Abstract

We propose the use of slow-light, band-edge waveguides for compact, integrated, tunable optical time delays. We show that slow group velocities at the photonic band edge give rise to large changes in time delay for small changes in refractive index, thereby shrinking device size. Figures of merit are introduced to quantify the sensitivity, as well as the accompanying signal degradation due to dispersion. It is shown that exact calculations of the figures of merit for a realistic, three-dimensional grating structure are well predicted by a simple quadratic-band model, simplifying device design. We present adiabatic taper designs that attain <0.1% reflection in short lengths of 10 to 20 times the grating period. We show further that cascading two gratings compensates for signal dispersion and gives rise to a constant tunable time delay across bandwidths greater than 100GHz. Given typical loss values for silicon-on-insulator waveguides, we estimate that gratings can be designed to exhibit tunable delays in the picosecond range using current fabrication technology.

© 2005 Optical Society of America

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Appl. Phys. Lett. (4)

H. Altug and J. Vu�?kovi�?, �??Two-dimensional coupled photonic crystal resonator arrays,�?? Appl. Phys. Lett. 84, 161�??163 (2004).
[CrossRef]

H. Altug and J. Vu�?kovi�?, �??Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays,�?? Appl. Phys. Lett. 86, 111,102 (2005).

D. Mori and T. Baba, �??Dispersion-contolled optical group delay device by chirped photonic crystal waveguides,�?? Appl. Phys. Lett. 85, 1101�??1103 (2004).
[CrossRef]

M. L. Povinelli, S. G. Johnson, E. Lidorikis, J. D. Joannopoulos, and M. Solja�?i�?, �??Effect of a photonic bandgap on scattering from waveguide disorder,�?? Appl. Phys. Lett. 84, 3639�??3641 (2004).
[CrossRef]

Conf. Transparent Optical Networks 2003 (1)

S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Solja�?i�?, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, �??Coupling, scattering and perturbation theory: Semi-analytical analyses of photonic-crystal waveguides,�?? in Proc. 2003 5th Intl. Conf. on Transparent Optical Networks and 2nd Eur opean Symp. on Photonic Crystals, vol. 1, pp. 103�??109 (2003).

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)

S. Mookherjea and A. Yariv, �??Coupled Resonator Optical Waveguides,�?? IEEE J. Sel. Top. Quantum Electron. 8, 448�??456 (2002).

IEEE Photonics Technol. Lett. (2)

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. LeGrange, and S. S. Patel, �??Integrated resonance-enhanced variable delay lines,�?? IEEE Photonics Technol. Lett. 17, 834�??6 (2005).
[CrossRef]

F. Grillot, L. Vivien, S. Laval, S. Pascal, and E. Cassan, �??Size Influence on the Propagation Loss Induced by Sidewall Roughness in Ultrasmall SOI Waveguides,�?? IEEE Photonics Technol. Lett. 16, 1661�??1663 (2004).
[CrossRef]

J. Appl. Phys. (1)

G. E. Jellison and H. H. Burke, �??The temperature depdendence of the refractive index of silicon at elevated temperatures at several laser wavelengths,�?? J. Appl. Phys. 60, 841�??843 (1986).
[CrossRef]

J. Appl. Phys. B (1)

S. G. Johnson, M. L. Povinelli, M. Solja�?i�?, A. Karalis, S. Jacobs, and J. D. Joannopoulos, �??Roughness losses and volume-current methods in photonic-crystal waveguides,�?? J. Appl. Phys. B 81(2�??3), 283�??293 (2005).

J. Lightwave Technol. (1)

J. Opt. A.: Pure Appl. Opt. (1)

J. Liu, B. Shi, D. Zhao, and X. Wang, �??Optical delay in defective photonic bandgap structures,�?? J. Opt. A.: Pure Appl. Opt. 4, 636�??639 (2002).
[CrossRef]

J. Vac. Sci. Technol. B (1)

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, �??Optical waveguides with apodized sidewall gratings via spatial-phase locked electron-beam lithography,�?? J. Vac. Sci. Technol. B 20, 2753�??2757 (2002).
[CrossRef]

Nature (1)

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, �??Photonic-bandgap microcavities in optical waveguides,�?? Nature 390, 143�??145 (1997).
[CrossRef]

Opt. Express (4)

Opt. Lett. (4)

Phys. Rev. A (1)

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, �??Coupled-resonator-induced transparency,�?? Phys. Rev. A 69, 063,804 (2004).

Phys. Rev. E (4)

M. Scalora, R. J. Flynn, S. B. Reinhardt, R. L. Fork, M. J. Bloemer, M. D. Tocci, C. M. Bowden, H. S. Ledbetter, J. M. Bendickson, and R. P. Leavitt, �??Ultrashort pulse propagation at the photonic band edge: Large tunable group delay with minimal distortion and loss,�?? Phys. Rev. E 54(2), R1078�??1081 (1996).
[CrossRef]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, �??Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,�?? Phys. Rev. E 66, 066,608 (2002).

Z. Wang and S. Fan, �??Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines,�?? Phys. Rev. E 68, 066,616 (2003).

M. Solja�?i�?, E. Lidorikis, L. V. Hau, and J. D. Joannopoulos, �??Enhancement of microcavity lifetimes using highly dispersive materials,�?? Phys. Rev. E 71, 026602 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, �??Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,�?? Phys. Rev. Lett. 94, 033,903 (2005).

M. F. Yanik and S. Fan, �??Stopping light all optically,�?? Phys. Rev. Lett. 92, 083,901 (2004).

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, �??Stopping Light in a Waveguide with an All-Optical Analog of Electromagnetically Induced Transparency,�?? Phys. Rev. Lett. 93, 233,903 (2004).

Other (4)

R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Perspective (Academic Press, London, 1998).

M. I. Skolnik, Introduction to Radar Systems, chap. 11.5 (McGraw-Hill, 1980).

J. D. Joannopoulos, R. D. Meade, and J. N.Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 1995).

S. J. Spector, M. W. Geis, and T. Lyszczarz. Private communication.

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