Electronically tunable optical true-time delay lines are proposed. The devices utilize the combination of apodised gratings and the free-carrier plasma effect to tune the enhanced delay of silicon waveguides at a fixed wavelength. Three variations of the proposed scheme are studied and compared. The compact and integrable devices can achieve tuning ranges as high as ~660 ps with a loss of < 2.2 dB when operated in the reflection mode of the gratings. A delay of ~40 ps with a loss of < 10 dB and an estimated operation bit rate of ~20 Gb/s can be achieved.

© 2011 OSA

1. J. L. Corral, J. Marti, J. M. Fuster, and R. I. Laming, “True time-delay scheme for feeding optically controlled phased-array antennas using chirped-fiber gratings,” IEEE Photon. Technol. Lett. 9(11), 1529–1531 (1997). [CrossRef]
2. Y. Okawachi, M. A. Foster, X. Chen, A. C. Turner-Foster, R. Salem, M. Lipson, C. Xu, and A. L. Gaeta, “Large tunable delays using parametric mixing and phase conjugation in Si nanowaveguides,” Opt. Express 16(14), 10349–10357 (2008). [CrossRef] [PubMed]
3. E. Choi, J. Na, S. Ryu, G. Mudhana, and B. Lee, “All-fiber variable optical delay line for applications in optical coherence tomography: feasibility study for a novel delay line,” Opt. Express 13(4), 1334–1345 (2005). [CrossRef] [PubMed]
4. V. Italia, M. Pisco, S. Campopiano, A. Cusano, and A. Cutolo, “Chirped fiber Bragg gratings for electrically tunable delay lines,” IEEE J. Sel. Top. Quantum Electron. 11(2), 408–416 (2005). [CrossRef]
5. M. Pisco, S. Campopiano, A. Cutolo, and A. Cusano, “Continuously variable optical delay line based on a chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 18(24), 2551–2553 (2006). [CrossRef]
6. B. Ortega, J. L. Cruz, J. Capmany, M. V. Andrés, and D. Pastor, “Analysis of a microwave time delay based on a perturbed uniform fiber Bragg grating operating at constant wavelength,” J. Lightwave Technol. 18(3), 430–436 (2000). [CrossRef]
7. S. Yegnanarayanan, P. D. Trinh, F. Coppinger, and B. Jalali, “Compact silicon-based integrated optic time delays,” IEEE Photon. Technol. Lett. 9(5), 634–635 (1997). [CrossRef]
8. J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20(12), 1030–1032 (2008). [CrossRef]
9. A. Melloni, F. Morichetti, C. Ferrari, and M. Martinelli, “Continuously tunable 1 byte delay in coupled-resonator optical waveguides,” Opt. Lett. 33(20), 2389–2391 (2008). [CrossRef] [PubMed]
10. J. Cardenas, M. A. Foster, N. Sherwood-Droz, C. B. Poitras, H. L. R. Lira, B. Zhang, A. L. Gaeta, J. B. Khurgin, P. Morton, and M. Lipson, “Wide-bandwidth continuously tunable optical delay line using silicon microring resonators,” Opt. Express 18(25), 26525–26534 (2010). [CrossRef] [PubMed]
11. A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photon. J. 2(2), 181–194 (2010). [CrossRef]
12. F. Xia, L. Sekaric, and Y. Yurii, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007). [CrossRef]
13. F. Morichetti, A. Melloni, C. Ferrari, and M. Martinelli, “Error-free continuously-tunable delay at 10 Gbit/s in a reconfigurable on-chip delay-line,” Opt. Express 16(12), 8395–8405 (2008). [CrossRef] [PubMed]
14. Y. Q. Jiang, W. Jiang, X. Chen, L. Gu, B. Howley, and R. T. Chen, “Nano-photonic crystal waveguides for ultra-compact tunable true time delay lines,” Proc. SPIE 5733, 166–175 (2005). [CrossRef]
15. J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “Wide range tuning of slow light pulse in SOI photonic crystal coupled waveguide via folded chirping,” IEEE J. Sel. Top. Quantum Electron. 16(1), 192–199 (2010). [CrossRef]
16. M. S. Rasras, C. K. Madsen, M. A. Cappuzzo, E. Chen, L. T. Gomez, E. J. Laskowski, A. Griffin, A. Wong-Foy, A. Gasparyan, A. Kasper, J. Le Grange, and S. S. Patel, “Integrated resonance-enhanced variable optical delay lines,” IEEE Photon. Technol. Lett. 17(4), 834–836 (2005). [CrossRef]
17. G. Bjork and O. Nilsson, “A new exact and efficient numerical matrix theory of complicated laser structures: properties of asymmetric phase-shifted DFB lasers,” J. Lightwave Technol. 5(1), 140–146 (1987). [CrossRef]
18. J. Hong, W. Huang, and T. Makino, “On the transfer matrix method for distributed-feedback waveguide devices,” J. Lightwave Technol. 10(12), 1860–1868 (1992). [CrossRef]
19. T. Makino, “Effective-index matrix analysis of distributed feedback semiconductor lasers,” J. Lightwave Technol. 28, 434–440 (1992).
20. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), p. 102.
21. R. A. Soref and B. R. Bennett, “Kramers-Kronig analysis of E-O switching in silicon,” Proc. SPIE 704, 32–37 (1986).
22. S. Fathpour, K. K. Tsia, and B. Jalali, “Two-photon photovoltaic effect in silicon,” J. Lightwave Technol. 3, 1211–1217 (2007).
23. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]
24. N. A. Riza, M. A. Arain, and S. A. Khan, “Hybrid analog–digital variable fiber-optic delay line,” J. Lightwave Technol. 22(2), 619–624 (2004). [CrossRef]
25. G. P. Agrawal, Fiber-optic communication systems (Wiley, New York, 2002), p. 26.
26. A. Ghatak and K. Thyagarajan, Introduction to fiber optics (Cambridge, UK, 1898), p. 257.
27. G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).
28. X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).
29. S. Ahn, J. Lee, J. Kim, S. Kim, S. H. Lee, J. Park, and P. Yoon, “Fabrication of subwavelength aluminum wire grating using nanoimprint lithography and reactive ion etching,” Microelectron. Eng. 78–79, 314–318 (2005). [CrossRef]
30. B. D. Lucas, J.-S. Kim, C. Chin, and L. J. Guo, “Nanoimprint lithography based approach for the fabrication of large-area, uniformly oriented plasmonic arrays,” Adv. Mater. (Deerfield Beach Fla.) 20(6), 1129–1134 (2008). [CrossRef]
31. S. Grego, A. Huffman, M. Lueck, B. R. Stoner, and J. Lannon, “Nanoimprint lithography fabrication of waveguide-integrated optical gratings with inexpensive stamps,” Microelectron. Eng. 87(10), 1846–1851 (2010). [CrossRef]
32. M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Slow-light, band-edge waveguides for tunable time delays,” Opt. Express 13(18), 7145–7159 (2005). [CrossRef] [PubMed]
33. J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Delage, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” in Advances in Optical Technologies 2008, Article ID 685489, Hindawi Publishing Corporation, 2008.

Adv. Mater. (Deerfield Beach Fla.)

• B. D. Lucas, J.-S. Kim, C. Chin, and L. J. Guo, “Nanoimprint lithography based approach for the fabrication of large-area, uniformly oriented plasmonic arrays,” Adv. Mater. (Deerfield Beach Fla.) 20(6), 1129–1134 (2008). [CrossRef]

IEEE J. Sel. Top. Quantum Electron.

• V. Italia, M. Pisco, S. Campopiano, A. Cusano, and A. Cutolo, “Chirped fiber Bragg gratings for electrically tunable delay lines,” IEEE J. Sel. Top. Quantum Electron. 11(2), 408–416 (2005). [CrossRef]
• J. Adachi, N. Ishikura, H. Sasaki, and T. Baba, “Wide range tuning of slow light pulse in SOI photonic crystal coupled waveguide via folded chirping,” IEEE J. Sel. Top. Quantum Electron. 16(1), 192–199 (2010). [CrossRef]

IEEE Photon. J.

• A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photon. J. 2(2), 181–194 (2010). [CrossRef]

IEEE Photon. Technol. Lett.

• M. Pisco, S. Campopiano, A. Cutolo, and A. Cusano, “Continuously variable optical delay line based on a chirped fiber Bragg grating,” IEEE Photon. Technol. Lett. 18(24), 2551–2553 (2006). [CrossRef]
• J. L. Corral, J. Marti, J. M. Fuster, and R. I. Laming, “True time-delay scheme for feeding optically controlled phased-array antennas using chirped-fiber gratings,” IEEE Photon. Technol. Lett. 9(11), 1529–1531 (1997). [CrossRef]
• M. S. Rasras, C. K. Madsen, M. A. Cappuzzo, E. Chen, L. T. Gomez, E. J. Laskowski, A. Griffin, A. Wong-Foy, A. Gasparyan, A. Kasper, J. Le Grange, and S. S. Patel, “Integrated resonance-enhanced variable optical delay lines,” IEEE Photon. Technol. Lett. 17(4), 834–836 (2005). [CrossRef]
• S. Yegnanarayanan, P. D. Trinh, F. Coppinger, and B. Jalali, “Compact silicon-based integrated optic time delays,” IEEE Photon. Technol. Lett. 9(5), 634–635 (1997). [CrossRef]
• J. Yang, N. K. Fontaine, Z. Pan, A. O. Karalar, S. S. Djordjevic, C. Yang, W. Chen, S. Chu, B. E. Little, and S. J. B. Yoo, “Continuously tunable, wavelength-selective buffering in optical packet switching networks,” IEEE Photon. Technol. Lett. 20(12), 1030–1032 (2008). [CrossRef]
• G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).
• X. Wang, W. Shi, R. Vafaei, N. A. F. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

J. Lightwave Technol.

• S. Fathpour, K. K. Tsia, and B. Jalali, “Two-photon photovoltaic effect in silicon,” J. Lightwave Technol. 3, 1211–1217 (2007).
• T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]
• N. A. Riza, M. A. Arain, and S. A. Khan, “Hybrid analog–digital variable fiber-optic delay line,” J. Lightwave Technol. 22(2), 619–624 (2004). [CrossRef]
• G. Bjork and O. Nilsson, “A new exact and efficient numerical matrix theory of complicated laser structures: properties of asymmetric phase-shifted DFB lasers,” J. Lightwave Technol. 5(1), 140–146 (1987). [CrossRef]
• J. Hong, W. Huang, and T. Makino, “On the transfer matrix method for distributed-feedback waveguide devices,” J. Lightwave Technol. 10(12), 1860–1868 (1992). [CrossRef]
• T. Makino, “Effective-index matrix analysis of distributed feedback semiconductor lasers,” J. Lightwave Technol. 28, 434–440 (1992).
• B. Ortega, J. L. Cruz, J. Capmany, M. V. Andrés, and D. Pastor, “Analysis of a microwave time delay based on a perturbed uniform fiber Bragg grating operating at constant wavelength,” J. Lightwave Technol. 18(3), 430–436 (2000). [CrossRef]

Microelectron. Eng.

• S. Grego, A. Huffman, M. Lueck, B. R. Stoner, and J. Lannon, “Nanoimprint lithography fabrication of waveguide-integrated optical gratings with inexpensive stamps,” Microelectron. Eng. 87(10), 1846–1851 (2010). [CrossRef]
• S. Ahn, J. Lee, J. Kim, S. Kim, S. H. Lee, J. Park, and P. Yoon, “Fabrication of subwavelength aluminum wire grating using nanoimprint lithography and reactive ion etching,” Microelectron. Eng. 78–79, 314–318 (2005). [CrossRef]

Nat. Photonics

• F. Xia, L. Sekaric, and Y. Yurii, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007). [CrossRef]

Opt. Express

• F. Morichetti, A. Melloni, C. Ferrari, and M. Martinelli, “Error-free continuously-tunable delay at 10 Gbit/s in a reconfigurable on-chip delay-line,” Opt. Express 16(12), 8395–8405 (2008). [CrossRef] [PubMed]
• Y. Okawachi, M. A. Foster, X. Chen, A. C. Turner-Foster, R. Salem, M. Lipson, C. Xu, and A. L. Gaeta, “Large tunable delays using parametric mixing and phase conjugation in Si nanowaveguides,” Opt. Express 16(14), 10349–10357 (2008). [CrossRef] [PubMed]
• E. Choi, J. Na, S. Ryu, G. Mudhana, and B. Lee, “All-fiber variable optical delay line for applications in optical coherence tomography: feasibility study for a novel delay line,” Opt. Express 13(4), 1334–1345 (2005). [CrossRef] [PubMed]
• J. Cardenas, M. A. Foster, N. Sherwood-Droz, C. B. Poitras, H. L. R. Lira, B. Zhang, A. L. Gaeta, J. B. Khurgin, P. Morton, and M. Lipson, “Wide-bandwidth continuously tunable optical delay line using silicon microring resonators,” Opt. Express 18(25), 26525–26534 (2010). [CrossRef] [PubMed]
• M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Slow-light, band-edge waveguides for tunable time delays,” Opt. Express 13(18), 7145–7159 (2005). [CrossRef] [PubMed]

Opt. Lett.

• A. Melloni, F. Morichetti, C. Ferrari, and M. Martinelli, “Continuously tunable 1 byte delay in coupled-resonator optical waveguides,” Opt. Lett. 33(20), 2389–2391 (2008). [CrossRef] [PubMed]

Proc. SPIE

• R. A. Soref and B. R. Bennett, “Kramers-Kronig analysis of E-O switching in silicon,” Proc. SPIE 704, 32–37 (1986).
• Y. Q. Jiang, W. Jiang, X. Chen, L. Gu, B. Howley, and R. T. Chen, “Nano-photonic crystal waveguides for ultra-compact tunable true time delay lines,” Proc. SPIE 5733, 166–175 (2005). [CrossRef]

Other

• P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), p. 102.
• J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Delage, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” in Advances in Optical Technologies 2008, Article ID 685489, Hindawi Publishing Corporation, 2008.
• G. P. Agrawal, Fiber-optic communication systems (Wiley, New York, 2002), p. 26.
• A. Ghatak and K. Thyagarajan, Introduction to fiber optics (Cambridge, UK, 1898), p. 257.

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