Abstract

We have studied the dispersion of ultrafast pulses in a photonic crystal waveguide as a function of optical frequency, in both experiment and theory. With phase-sensitive and time-resolved near-field microscopy, the light was probed inside the waveguide in a non-invasive manner. The effect of dispersion on the shape of the pulses was determined. As the optical frequency decreased, the group velocity decreased. Simultaneously, the measured pulses were broadened during propagation, due to an increase in group velocity dispersion. On top of that, the pulses exhibited a strong asymmetric distortion as the propagation distance increased. The asymmetry increased as the group velocity decreased. The asymmetry of the pulses is caused by a strong increase of higher-order dispersion. As the group velocity was reduced to 0.116(9)·c, we found group velocity dispersion of -1.1(3)·106 ps2/km and third order dispersion of up to 1.1(4)·105 ps3/km. We have modelled our interferometric measurements and included the full dispersion of the photonic crystal waveguide. Our mathematical model and the experimental findings showed a good correspondence. Our findings show that if the most commonly used slow light regime in photonic crystals is to be exploited, great care has to be taken about higher-order dispersion.

© 2006 Optical Society of America

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    [CrossRef]

2005 (6)

2004 (7)

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, J. Marti, "Analysis of butt coupling in photonic crystals," IEEE J. Quantum Electron. 40, 541-550 (2004)
[CrossRef]

H. Gersen, E.M.P.H. van Dijk, J.P. Korterik, N.F. van Hulst, L. Kuipers, "Phase mapping of ultrashort pulses in bimodal photonic structures: A window on local group velocity dispersion," Phys. Rev. E 70, 066609 (2004)
[CrossRef]

A. Sugitatsu, T. Asano T, S. Noda, "Characterization of line-defect-waveguide lasers in two-dimensional photonic-crystal slabs," Appl. Phys. Lett. 845395-5397 (2004)
[CrossRef]

for a review see M. Soljacic, J.D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nature Mater. 3211-219 (2004)
[CrossRef]

T. Asano, K. Kiyota, D. Kumamoto, B.S. Song, S. Noda, "Time-domain measurement of picosecond light-pulse propagation in a two-dimensional photonic crystal-slab waveguide," Appl. Phys. Lett. 84, 4690-4692 (2004)
[CrossRef]

Y. Sugimoto, Y. Tanaka, N. Ikeda, Y. Nakamura, K. Asakawa, K. Inoue, "Low propagation loss of 0.76 dB/mm in GaAs-based single-line-defect two-dimensional photonic crystal slab waveguides up to 1 cm in length," Opt. Express 12, 1090-1096 (2004) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1090
[CrossRef] [PubMed]

A.Y. Petrov, M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004)
[CrossRef]

2003 (3)

Y. Akahane, T. Asano, B.S. Song, S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003)
[CrossRef] [PubMed]

S. Yamada, Y. Watanabe, Y. Katayama, J.B. Cole, "Simulation of optical pulse propagation in a two-dimensional photonic crystal waveguide using a high accuracy finite-difference time-domain algorithm," J. Appl. Phys. 93, 1859-1864 (2003)
[CrossRef]

H. Gersen, J.P. Korterik, N.F. van Hulst, L. Kuipers, "Tracking ultrashort pulses through dispersive media: Experiment and theory" Phys. Rev. E 68, 026604 (2003)
[CrossRef]

2002 (2)

M.D. Rahn, A.M. Fox, M.S. Skolnick, T.F. Krauss, "Propagation of ultrashort nonlinear pulses through twodimensional AlGaAs high-contrast photonic crystal waveguides," J. Opt. Soc. Am. B 19, 716-721 (2002)
[CrossRef]

K. Inoue, N. Kawai, Y. Sugimoto, N. Ikeda, K. Asakawa, "Observation of small group velocity in twodimensional AlGaAs-based photonic crystal slabs," Phys. Rev. B 65, 121308 (2002)
[CrossRef]

2001 (4)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001)
[CrossRef] [PubMed]

E. Chow, S.Y. Lin, J.R. Wendt, S.G. Johnson, J.D. Joannopoulos, "Quantitative analysis of bending effiency in photonic crystal wavgeuide bends at ⌊= 1.55 m wavelengths," Opt. Lett. 26, 286-288 (2001)
[CrossRef]

M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, N.F. van Hulst, "Tracking femtosecond laser pulses in space and time," Science 294, 1080-1082 (2001)
[CrossRef] [PubMed]

S.G. Johnson, J.D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8173-190 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173
[CrossRef] [PubMed]

2000 (4)

M.L.M. Balistreri, A. Driessen, J.P. Korterik, L. Kuipers, N.F. van Hulst, "Quasi interference of perpendicularly polarized guided modes observed with a photon scanning tunneling microscope," Opt. Lett. 25, 637-639 (2000)
[CrossRef]

S.G. Johnson, P.R. Villeneuve, S. Fan, J.D. Joannopoulos, "Linear waveguides in photonic crystal slabs," Phys. Rev. B 62, 8212-8222 (2000)
[CrossRef]

V.N. Astratov, R.M. Stevenson, I.S. Culshaw, D.M. Whittaker, M.S. Skolnick, T.F. Krauss, R.M. de la Rue, "Heavy photon dispersions in photonic crystal waveguides," Appl. Phys. Lett. 77, 178-180 (2000)
[CrossRef]

S.F. Mingaleev, Yu.S. Kivshar, R.A. Sammut, "Longrange interaction and nonlinear localized modes in photonic crystal waveguides," Phys. Rev. E 625777 (2000)
[CrossRef]

1999 (1)

A. Imhof, W.L. Vos, R. Sprik, A. Lagendijk, "Large dispersive effects near the band edges of photonic crystals," Phys. Rev. Lett. 83, 2942-2945 (1999)
[CrossRef]

1986 (1)

P.St.J. Russell, "Optics of Floquet-Bloch Waves in Dielectric Gratings," Appl. Phys. B 39, 231-246 (1986)
[CrossRef]

1979 (1)

Akahane, Y.

Y. Akahane, T. Asano, B.S. Song, S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003)
[CrossRef] [PubMed]

Asakawa, K.

Asano, T.

T. Asano, K. Kiyota, D. Kumamoto, B.S. Song, S. Noda, "Time-domain measurement of picosecond light-pulse propagation in a two-dimensional photonic crystal-slab waveguide," Appl. Phys. Lett. 84, 4690-4692 (2004)
[CrossRef]

Y. Akahane, T. Asano, B.S. Song, S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003)
[CrossRef] [PubMed]

Astratov, V.N.

V.N. Astratov, R.M. Stevenson, I.S. Culshaw, D.M. Whittaker, M.S. Skolnick, T.F. Krauss, R.M. de la Rue, "Heavy photon dispersions in photonic crystal waveguides," Appl. Phys. Lett. 77, 178-180 (2000)
[CrossRef]

Baets, R.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, J. Marti, "Analysis of butt coupling in photonic crystals," IEEE J. Quantum Electron. 40, 541-550 (2004)
[CrossRef]

Balistreri, M.L.M.

Bienstman, P.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, J. Marti, "Analysis of butt coupling in photonic crystals," IEEE J. Quantum Electron. 40, 541-550 (2004)
[CrossRef]

Bogaerts, W.

H. Gersen, T.J. Karle, R.J.P. Engelen, W. Bogaerts, J.P. Korterik, N.F. van Hulst, T.F. Krauss, L. Kuipers, "Real space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005)
[CrossRef] [PubMed]

Chow, E.

Cole, J.B.

S. Yamada, Y. Watanabe, Y. Katayama, J.B. Cole, "Simulation of optical pulse propagation in a two-dimensional photonic crystal waveguide using a high accuracy finite-difference time-domain algorithm," J. Appl. Phys. 93, 1859-1864 (2003)
[CrossRef]

Culshaw, I.S.

V.N. Astratov, R.M. Stevenson, I.S. Culshaw, D.M. Whittaker, M.S. Skolnick, T.F. Krauss, R.M. de la Rue, "Heavy photon dispersions in photonic crystal waveguides," Appl. Phys. Lett. 77, 178-180 (2000)
[CrossRef]

de la Rue, R.M.

V.N. Astratov, R.M. Stevenson, I.S. Culshaw, D.M. Whittaker, M.S. Skolnick, T.F. Krauss, R.M. de la Rue, "Heavy photon dispersions in photonic crystal waveguides," Appl. Phys. Lett. 77, 178-180 (2000)
[CrossRef]

Driessen, A.

Dunbar, L.A.

Eich, M.

A.Y. Petrov, M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004)
[CrossRef]

Engelen, R.J.P

Engelen, R.J.P.

H. Gersen, T.J. Karle, R.J.P. Engelen, W. Bogaerts, J.P. Korterik, N.F. van Hulst, T.F. Krauss, L. Kuipers, "Real space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005)
[CrossRef] [PubMed]

Fan, S.

S.G. Johnson, P.R. Villeneuve, S. Fan, J.D. Joannopoulos, "Linear waveguides in photonic crystal slabs," Phys. Rev. B 62, 8212-8222 (2000)
[CrossRef]

Ferrini, R.

Fox, A.M.

Gersen, H.

R.J.P Engelen, T.J. Karle, H. Gersen, J.P. Korterik, T.F. Krauss, L. Kuipers, N.F. van Hulst, "Local probing of Bloch mode dispersion in a photonic crystal waveguide," Opt. Express 13, 4457-4464 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4457
[CrossRef] [PubMed]

H. Gersen, T.J. Karle, R.J.P. Engelen, W. Bogaerts, J.P. Korterik, N.F. van Hulst, T.F. Krauss, L. Kuipers, "Real space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005)
[CrossRef] [PubMed]

H. Gersen, E.M.P.H. van Dijk, J.P. Korterik, N.F. van Hulst, L. Kuipers, "Phase mapping of ultrashort pulses in bimodal photonic structures: A window on local group velocity dispersion," Phys. Rev. E 70, 066609 (2004)
[CrossRef]

H. Gersen, J.P. Korterik, N.F. van Hulst, L. Kuipers, "Tracking ultrashort pulses through dispersive media: Experiment and theory" Phys. Rev. E 68, 026604 (2003)
[CrossRef]

M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, N.F. van Hulst, "Tracking femtosecond laser pulses in space and time," Science 294, 1080-1082 (2001)
[CrossRef] [PubMed]

Hamann, H.F.

Y.A. Vlasov, M. O’Boyle, H.F. Hamann, S.J. McNab, "Active control of slow light on a chip with photonic crystal waveguides" Nature 438, 65-69 (2005)
[CrossRef] [PubMed]

Houdre, R.

Ikeda, N.

Imhof, A.

A. Imhof, W.L. Vos, R. Sprik, A. Lagendijk, "Large dispersive effects near the band edges of photonic crystals," Phys. Rev. Lett. 83, 2942-2945 (1999)
[CrossRef]

Inoue, K.

Joannopoulos, J.D.

Johnson, S.G.

Karle, T.J.

H. Gersen, T.J. Karle, R.J.P. Engelen, W. Bogaerts, J.P. Korterik, N.F. van Hulst, T.F. Krauss, L. Kuipers, "Real space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005)
[CrossRef] [PubMed]

R.J.P Engelen, T.J. Karle, H. Gersen, J.P. Korterik, T.F. Krauss, L. Kuipers, N.F. van Hulst, "Local probing of Bloch mode dispersion in a photonic crystal waveguide," Opt. Express 13, 4457-4464 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4457
[CrossRef] [PubMed]

Katayama, Y.

S. Yamada, Y. Watanabe, Y. Katayama, J.B. Cole, "Simulation of optical pulse propagation in a two-dimensional photonic crystal waveguide using a high accuracy finite-difference time-domain algorithm," J. Appl. Phys. 93, 1859-1864 (2003)
[CrossRef]

Kawai, N.

K. Inoue, N. Kawai, Y. Sugimoto, N. Ikeda, K. Asakawa, "Observation of small group velocity in twodimensional AlGaAs-based photonic crystal slabs," Phys. Rev. B 65, 121308 (2002)
[CrossRef]

Khurgin, J.

Kira, G.

Kivshar, Yu.S.

S.F. Mingaleev, Yu.S. Kivshar, R.A. Sammut, "Longrange interaction and nonlinear localized modes in photonic crystal waveguides," Phys. Rev. E 625777 (2000)
[CrossRef]

Kiyota, K.

T. Asano, K. Kiyota, D. Kumamoto, B.S. Song, S. Noda, "Time-domain measurement of picosecond light-pulse propagation in a two-dimensional photonic crystal-slab waveguide," Appl. Phys. Lett. 84, 4690-4692 (2004)
[CrossRef]

Korterik, J.P.

H. Gersen, T.J. Karle, R.J.P. Engelen, W. Bogaerts, J.P. Korterik, N.F. van Hulst, T.F. Krauss, L. Kuipers, "Real space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005)
[CrossRef] [PubMed]

R.J.P Engelen, T.J. Karle, H. Gersen, J.P. Korterik, T.F. Krauss, L. Kuipers, N.F. van Hulst, "Local probing of Bloch mode dispersion in a photonic crystal waveguide," Opt. Express 13, 4457-4464 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4457
[CrossRef] [PubMed]

H. Gersen, E.M.P.H. van Dijk, J.P. Korterik, N.F. van Hulst, L. Kuipers, "Phase mapping of ultrashort pulses in bimodal photonic structures: A window on local group velocity dispersion," Phys. Rev. E 70, 066609 (2004)
[CrossRef]

H. Gersen, J.P. Korterik, N.F. van Hulst, L. Kuipers, "Tracking ultrashort pulses through dispersive media: Experiment and theory" Phys. Rev. E 68, 026604 (2003)
[CrossRef]

M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, N.F. van Hulst, "Tracking femtosecond laser pulses in space and time," Science 294, 1080-1082 (2001)
[CrossRef] [PubMed]

M.L.M. Balistreri, A. Driessen, J.P. Korterik, L. Kuipers, N.F. van Hulst, "Quasi interference of perpendicularly polarized guided modes observed with a photon scanning tunneling microscope," Opt. Lett. 25, 637-639 (2000)
[CrossRef]

Krauss, T.F.

R.J.P Engelen, T.J. Karle, H. Gersen, J.P. Korterik, T.F. Krauss, L. Kuipers, N.F. van Hulst, "Local probing of Bloch mode dispersion in a photonic crystal waveguide," Opt. Express 13, 4457-4464 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4457
[CrossRef] [PubMed]

H. Gersen, T.J. Karle, R.J.P. Engelen, W. Bogaerts, J.P. Korterik, N.F. van Hulst, T.F. Krauss, L. Kuipers, "Real space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005)
[CrossRef] [PubMed]

M.D. Rahn, A.M. Fox, M.S. Skolnick, T.F. Krauss, "Propagation of ultrashort nonlinear pulses through twodimensional AlGaAs high-contrast photonic crystal waveguides," J. Opt. Soc. Am. B 19, 716-721 (2002)
[CrossRef]

V.N. Astratov, R.M. Stevenson, I.S. Culshaw, D.M. Whittaker, M.S. Skolnick, T.F. Krauss, R.M. de la Rue, "Heavy photon dispersions in photonic crystal waveguides," Appl. Phys. Lett. 77, 178-180 (2000)
[CrossRef]

Kuipers, L.

H. Gersen, T.J. Karle, R.J.P. Engelen, W. Bogaerts, J.P. Korterik, N.F. van Hulst, T.F. Krauss, L. Kuipers, "Real space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005)
[CrossRef] [PubMed]

R.J.P Engelen, T.J. Karle, H. Gersen, J.P. Korterik, T.F. Krauss, L. Kuipers, N.F. van Hulst, "Local probing of Bloch mode dispersion in a photonic crystal waveguide," Opt. Express 13, 4457-4464 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4457
[CrossRef] [PubMed]

H. Gersen, E.M.P.H. van Dijk, J.P. Korterik, N.F. van Hulst, L. Kuipers, "Phase mapping of ultrashort pulses in bimodal photonic structures: A window on local group velocity dispersion," Phys. Rev. E 70, 066609 (2004)
[CrossRef]

H. Gersen, J.P. Korterik, N.F. van Hulst, L. Kuipers, "Tracking ultrashort pulses through dispersive media: Experiment and theory" Phys. Rev. E 68, 026604 (2003)
[CrossRef]

M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, N.F. van Hulst, "Tracking femtosecond laser pulses in space and time," Science 294, 1080-1082 (2001)
[CrossRef] [PubMed]

M.L.M. Balistreri, A. Driessen, J.P. Korterik, L. Kuipers, N.F. van Hulst, "Quasi interference of perpendicularly polarized guided modes observed with a photon scanning tunneling microscope," Opt. Lett. 25, 637-639 (2000)
[CrossRef]

Kumamoto, D.

T. Asano, K. Kiyota, D. Kumamoto, B.S. Song, S. Noda, "Time-domain measurement of picosecond light-pulse propagation in a two-dimensional photonic crystal-slab waveguide," Appl. Phys. Lett. 84, 4690-4692 (2004)
[CrossRef]

Kuramochi, E.

Lagendijk, A.

A. Imhof, W.L. Vos, R. Sprik, A. Lagendijk, "Large dispersive effects near the band edges of photonic crystals," Phys. Rev. Lett. 83, 2942-2945 (1999)
[CrossRef]

Lin, S.Y.

Lombardet, B.

Luyssaert, B.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, J. Marti, "Analysis of butt coupling in photonic crystals," IEEE J. Quantum Electron. 40, 541-550 (2004)
[CrossRef]

Marti, J.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, J. Marti, "Analysis of butt coupling in photonic crystals," IEEE J. Quantum Electron. 40, 541-550 (2004)
[CrossRef]

McNab, S.J.

Y.A. Vlasov, M. O’Boyle, H.F. Hamann, S.J. McNab, "Active control of slow light on a chip with photonic crystal waveguides" Nature 438, 65-69 (2005)
[CrossRef] [PubMed]

Mingaleev, S.F.

S.F. Mingaleev, Yu.S. Kivshar, R.A. Sammut, "Longrange interaction and nonlinear localized modes in photonic crystal waveguides," Phys. Rev. E 625777 (2000)
[CrossRef]

Mitsugi, S.

Miyagi, M.

Nakamura, Y.

Nishida, S.

Noda, S.

T. Asano, K. Kiyota, D. Kumamoto, B.S. Song, S. Noda, "Time-domain measurement of picosecond light-pulse propagation in a two-dimensional photonic crystal-slab waveguide," Appl. Phys. Lett. 84, 4690-4692 (2004)
[CrossRef]

Y. Akahane, T. Asano, B.S. Song, S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003)
[CrossRef] [PubMed]

Notomi, M.

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 132678-2687 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2678
[CrossRef] [PubMed]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001)
[CrossRef] [PubMed]

O’Boyle, M.

Y.A. Vlasov, M. O’Boyle, H.F. Hamann, S.J. McNab, "Active control of slow light on a chip with photonic crystal waveguides" Nature 438, 65-69 (2005)
[CrossRef] [PubMed]

Petrov, A.Y.

A.Y. Petrov, M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004)
[CrossRef]

Rahn, M.D.

Russell, P.St.J.

P.St.J. Russell, "Optics of Floquet-Bloch Waves in Dielectric Gratings," Appl. Phys. B 39, 231-246 (1986)
[CrossRef]

Sammut, R.A.

S.F. Mingaleev, Yu.S. Kivshar, R.A. Sammut, "Longrange interaction and nonlinear localized modes in photonic crystal waveguides," Phys. Rev. E 625777 (2000)
[CrossRef]

Sanchis, P.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, J. Marti, "Analysis of butt coupling in photonic crystals," IEEE J. Quantum Electron. 40, 541-550 (2004)
[CrossRef]

Shinya, A.

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 132678-2687 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2678
[CrossRef] [PubMed]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001)
[CrossRef] [PubMed]

Skolnick, M.S.

M.D. Rahn, A.M. Fox, M.S. Skolnick, T.F. Krauss, "Propagation of ultrashort nonlinear pulses through twodimensional AlGaAs high-contrast photonic crystal waveguides," J. Opt. Soc. Am. B 19, 716-721 (2002)
[CrossRef]

V.N. Astratov, R.M. Stevenson, I.S. Culshaw, D.M. Whittaker, M.S. Skolnick, T.F. Krauss, R.M. de la Rue, "Heavy photon dispersions in photonic crystal waveguides," Appl. Phys. Lett. 77, 178-180 (2000)
[CrossRef]

Song, B.S.

T. Asano, K. Kiyota, D. Kumamoto, B.S. Song, S. Noda, "Time-domain measurement of picosecond light-pulse propagation in a two-dimensional photonic crystal-slab waveguide," Appl. Phys. Lett. 84, 4690-4692 (2004)
[CrossRef]

Y. Akahane, T. Asano, B.S. Song, S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003)
[CrossRef] [PubMed]

Sprik, R.

A. Imhof, W.L. Vos, R. Sprik, A. Lagendijk, "Large dispersive effects near the band edges of photonic crystals," Phys. Rev. Lett. 83, 2942-2945 (1999)
[CrossRef]

Stevenson, R.M.

V.N. Astratov, R.M. Stevenson, I.S. Culshaw, D.M. Whittaker, M.S. Skolnick, T.F. Krauss, R.M. de la Rue, "Heavy photon dispersions in photonic crystal waveguides," Appl. Phys. Lett. 77, 178-180 (2000)
[CrossRef]

Sugimoto, Y.

Sugitatsu, A.

A. Sugitatsu, T. Asano T, S. Noda, "Characterization of line-defect-waveguide lasers in two-dimensional photonic-crystal slabs," Appl. Phys. Lett. 845395-5397 (2004)
[CrossRef]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001)
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001)
[CrossRef] [PubMed]

Tanabe, T.

Tanaka, Y.

van Dijk, E.M.P.H.

H. Gersen, E.M.P.H. van Dijk, J.P. Korterik, N.F. van Hulst, L. Kuipers, "Phase mapping of ultrashort pulses in bimodal photonic structures: A window on local group velocity dispersion," Phys. Rev. E 70, 066609 (2004)
[CrossRef]

van Hulst, N.F.

R.J.P Engelen, T.J. Karle, H. Gersen, J.P. Korterik, T.F. Krauss, L. Kuipers, N.F. van Hulst, "Local probing of Bloch mode dispersion in a photonic crystal waveguide," Opt. Express 13, 4457-4464 (2005) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4457
[CrossRef] [PubMed]

H. Gersen, T.J. Karle, R.J.P. Engelen, W. Bogaerts, J.P. Korterik, N.F. van Hulst, T.F. Krauss, L. Kuipers, "Real space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005)
[CrossRef] [PubMed]

H. Gersen, E.M.P.H. van Dijk, J.P. Korterik, N.F. van Hulst, L. Kuipers, "Phase mapping of ultrashort pulses in bimodal photonic structures: A window on local group velocity dispersion," Phys. Rev. E 70, 066609 (2004)
[CrossRef]

H. Gersen, J.P. Korterik, N.F. van Hulst, L. Kuipers, "Tracking ultrashort pulses through dispersive media: Experiment and theory" Phys. Rev. E 68, 026604 (2003)
[CrossRef]

M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, N.F. van Hulst, "Tracking femtosecond laser pulses in space and time," Science 294, 1080-1082 (2001)
[CrossRef] [PubMed]

M.L.M. Balistreri, A. Driessen, J.P. Korterik, L. Kuipers, N.F. van Hulst, "Quasi interference of perpendicularly polarized guided modes observed with a photon scanning tunneling microscope," Opt. Lett. 25, 637-639 (2000)
[CrossRef]

Villeneuve, P.R.

S.G. Johnson, P.R. Villeneuve, S. Fan, J.D. Joannopoulos, "Linear waveguides in photonic crystal slabs," Phys. Rev. B 62, 8212-8222 (2000)
[CrossRef]

Vlasov, Y.A.

Y.A. Vlasov, M. O’Boyle, H.F. Hamann, S.J. McNab, "Active control of slow light on a chip with photonic crystal waveguides" Nature 438, 65-69 (2005)
[CrossRef] [PubMed]

Vos, W.L.

A. Imhof, W.L. Vos, R. Sprik, A. Lagendijk, "Large dispersive effects near the band edges of photonic crystals," Phys. Rev. Lett. 83, 2942-2945 (1999)
[CrossRef]

Watanabe, Y.

S. Yamada, Y. Watanabe, Y. Katayama, J.B. Cole, "Simulation of optical pulse propagation in a two-dimensional photonic crystal waveguide using a high accuracy finite-difference time-domain algorithm," J. Appl. Phys. 93, 1859-1864 (2003)
[CrossRef]

Wendt, J.R.

Whittaker, D.M.

V.N. Astratov, R.M. Stevenson, I.S. Culshaw, D.M. Whittaker, M.S. Skolnick, T.F. Krauss, R.M. de la Rue, "Heavy photon dispersions in photonic crystal waveguides," Appl. Phys. Lett. 77, 178-180 (2000)
[CrossRef]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001)
[CrossRef] [PubMed]

Yamada, S.

S. Yamada, Y. Watanabe, Y. Katayama, J.B. Cole, "Simulation of optical pulse propagation in a two-dimensional photonic crystal waveguide using a high accuracy finite-difference time-domain algorithm," J. Appl. Phys. 93, 1859-1864 (2003)
[CrossRef]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001)
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. B (1)

P.St.J. Russell, "Optics of Floquet-Bloch Waves in Dielectric Gratings," Appl. Phys. B 39, 231-246 (1986)
[CrossRef]

Appl. Phys. Lett. (4)

A.Y. Petrov, M. Eich, "Zero dispersion at small group velocities in photonic crystal waveguides," Appl. Phys. Lett. 85, 4866-4868 (2004)
[CrossRef]

V.N. Astratov, R.M. Stevenson, I.S. Culshaw, D.M. Whittaker, M.S. Skolnick, T.F. Krauss, R.M. de la Rue, "Heavy photon dispersions in photonic crystal waveguides," Appl. Phys. Lett. 77, 178-180 (2000)
[CrossRef]

A. Sugitatsu, T. Asano T, S. Noda, "Characterization of line-defect-waveguide lasers in two-dimensional photonic-crystal slabs," Appl. Phys. Lett. 845395-5397 (2004)
[CrossRef]

T. Asano, K. Kiyota, D. Kumamoto, B.S. Song, S. Noda, "Time-domain measurement of picosecond light-pulse propagation in a two-dimensional photonic crystal-slab waveguide," Appl. Phys. Lett. 84, 4690-4692 (2004)
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, J. Marti, "Analysis of butt coupling in photonic crystals," IEEE J. Quantum Electron. 40, 541-550 (2004)
[CrossRef]

J. Appl. Phys. (1)

S. Yamada, Y. Watanabe, Y. Katayama, J.B. Cole, "Simulation of optical pulse propagation in a two-dimensional photonic crystal waveguide using a high accuracy finite-difference time-domain algorithm," J. Appl. Phys. 93, 1859-1864 (2003)
[CrossRef]

J. Opt. Soc. Am. B (2)

Nature (2)

Y.A. Vlasov, M. O’Boyle, H.F. Hamann, S.J. McNab, "Active control of slow light on a chip with photonic crystal waveguides" Nature 438, 65-69 (2005)
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B.S. Song, S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003)
[CrossRef] [PubMed]

Nature Mater. (1)

for a review see M. Soljacic, J.D. Joannopoulos, "Enhancement of nonlinear effects using photonic crystals," Nature Mater. 3211-219 (2004)
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. B (2)

S.G. Johnson, P.R. Villeneuve, S. Fan, J.D. Joannopoulos, "Linear waveguides in photonic crystal slabs," Phys. Rev. B 62, 8212-8222 (2000)
[CrossRef]

K. Inoue, N. Kawai, Y. Sugimoto, N. Ikeda, K. Asakawa, "Observation of small group velocity in twodimensional AlGaAs-based photonic crystal slabs," Phys. Rev. B 65, 121308 (2002)
[CrossRef]

Phys. Rev. E (3)

S.F. Mingaleev, Yu.S. Kivshar, R.A. Sammut, "Longrange interaction and nonlinear localized modes in photonic crystal waveguides," Phys. Rev. E 625777 (2000)
[CrossRef]

H. Gersen, E.M.P.H. van Dijk, J.P. Korterik, N.F. van Hulst, L. Kuipers, "Phase mapping of ultrashort pulses in bimodal photonic structures: A window on local group velocity dispersion," Phys. Rev. E 70, 066609 (2004)
[CrossRef]

H. Gersen, J.P. Korterik, N.F. van Hulst, L. Kuipers, "Tracking ultrashort pulses through dispersive media: Experiment and theory" Phys. Rev. E 68, 026604 (2003)
[CrossRef]

Phys. Rev. Lett. (3)

A. Imhof, W.L. Vos, R. Sprik, A. Lagendijk, "Large dispersive effects near the band edges of photonic crystals," Phys. Rev. Lett. 83, 2942-2945 (1999)
[CrossRef]

H. Gersen, T.J. Karle, R.J.P. Engelen, W. Bogaerts, J.P. Korterik, N.F. van Hulst, T.F. Krauss, L. Kuipers, "Real space observation of ultraslow light in photonic crystal waveguides," Phys. Rev. Lett. 94, 073903 (2005)
[CrossRef] [PubMed]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokohama, "Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs," Phys. Rev. Lett. 87, 253902 (2001)
[CrossRef] [PubMed]

Science (1)

M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, N.F. van Hulst, "Tracking femtosecond laser pulses in space and time," Science 294, 1080-1082 (2001)
[CrossRef] [PubMed]

Other (3)

Product information sheet, "Corning SMF-28e Optical Fiber, Product Information" (Corning Inc., 2005) http://corning.com/opticalfiber/products%5F%5Fapplications/products/smf%5F28e.aspx

G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, Calif., 2001)

See for example, Photonic Crystals and Light Localization in the 21st Century, in NATO Science Series, C.M. Soukoulis, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2001)

Cited By

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Figures (8)

Fig. 1.
Fig. 1.

Scanning electron microscopy image of the photonic crystal structure. The inset denotes the used cartesian coordinate system used in this paper. The PhCW is oriented in the z-direction. The x-direction is in the plane of the PhC and is perpendicular to z. The y-direction is perpendicular to the plane of the membrane.

Fig. 2.
Fig. 2.

(a) Portion of the dispersion relation of the W1 waveguide calculated by 3D plane wave expansion. In the 2D bandgap, two waveguide modes are allowed to propagate for TE polarization. They are denoted “even” and “odd” by their in-plane symmetry with respect to the waveguide. The light line (ω = ckz ) is represented by the dashed line. (b) Group velocity (νg ) as a function of frequency, calculated by taking the derivative of k(ω). (c) The second order derivative of k(ω) gives the group velocity dispersion (β 2 = d 2 k/ 2). As the group velocity reduces around ω = 0.254, the GVD increases several orders of magnitude.

Fig. 3.
Fig. 3.

(a) Focussed ion beam micrograph of the near-field probe, that consisted of a metal-coated tapered optical fiber. The typical aperture diameter is 200 nm, for measurements in the infrared. The image was obtained after ion beam milling of the tip apex. View angle: ~45deg. (b) Schematic representation of the experimental setup. Pulsed laser light was coupled into the PhCW. The fiber probe collected a fraction of the propagating light. This light was mixed interferometrically with a reference pulse from the same laser. Only the interference between the two pulses was detected. Two measurement modes were possible: either scanning the fiber probe over the surface with a fixed optical delay line, or scanning the delay line for a single probe position.

Fig. 4.
Fig. 4.

Near-field optical measurement obtained by scanning the surface of the PhC sample. The false-color images represent the amplitude of optical interference. Measurements at normalized optical frequencies 0.2664, 0.2635 and 0.2603 are shown in (a), (b) and (c) respectively. Images size: 106μm × 4μm. The crosses “A” up to “F”represent the positions were additional experiments were conducted.

Fig. 5.
Fig. 5.

(a-c) Cross-correlation functions of the pulses in reference and signal branch of the interferometric setup. At the optical frequencies 0.2664, 0.2635 and 0.2603, the interfero-grams are measured at 6 equidistantly spaced points on the waveguide between 10 μm and 116 μm from the membrane facet. These measurement points are highlighted with crosses in Fig. 4. The measurement points “A”-“F” correspond to the points in Fig. 4, i.e. the inter-ferogram “A” is measured at location “A”. The interference amplitudes are normalized with respect to their maximum. In the first curve in (c), our detector saturates because this close to the incoupling point, light from the coupling objective is picked up directly. (d-f) Details of the measurement at position “A” at ω= 0.2635, showing the interference amplitude (d) and the underlaying interference fringes (e and f).

Fig. 6.
Fig. 6.

Summary of the found experimental results. The carrier frequency of the pulses is found by Fourier Transformation of the interferograms. In both figures, the theoretical values are depicted by a straight line. (a) The theoretical dispersion curve and the experimentally found dispersion relation of the TE mode. The values of kz are found by Fourier Transformation of the data from the SID measurements in Fig. 4. (b) Group velocity of the pulses, found by evaluating the center-of-mass of the interferograms in Fig. 5.

Fig. 7.
Fig. 7.

Calculated amplitude of the interferograms at frequencies 0.2620, 0.2585 and 0.2565, using the dispersion relation from the simulations (Fig. 3(a)). For each frequency, the interferogram is calculated for 6 waveguide lengths, equidistantly spaced between 10 and 116 μm.

Fig. 8.
Fig. 8.

The effect of higher-order dispersion on the propagation of a slow pulse. The pulse shape is calculated after 116 μm of propagation at ω = 0.2565. The blue curve represents the interferogram of dispersion-free propagating pulses. In the green curve, the effect of GVD is included. The third order dispersion is included in the red curve. In the dashed black curve, the full dispersion relation is included.

Equations (11)

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

E ˜ z ω = m E ˜ m ( ω ) exp ( i k m ( ω ) z ) ,
with k m ( ω ) = k 0 ( ω ) + 2 π a m and m ,
E ˜ z ω = E ˜ 0 ( ω ) exp ( i k 0 ( ω ) z ) ,
k 0 ( ω ) = β 0 + β 1 ( ω ω 0 ) + β 2 2 ( ω ω 0 ) 2 + β 3 6 ( ω ω 0 ) 3 + .
E z t = 1 { E ˜ ( ω ) e ik ( ω ) z } .
E z t = τ p E 0 τ p 2 4 iz β 2 exp [ iz β 0 + i ω 0 t ( t z β 1 ) 2 τ p 2 4 iz β 2 ] .
I det z t = e i Δ ω ( t τ ) E ref ( t τ ) + E sig z t 2 .
I det z t = E ref ( t τ ) 2 + E sig z t 2 + 2 Re [ E ref * ( t τ ) E sig z t e i ( Δ ωt ω τ Δ ωτ ) ] .
V LIA Δ t 2 Re [ E ref * ( t τ ) E sig z t ] dt .
V LIA z τ 2 Re { 1 [ E ref * ( ω ) E sig z ω ] } .
V LIA z τ 2 Re [ 1 { E ref ( ω ) E sig ( ω ) e ikz ] } .

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