Abstract

We introduce a dynamic optical arbitrary waveform generation (OAWG) technique that produces bandwidth scalable, continuous waveforms of near perfect fidelity. Additionally, OAWG’s complement, real-time arbitrary optical waveform measurement (OAWM) is discussed. These approaches utilize gigahertz-bandwidth electronics to generate, or measure, truly arbitrary and dynamic optical waveforms scalable to terahertz bandwidths and infinite record lengths. We describe the theory, algorithms and enabling technologies necessary to calculate and produce a set of spectral modulations that create continuous, high-fidelity waveforms in the presence of spectral filtering from multiplexers.

© 2010 OSA

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  1. K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, “Flexible pulse waveform generation using silica-waveguide-based spectrum synthesis circuit,” Electron. Lett. 40(9), 537–538 (2004).
    [CrossRef]
  2. Z. Jiang, D. E. Leaird, and A. M. Weiner, “Line-by-line pulse shaping control for optical arbitrary waveform generation,” Opt. Express 13(25), 10431–10439 (2005).
    [CrossRef] [PubMed]
  3. P. J. Delfyett, S. Gee, C. Myoung-Taek, H. Izadpanah, L. Wangkuen, S. Ozharar, F. Quinlan, and T. Yilmaz, “Optical frequency combs from semiconductor lasers and applications in ultrawideband signal processing and communications,” J. Lightwave Technol. 24(7), 2701–2719 (2006).
    [CrossRef]
  4. N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. Yoo, “32 Phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 (2007).
    [CrossRef] [PubMed]
  5. R. P. Scott, N. K. Fontaine, J. Cao, K. Okamoto, B. H. Kolner, J. P. Heritage, and S. J. B. Yoo, “High-fidelity line-by-line optical waveform generation and complete characterization using FROG,” Opt. Express 15(16), 9977–9988 (2007).
    [CrossRef] [PubMed]
  6. Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
    [CrossRef]
  7. R. P. Scott, N. K. Fontaine, C. Yang, D. J. Geisler, K. Okamoto, J. P. Heritage, and S. J. B. Yoo, “Rapid updating of optical arbitrary waveforms via time-domain multiplexing,” Opt. Lett. 33(10), 1068–1070 (2008).
    [CrossRef] [PubMed]
  8. N. K. Fontaine, R. P. Scott, L. Zhou, F. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
    [CrossRef]
  9. N. K. Fontaine, “Optical arbitrary waveform generation and measurement,” Ph.D. dissertation (University of California, Davis, 2010).
  10. 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 (submitted for publication).
    [PubMed]
  11. N. K. Fontaine, R. P. Scott, C. Yang, D. J. Geisler, J. P. Heritage, K. Okamoto, and S. J. B. Yoo, “Compact 10 GHz loopback arrayed-waveguide grating for high-fidelity optical arbitrary waveform generation,” Opt. Lett. 33(15), 1714–1716 (2008).
    [CrossRef] [PubMed]
  12. F. M. Soares, J. H. Baek, N. K. Fontaine, X. Zhou, Y. Wang, R. P. Scott, J. P. Heritage, C. Junesand, S. Lourdudoss, K. Y. Liou, R. A. Hamm, W. Wang, B. Patel, S. Vatanapradit, L. A. Gruezke, W. T. Tsang, and S. J. B. Yoo, “Monolithically integrated InP wafer-scale 100-channel × 10-GHz AWG and Michelson interferometers for 1-THz-bandwidth optical arbitrary waveform generation,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), Paper OThS1.
  13. T. He, N. K. Fontaine, R. P. Scott, D. J. Geisler, J. P. Heritage, and S. J. B. Yoo, “Optical arbitrary waveform generation based packet generation and all-optical separation for optical-label switching,” IEEE Photon. Technol. Lett. 22(10), 715–717 (2010).
    [CrossRef]
  14. D. J. Geisler, N. K. Fontaine, T. He, R. P. Scott, L. Paraschis, J. P. Heritage, and S. J. Yoo, “Modulation-format agile, reconfigurable Tb/s transmitter based on optical arbitrary waveform generation,” Opt. Express 17(18), 15911–15925 (2009).
    [CrossRef] [PubMed]
  15. C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Time-multiplexed photonically enabled radio-frequency arbitrary waveform generation with 100 ps transitions,” Opt. Lett. 32(22), 3242–3244 (2007).
    [CrossRef] [PubMed]
  16. J. T. Willits, A. M. Weiner, and S. T. Cundiff, “Theory of rapid-update line-by-line pulse shaping,” Opt. Express 16(1), 315–327 (2008).
    [CrossRef] [PubMed]
  17. R. G. Lyons, Understanding Digital Signal Processing, 2nd ed. (Prentice Hall PTR, Upper Saddle River, 2004).
  18. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic, Boston, 2000).
  19. M. K. Smit and C. Van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. 2(2), 236–250 (1996).
    [CrossRef]
  20. K. Okamoto, “Recent progress of integrated optics planar lightwave circuits,” Opt. Quantum Electron. 31(2), 107–129 (1999).
    [CrossRef]
  21. N. K. Fontaine, Y. Jie, J. Wei, D. J. Geisler, K. Okamoto, H. Ray, and S. Yoo, “Active arrayed-waveguide grating with amplitude and phase control for arbitrary filter generation and high-order dispersion compensation,” in 34th European Conference on Optical Communication (ECOC 2008), Technical Digest (CD) (IEEE, 2008), 1–2. http://dx.doi.org/10.1109/ECOC.2008.4729152

2010 (2)

N. K. Fontaine, R. P. Scott, L. Zhou, F. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[CrossRef]

T. He, N. K. Fontaine, R. P. Scott, D. J. Geisler, J. P. Heritage, and S. J. B. Yoo, “Optical arbitrary waveform generation based packet generation and all-optical separation for optical-label switching,” IEEE Photon. Technol. Lett. 22(10), 715–717 (2010).
[CrossRef]

2009 (1)

2008 (3)

2007 (4)

2006 (1)

2005 (1)

2004 (1)

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, “Flexible pulse waveform generation using silica-waveguide-based spectrum synthesis circuit,” Electron. Lett. 40(9), 537–538 (2004).
[CrossRef]

1999 (1)

K. Okamoto, “Recent progress of integrated optics planar lightwave circuits,” Opt. Quantum Electron. 31(2), 107–129 (1999).
[CrossRef]

1996 (1)

M. K. Smit and C. Van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. 2(2), 236–250 (1996).
[CrossRef]

Cao, J.

Cundiff, S. T.

Delfyett, P. J.

Fontaine, N. K.

T. He, N. K. Fontaine, R. P. Scott, D. J. Geisler, J. P. Heritage, and S. J. B. Yoo, “Optical arbitrary waveform generation based packet generation and all-optical separation for optical-label switching,” IEEE Photon. Technol. Lett. 22(10), 715–717 (2010).
[CrossRef]

N. K. Fontaine, R. P. Scott, L. Zhou, F. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[CrossRef]

D. J. Geisler, N. K. Fontaine, T. He, R. P. Scott, L. Paraschis, J. P. Heritage, and S. J. Yoo, “Modulation-format agile, reconfigurable Tb/s transmitter based on optical arbitrary waveform generation,” Opt. Express 17(18), 15911–15925 (2009).
[CrossRef] [PubMed]

R. P. Scott, N. K. Fontaine, C. Yang, D. J. Geisler, K. Okamoto, J. P. Heritage, and S. J. B. Yoo, “Rapid updating of optical arbitrary waveforms via time-domain multiplexing,” Opt. Lett. 33(10), 1068–1070 (2008).
[CrossRef] [PubMed]

N. K. Fontaine, R. P. Scott, C. Yang, D. J. Geisler, J. P. Heritage, K. Okamoto, and S. J. B. Yoo, “Compact 10 GHz loopback arrayed-waveguide grating for high-fidelity optical arbitrary waveform generation,” Opt. Lett. 33(15), 1714–1716 (2008).
[CrossRef] [PubMed]

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. Yoo, “32 Phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 (2007).
[CrossRef] [PubMed]

R. P. Scott, N. K. Fontaine, J. Cao, K. Okamoto, B. H. Kolner, J. P. Heritage, and S. J. B. Yoo, “High-fidelity line-by-line optical waveform generation and complete characterization using FROG,” Opt. Express 15(16), 9977–9988 (2007).
[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 (submitted for publication).
[PubMed]

Gee, S.

Geisler, D. J.

He, T.

T. He, N. K. Fontaine, R. P. Scott, D. J. Geisler, J. P. Heritage, and S. J. B. Yoo, “Optical arbitrary waveform generation based packet generation and all-optical separation for optical-label switching,” IEEE Photon. Technol. Lett. 22(10), 715–717 (2010).
[CrossRef]

D. J. Geisler, N. K. Fontaine, T. He, R. P. Scott, L. Paraschis, J. P. Heritage, and S. J. Yoo, “Modulation-format agile, reconfigurable Tb/s transmitter based on optical arbitrary waveform generation,” Opt. Express 17(18), 15911–15925 (2009).
[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 (submitted for publication).
[PubMed]

Heritage, J. P.

N. K. Fontaine, R. P. Scott, L. Zhou, F. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[CrossRef]

T. He, N. K. Fontaine, R. P. Scott, D. J. Geisler, J. P. Heritage, and S. J. B. Yoo, “Optical arbitrary waveform generation based packet generation and all-optical separation for optical-label switching,” IEEE Photon. Technol. Lett. 22(10), 715–717 (2010).
[CrossRef]

D. J. Geisler, N. K. Fontaine, T. He, R. P. Scott, L. Paraschis, J. P. Heritage, and S. J. Yoo, “Modulation-format agile, reconfigurable Tb/s transmitter based on optical arbitrary waveform generation,” Opt. Express 17(18), 15911–15925 (2009).
[CrossRef] [PubMed]

R. P. Scott, N. K. Fontaine, C. Yang, D. J. Geisler, K. Okamoto, J. P. Heritage, and S. J. B. Yoo, “Rapid updating of optical arbitrary waveforms via time-domain multiplexing,” Opt. Lett. 33(10), 1068–1070 (2008).
[CrossRef] [PubMed]

N. K. Fontaine, R. P. Scott, C. Yang, D. J. Geisler, J. P. Heritage, K. Okamoto, and S. J. B. Yoo, “Compact 10 GHz loopback arrayed-waveguide grating for high-fidelity optical arbitrary waveform generation,” Opt. Lett. 33(15), 1714–1716 (2008).
[CrossRef] [PubMed]

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. Yoo, “32 Phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 (2007).
[CrossRef] [PubMed]

R. P. Scott, N. K. Fontaine, J. Cao, K. Okamoto, B. H. Kolner, J. P. Heritage, and S. J. B. Yoo, “High-fidelity line-by-line optical waveform generation and complete characterization using FROG,” Opt. Express 15(16), 9977–9988 (2007).
[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 (submitted for publication).
[PubMed]

Huang, C.-B.

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[CrossRef]

C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Time-multiplexed photonically enabled radio-frequency arbitrary waveform generation with 100 ps transitions,” Opt. Lett. 32(22), 3242–3244 (2007).
[CrossRef] [PubMed]

Izadpanah, H.

Jiang, W.

Jiang, Z.

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[CrossRef]

Z. Jiang, D. E. Leaird, and A. M. Weiner, “Line-by-line pulse shaping control for optical arbitrary waveform generation,” Opt. Express 13(25), 10431–10439 (2005).
[CrossRef] [PubMed]

Karalar, A.

Kolner, B. H.

Kominato, T.

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, “Flexible pulse waveform generation using silica-waveguide-based spectrum synthesis circuit,” Electron. Lett. 40(9), 537–538 (2004).
[CrossRef]

Leaird, D. E.

Myoung-Taek, C.

Okamoto, K.

Ozharar, S.

Paraschis, L.

Quinlan, F.

Scott, R. P.

T. He, N. K. Fontaine, R. P. Scott, D. J. Geisler, J. P. Heritage, and S. J. B. Yoo, “Optical arbitrary waveform generation based packet generation and all-optical separation for optical-label switching,” IEEE Photon. Technol. Lett. 22(10), 715–717 (2010).
[CrossRef]

N. K. Fontaine, R. P. Scott, L. Zhou, F. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[CrossRef]

D. J. Geisler, N. K. Fontaine, T. He, R. P. Scott, L. Paraschis, J. P. Heritage, and S. J. Yoo, “Modulation-format agile, reconfigurable Tb/s transmitter based on optical arbitrary waveform generation,” Opt. Express 17(18), 15911–15925 (2009).
[CrossRef] [PubMed]

R. P. Scott, N. K. Fontaine, C. Yang, D. J. Geisler, K. Okamoto, J. P. Heritage, and S. J. B. Yoo, “Rapid updating of optical arbitrary waveforms via time-domain multiplexing,” Opt. Lett. 33(10), 1068–1070 (2008).
[CrossRef] [PubMed]

N. K. Fontaine, R. P. Scott, C. Yang, D. J. Geisler, J. P. Heritage, K. Okamoto, and S. J. B. Yoo, “Compact 10 GHz loopback arrayed-waveguide grating for high-fidelity optical arbitrary waveform generation,” Opt. Lett. 33(15), 1714–1716 (2008).
[CrossRef] [PubMed]

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. Yoo, “32 Phase X 32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32(7), 865–867 (2007).
[CrossRef] [PubMed]

R. P. Scott, N. K. Fontaine, J. Cao, K. Okamoto, B. H. Kolner, J. P. Heritage, and S. J. B. Yoo, “High-fidelity line-by-line optical waveform generation and complete characterization using FROG,” Opt. Express 15(16), 9977–9988 (2007).
[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 (submitted for publication).
[PubMed]

Shibata, T.

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, “Flexible pulse waveform generation using silica-waveguide-based spectrum synthesis circuit,” Electron. Lett. 40(9), 537–538 (2004).
[CrossRef]

Smit, M. K.

M. K. Smit and C. Van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. 2(2), 236–250 (1996).
[CrossRef]

Soares, F.

N. K. Fontaine, R. P. Scott, L. Zhou, F. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[CrossRef]

Takahashi, H.

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, “Flexible pulse waveform generation using silica-waveguide-based spectrum synthesis circuit,” Electron. Lett. 40(9), 537–538 (2004).
[CrossRef]

Takiguchi, K.

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, “Flexible pulse waveform generation using silica-waveguide-based spectrum synthesis circuit,” Electron. Lett. 40(9), 537–538 (2004).
[CrossRef]

Van Dam, C.

M. K. Smit and C. Van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. 2(2), 236–250 (1996).
[CrossRef]

Wangkuen, L.

Weiner, A. M.

Willits, J. T.

Yang, C.

Yilmaz, T.

Yoo, S. J.

Yoo, S. J. B.

T. He, N. K. Fontaine, R. P. Scott, D. J. Geisler, J. P. Heritage, and S. J. B. Yoo, “Optical arbitrary waveform generation based packet generation and all-optical separation for optical-label switching,” IEEE Photon. Technol. Lett. 22(10), 715–717 (2010).
[CrossRef]

N. K. Fontaine, R. P. Scott, L. Zhou, F. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[CrossRef]

N. K. Fontaine, R. P. Scott, C. Yang, D. J. Geisler, J. P. Heritage, K. Okamoto, and S. J. B. Yoo, “Compact 10 GHz loopback arrayed-waveguide grating for high-fidelity optical arbitrary waveform generation,” Opt. Lett. 33(15), 1714–1716 (2008).
[CrossRef] [PubMed]

R. P. Scott, N. K. Fontaine, C. Yang, D. J. Geisler, K. Okamoto, J. P. Heritage, and S. J. B. Yoo, “Rapid updating of optical arbitrary waveforms via time-domain multiplexing,” Opt. Lett. 33(10), 1068–1070 (2008).
[CrossRef] [PubMed]

R. P. Scott, N. K. Fontaine, J. Cao, K. Okamoto, B. H. Kolner, J. P. Heritage, and S. J. B. Yoo, “High-fidelity line-by-line optical waveform generation and complete characterization using FROG,” Opt. Express 15(16), 9977–9988 (2007).
[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 (submitted for publication).
[PubMed]

Zhou, L.

N. K. Fontaine, R. P. Scott, L. Zhou, F. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[CrossRef]

Electron. Lett. (1)

K. Takiguchi, K. Okamoto, T. Kominato, H. Takahashi, and T. Shibata, “Flexible pulse waveform generation using silica-waveguide-based spectrum synthesis circuit,” Electron. Lett. 40(9), 537–538 (2004).
[CrossRef]

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

M. K. Smit and C. Van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. 2(2), 236–250 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. He, N. K. Fontaine, R. P. Scott, D. J. Geisler, J. P. Heritage, and S. J. B. Yoo, “Optical arbitrary waveform generation based packet generation and all-optical separation for optical-label switching,” IEEE Photon. Technol. Lett. 22(10), 715–717 (2010).
[CrossRef]

J. Lightwave Technol. (1)

Nat. Photonics (2)

N. K. Fontaine, R. P. Scott, L. Zhou, F. Soares, J. P. Heritage, and S. J. B. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4(4), 248–254 (2010).
[CrossRef]

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[CrossRef]

Opt. Express (5)

Opt. Lett. (4)

Opt. Quantum Electron. (1)

K. Okamoto, “Recent progress of integrated optics planar lightwave circuits,” Opt. Quantum Electron. 31(2), 107–129 (1999).
[CrossRef]

Other (5)

N. K. Fontaine, Y. Jie, J. Wei, D. J. Geisler, K. Okamoto, H. Ray, and S. Yoo, “Active arrayed-waveguide grating with amplitude and phase control for arbitrary filter generation and high-order dispersion compensation,” in 34th European Conference on Optical Communication (ECOC 2008), Technical Digest (CD) (IEEE, 2008), 1–2. http://dx.doi.org/10.1109/ECOC.2008.4729152

R. G. Lyons, Understanding Digital Signal Processing, 2nd ed. (Prentice Hall PTR, Upper Saddle River, 2004).

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic, Boston, 2000).

F. M. Soares, J. H. Baek, N. K. Fontaine, X. Zhou, Y. Wang, R. P. Scott, J. P. Heritage, C. Junesand, S. Lourdudoss, K. Y. Liou, R. A. Hamm, W. Wang, B. Patel, S. Vatanapradit, L. A. Gruezke, W. T. Tsang, and S. J. B. Yoo, “Monolithically integrated InP wafer-scale 100-channel × 10-GHz AWG and Michelson interferometers for 1-THz-bandwidth optical arbitrary waveform generation,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), Paper OThS1.

N. K. Fontaine, “Optical arbitrary waveform generation and measurement,” Ph.D. dissertation (University of California, Davis, 2010).

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Figures (12)

Fig. 1
Fig. 1

An illustration which shows a typical static-OAWG arrangement for waveform shaping via Fourier synthesis. M 1Mn represent modulators that adjust the relative amplitude and phase of the comb lines. Spectral power is represented by arrow height and phase by the vertical position of the dashed line.

Fig. 2
Fig. 2

Overview of dynamic-OAWG. (a) Each line of an OFC is simultaneously and independently modulated to create the desired spectral slices. A gapless multiplexer coherently combines the spectral slices to create the desired waveform. (b) In DSP, the target waveform is temporally sliced into subwaveforms. (c) The subwaveforms are spectrally sliced. (d) Baseband electrical I/Q modulations are calculated and produced. DAC: digital-to-analog converter.

Fig. 3
Fig. 3

(a) A complex modulation example showing the amplitude and phase of a 400-ps-long trajectory across the real-imaginary plane. (b) Corresponding calculated complex optical spectrum of the trajectory. ω 0 is the optical carrier.

Fig. 4
Fig. 4

Two different optical vector modulator structures. (a) Amplitude and phase modulators. (b) Electrical signals required to recreate the trajectory in Fig. 3(a). (c) Electrical power spectra of signals in (b). (d) I/Q modulator. (e) Electrical signals required to recreate the trajectory in Fig. 3(a). (f) Electrical power spectra of signals in (e).

Fig. 5
Fig. 5

Illustration of an arbitrary filter arrayed-waveguide grating (AWG).

Fig. 6
Fig. 6

Transmission measurements of an arbitrary filter AWG when configured for three different passband shapes. (a) A low-loss, narrow-bandwidth, and high adjacent-channel isolation passband. (b) A gapless, flat-top passband. (c) A gapless, broad-bandwidth passband (defocused AWG).

Fig. 7
Fig. 7

Examples of two frequency combs with different sets of Rn. (a) Spectral coefficients for a zero-π pulse and (b) a transform-limited pulse. (c) Corresponding time domain plots where shading indicates coefficients used.

Fig. 8
Fig. 8

Examples of slice filters in the (a,b) time and (c,d) frequency domains. Temporal slice filters have flexible spacing, TS . Spectral slice filters are at the OFC repetition rate (1/T).

Fig. 9
Fig. 9

Simulation example of the spectral-slice OAWG algorithm applied to a (a) periodic transform limited waveform, and (b) isolated transform limited waveform. (0.1) Temporal waveform. (0.2) Waveform spectral intensity. (0.3) Intensity of spectral modulations on three center comb lines. (0.4) Temporal modulations of the center comb line.

Fig. 10
Fig. 10

Selected simulation results using the dynamic-OAWG algorithm for (a) rapid-update static-OAWG and (b) a more optimum case. (0.1) Target a(t) and temporal slice filter w(t). (0.2) Center three subwaveforms, ak (t). (0.3) Center line modulations, mk,n (t), for the three subwaveforms. (0.4) Center line modulation after summing all subwaveform modulations. (0.5) Spectral modulations (i.e., FT of temporal modulations). (0.6) Waveform d(t) (blue) at the output of the multiplexer.

Fig. 11
Fig. 11

Optimization of the dynamic-OAWG algorithm for waveform fidelity and latency. (a,b) Error energy for (a) a rectangular w(t) and (b) an overlapping w(t) in conjunction with the (c) corrected slice filters A, B, C, and D. (d) Comparison of the target and generated waveforms with 1% error (−20 dB) and 0.0001% error (−60 dB).

Fig. 12
Fig. 12

An illustration showing the OAWG and OAWM analogy. BPD: balanced photodiodes.

Equations (7)

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

a R ( t ) = n = + R n exp ( j n Δ ω t ) ,
a m ( t ) = n = + m n ( t ) R n exp ( j n Δ ω t ) .
A ( ω ) = n = + R n M n ( ω n Δ ω ) H n ( ω ) ,
M k , n ( ω n Δ ω ) = [ A k ( ω ) / R n ] [ S n ( ω ) / H n ( ω ) ] .
A k ( ω ) = n = + A k ( ω ) S n ( ω ) ,
m n ( t ) = k = + m k , n ( t ) rect [ ( t k T S ) / T L ] ,
NEE = [ + | μ d ( t ) a ( t ) | 2 d t ] [ + | a ( t ) | 2 d t ] 1

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