

Ibrahim, S.

B. Guan, S. S. Djordjevic, N. K. Fontaine, L. Zhou, S. Ibrahim, R. P. Scott, D. J. Geisler, Zh. Ding, and S. J. Ben Yoo, “CMOS compatible reconfigurable silicon photonic lattice filters using cascaded unit cells for RF-photonic processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202110 (2014).

Ibsen, M.

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photonics Technol. Lett. 14(2), 227–229 (2002).
[Crossref]

Jessop, P. E.

Jinguji, K.

K. Jinguji and M. Kawachi, “Synthesis of Coherent Two-Port Lattice-Form Optical Delay-Line Circuit,” J. Lightwave Technol. 13(1), 73–82 (1995).
[Crossref]

Kavehrad, M.

F. Khaleghi, M. Kavehrad, and C. Barnard, “Tunable Coherent Optical Transversal EDFA Gain Equalization,” J. Lightwave Technol. 13(4), 581–587 (1995).
[Crossref]

Kawachi, M.

K. Jinguji and M. Kawachi, “Synthesis of Coherent Two-Port Lattice-Form Optical Delay-Line Circuit,” J. Lightwave Technol. 13(1), 73–82 (1995).
[Crossref]

Khaleghi, F.

F. Khaleghi, M. Kavehrad, and C. Barnard, “Tunable Coherent Optical Transversal EDFA Gain Equalization,” J. Lightwave Technol. 13(4), 581–587 (1995).
[Crossref]

Knights, A. P.

Kogelnik, H.

H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55(1), 109–126 (1976).
[Crossref]

H. Kogelnik, “An introduction to integrated optics,” IEEE Trans. Microw. Theory Tech. 23(1), 2–16 (1975).
[Crossref]

LaRochelle, S.

Leaird, D. E.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Lee, J. H.

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photonics Technol. Lett. 14(2), 227–229 (2002).
[Crossref]

Li, M.

Liao, S.

Miao, H.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Morandotti, R.

Muralidharan, B.

Ohmori, Y.

K. Takiguchi, K. Okamoto, S. Suzuki, and Y. Ohmori, “Planar Lightwave Circuit Optical Dispersion Equalizer,” IEEE Photonics Technol. Lett. 6(1), 86–88 (1994).
[Crossref]

Okamoto, K.

K. Takiguchi, K. Okamoto, S. Suzuki, and Y. Ohmori, “Planar Lightwave Circuit Optical Dispersion Equalizer,” IEEE Photonics Technol. Lett. 6(1), 86–88 (1994).
[Crossref]

Painchaud, Y.

Petropoulos, P.

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photonics Technol. Lett. 14(2), 227–229 (2002).
[Crossref]

Richardson, D. J.

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photonics Technol. Lett. 14(2), 227–229 (2002).
[Crossref]

Rivas, L.-M.

Salehi, J. A.

J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. 8(3), 478–491 (1990).
[Crossref]

Scott, R. P.

B. Guan, S. S. Djordjevic, N. K. Fontaine, L. Zhou, S. Ibrahim, R. P. Scott, D. J. Geisler, Zh. Ding, and S. J. Ben Yoo, “CMOS compatible reconfigurable silicon photonic lattice filters using cascaded unit cells for RF-photonic processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202110 (2014).

R. P. Scott, N. K. Fontaine, J. P. Heritage, and S. J. B. Yoo, “Dynamic optical arbitrary waveform generation and measurement,” Opt. Express 18(18), 18655–18670 (2010).
[Crossref] [PubMed]

N. K. Fontaine, D. J. Geisler, R. P. Scott, T. He, J. P. Heritage, and S. J. B. Yoo, “Demonstration of high-fidelity dynamic optical arbitrary waveform generation,” Opt. Express 18(22), 22988–22995 (2010).
[Crossref] [PubMed]

Selvaraja, S. K.

W. Bogaerts and S. K. Selvaraja, “Compact Single-Mode Silicon Hybrid Rib/Strip Waveguide With Adiabatic Bends,” IEEE Photonics J. 3(3), 422–432 (2011).
[Crossref]

Simard, A. D.

Sorel, M.

Srinivasan, K.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Strain, M. J.

Suzuki, S.

K. Takiguchi, K. Okamoto, S. Suzuki, and Y. Ohmori, “Planar Lightwave Circuit Optical Dispersion Equalizer,” IEEE Photonics Technol. Lett. 6(1), 86–88 (1994).
[Crossref]

Takiguchi, K.

K. Takiguchi, K. Okamoto, S. Suzuki, and Y. Ohmori, “Planar Lightwave Circuit Optical Dispersion Equalizer,” IEEE Photonics Technol. Lett. 6(1), 86–88 (1994).
[Crossref]

Teh, P. C.

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photonics Technol. Lett. 14(2), 227–229 (2002).
[Crossref]

Varghese, L. T.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Wang, J.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Weiner, A. M.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

B. Muralidharan, V. Balakrishnan, and A. M. Weiner, “Design of double-passed arrayed-waveguide gratings for the generation of flat-topped femtosecond pulse trains,” J. Lightwave Technol. 24(1), 586–597 (2006).
[Crossref]

J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. 8(3), 478–491 (1990).
[Crossref]

Yang, T.

Yoo, S. J. B.

Zhang, X.

Zhou, L.

B. Guan, S. S. Djordjevic, N. K. Fontaine, L. Zhou, S. Ibrahim, R. P. Scott, D. J. Geisler, Zh. Ding, and S. J. Ben Yoo, “CMOS compatible reconfigurable silicon photonic lattice filters using cascaded unit cells for RF-photonic processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202110 (2014).

Bell Syst. Tech. J. (1)

H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55(1), 109–126 (1976).
[Crossref]

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

B. Guan, S. S. Djordjevic, N. K. Fontaine, L. Zhou, S. Ibrahim, R. P. Scott, D. J. Geisler, Zh. Ding, and S. J. Ben Yoo, “CMOS compatible reconfigurable silicon photonic lattice filters using cascaded unit cells for RF-photonic processing,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8202110 (2014).

IEEE Photonics J. (1)

W. Bogaerts and S. K. Selvaraja, “Compact Single-Mode Silicon Hybrid Rib/Strip Waveguide With Adiabatic Bends,” IEEE Photonics J. 3(3), 422–432 (2011).
[Crossref]

IEEE Photonics Technol. Lett. (2)

K. Takiguchi, K. Okamoto, S. Suzuki, and Y. Ohmori, “Planar Lightwave Circuit Optical Dispersion Equalizer,” IEEE Photonics Technol. Lett. 6(1), 86–88 (1994).
[Crossref]

P. C. Teh, M. Ibsen, J. H. Lee, P. Petropoulos, and D. J. Richardson, “Demonstration of a four-channel WDM/OCDMA system using 255-chip 320-Gchip/s quarternary phase coding gratings,” IEEE Photonics Technol. Lett. 14(2), 227–229 (2002).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

H. Kogelnik, “An introduction to integrated optics,” IEEE Trans. Microw. Theory Tech. 23(1), 2–16 (1975).
[Crossref]

J. Lightwave Technol. (4)

J. A. Salehi, A. M. Weiner, and J. P. Heritage, “Coherent ultrashort light pulse code-division multiple access communication systems,” J. Lightwave Technol. 8(3), 478–491 (1990).
[Crossref]

B. Muralidharan, V. Balakrishnan, and A. M. Weiner, “Design of double-passed arrayed-waveguide gratings for the generation of flat-topped femtosecond pulse trains,” J. Lightwave Technol. 24(1), 586–597 (2006).
[Crossref]

F. Khaleghi, M. Kavehrad, and C. Barnard, “Tunable Coherent Optical Transversal EDFA Gain Equalization,” J. Lightwave Technol. 13(4), 581–587 (1995).
[Crossref]

K. Jinguji and M. Kawachi, “Synthesis of Coherent Two-Port Lattice-Form Optical Delay-Line Circuit,” J. Lightwave Technol. 13(1), 73–82 (1995).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Photonics (1)

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770–776 (2011).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Other (3)

A. M. Weiner, Ultrafast optics, (John Wiley & sons, 2011).

L. Chrostowski and M. Hochberg, Silicon Photonics Design Book-from Devices to Systems, (Cambridge University press, 2011).

H. Pishvai Bazargani, J. Azaña, L. Chrostowski, and J. Flueckiger, “Microring resonator design with improved quality factors using quarter Bezier curves,” in Conference on Lasers and Electro-Optics: Science and Innovations, (OSA, 2015), paper JTu5A.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic of the proposed pulse-shaping device and its principle of operation (discrete STM); (b) Amplitude coding by tuning the coupling length (the overall length of the directional coupler has to be fixed in order to avoid unwanted phase change in different stages of the device); (c) Phase coding by tuning the waveguide length in the differential delay lines.
Fig. 2
Fig. 2 (a) Power coupling ratios in cross and through ports of the directional coupler for 500 nm wide waveguides while changing the coupling gap. (b) The percentage of error for the power coupling ratio due to the deviation of coupling gap with respect to its ideally designed value. In this case the target design is a coupling gap of 200 nm. (c) Power coupling ratios in cross and through ports of the directional coupler with a fixed coupling gap 0f 200 nm and unbalanced waveguide widths at the coupling region. (d) The percentage of error for the power coupling ratio due to unbalanced waveguide width with respect to the target design being a pair of balanced 500 nm wide waveguides (T: Through port, C: Cross port, CG: Coupling gap).
Fig. 3
Fig. 3 Weak coupling condition in a 7-stage device. (a) Deviation of a flat-top from its ideal case by increasing the power coupling ratio (DEV: Deviation). (b) Power spectral response (PSR) of the device at bus- and main-waveguides for different values of coupling coefficient. It is shown that, increasing the PSR peak up to 50% of its maximum value (PSR at the output of the main-waveguide), the device still offers the desired weak-coupling performance, so that the flat-top only deviates as much as ~6% with respect to the ideal case.
Fig. 4
Fig. 4 (a) Schematic of the flat-top optical pulse generator; (b-c) Profile of the coupling coefficients for the flat-top pulse shaper made of ten and twenty cascaded couplers, respectively; (d-e) Output pulses generated from the designed device for 100 times simulations with random fluctuations in the fabrication parameters, as detailed in the text; (f-g) PSRs from the main and bus-waveguides (red and black solid lines, respectively), and input pulse spectrum (pink, dashed line). (h-i) PSRs from the main and bus-waveguides in logarithmic scale (red and black solid lines, respectively). PSRs are shown only for a single simulation.
Fig. 5
Fig. 5 (a) Maximum phase variation of ~0.25 rad has been observed for the 1.7-ps, flat-top pulse synthesis design. (b) The phase profile of the flat-top pulse after repeating the simulation for 100 times.
Fig. 6
Fig. 6 (a) Schematic of the QAM optical pulse generator; (b) Profile of the amplitude and phase of the coupling coefficients for the QAM pulse coder; (c) Constellation diagram of the 16-QAM modulated signal; (d) 24 Gsymbol/s QAM code; (e) PSRs from main and bus-waveguides.

Tables (1)

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Table 1 Weak coupling condition for n couplers. MA stands for maximum relative deviation of the waveform with respect to the ideal one along the flat-top region.

Equations (10)

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{ r 0 ( t ) = δ ( t ) s 0 ( t ) = 0
{ r 1 ( t ) = 1 κ 0 δ ( t τ ) δ ( t τ ) s 1 ( t ) = j κ 0 δ ( t )
{ r 2 ( t ) = 1 κ 0 1 κ 1 δ ( t 2 τ ) κ 0 κ 1 δ ( t τ ) δ ( t 2 τ ) s 2 ( t ) = j κ 0 1 κ 1 δ ( t ) + j κ 1 1 κ 0 δ ( t τ ) j κ 0 δ ( t ) + j κ 1 δ ( t τ )
{ r n ( t ) δ ( t n τ ) s n ( t ) j i = 0 n 1 κ i δ ( t i τ )
h ( t ) = s n ( t ) j i = 0 n 1 κ i δ ( t i τ )
T w a v e g u i d e , i = [ exp ( j ( 2 π n e f f ( λ ) λ ) L u , i + α l o s s , u L u , i ) 0 0 exp ( j ( 2 π n e f f ( λ ) λ ) L l , i + α l o s s , l L l , i ) ]
T c o u p l e r , i = [ 1 κ i ( λ ) j κ i ( λ ) j κ i ( λ ) 1 κ i ( λ ) ]
[ ( s i + 1 ( t ) ) ( r i + 1 ( t ) ) ] = T c o u p l e r , i T w a v e g u i d e , i [ ( s i ( t ) ) ( r i ( t ) ) ]
T = ( i = n 1 1 T c o u p l e r , i T w a v e g u i d e , i ) T c o u p l e r , 0
T = [ T 11 T 12 T 21 T 22 ]

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