Abstract

Large and periodically corrugated optical waveguide structures are shown to possess specific modal regimes of slow-light propagation that are easily attainable. The very multimode nature of the coupling is studied by employing coupled-mode theory and the plane-wave expansion method. Given a large enough light cone, associated with a surrounding medium with low enough refractive index, we notably identify a critical slowdown regime with an interesting bandwidth-slowdown product. Essential features of these original systems are further explored: the nature of the coupled modes, the role of gain, symmetry effects, polarization, and relation with photonic-crystal systems. Practical systems are introduced using finite-difference time-domain methods, which provides first-order rules for the use of the above phenomena and their implementation in devices.

© 2008 Optical Society of America

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  35. We believe that the extent of slowdown in (k,ω) space is akin to the issue of the natural radius of Fabry-Perot modes (rFP~λ×thickness×finesse), which is itself tightly related to Fresnel zones (r~λ×distance), that is, to the generic quadratic transverse behavior of transverse phase lags off an unfolded reference path). We may, along the same line, conjecture that thickness tolerances would be similar to those of high-finesse Fabry-Perot resonators, demanding thickness variations of less than δW=λ/2/finesse but with a precise finesse definition depending on the frequency span and thus on the number of oscillations being exploited.

2007

2006

S. Combrié, E. Weidner, A. De Rossi, S. Bansropun, S. Cassette, A. Talneau, and H. Benisty, “Detailed analysis by Fabry-Perot method of slab photonic crystal line-defect waveguides and cavities in aluminium-free material system,” Opt. Express 14, 7353-7361 (2006).
[CrossRef] [PubMed]

M. Ghulinyan, Z. Gaburro, D. S. Wiersma, and L. Pavesi, “Tuning of resonant Zener tunneling by vapor diffusion and condensation in porous optical superlattices,” Phys. Rev. B 74, 045118 (2006).
[CrossRef]

H. Benisty, A. David, L. Martinelli, E. Viasnoff-Schwoob, C. Weisbuch, G.-H. Duan, K. Janiak, and H. Heidrich, “From modal control to spontaneous emission and gain in photonic crystal waveguides,” Photonics Nanostruct. Fundam. Appl. 4, 1-11 (2006).
[CrossRef]

2005

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

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

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

B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdré, “Fourier analysis of Bloch wave propagation in photonic crystals,” J. Opt. Soc. Am. B 22, 1179-1190 (2005).
[CrossRef]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement at a photonic wire miniband edge,” Opt. Lett. 26, 2113-2115 (2005).
[CrossRef]

2004

T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, “Light localizations in photonic crystal line defect waveguides,” IEEE J. Sel. Top. Quantum Electron. 10, 484-491 (2004).
[CrossRef]

2003

2001

P. Ferrand, R. Romestain, and J. C. Vial, “Photonic band-gap properties of a porous silicon periodic planar waveguide,” Phys. Rev. B 63, 115106 (2001).
[CrossRef]

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one-dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

1999

1998

1997

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038-2059 (1997).
[CrossRef]

1996

H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 79, 7483-7492 (1996).
[CrossRef]

1977

A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. 13, 233-253 (1977).
[CrossRef]

1973

A. Yariv, “Coupled mode theory for guided wave optics,” IEEE J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).

Albaledejo, S.

S. Albaledejo, J. J. Saenz, M. Lester, L. S. Froufe-Pérez, and A. Garcia-Martin, “Optical conductance of waveguides built into finite photonic crystals,” Appl. Phys. Lett. 91, 061107 (2007).
[CrossRef]

Ayre, M.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, and G. H. Duan, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Baba, T.

T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, “Light localizations in photonic crystal line defect waveguides,” IEEE J. Sel. Top. Quantum Electron. 10, 484-491 (2004).
[CrossRef]

Bansropun, S.

Benisty, H.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, and G. H. Duan, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

L. Martinelli, H. Benisty, O. Khayam, G. H. Duan, H. Heidrich, and K. Janiak, “Analysis and optimization of compact demultiplexer monitor based on photonic crystal waveguide,” J. Lightwave Technol. 25, 2385-2394 (2007).
[CrossRef]

H. Benisty, A. David, L. Martinelli, E. Viasnoff-Schwoob, C. Weisbuch, G.-H. Duan, K. Janiak, and H. Heidrich, “From modal control to spontaneous emission and gain in photonic crystal waveguides,” Photonics Nanostruct. Fundam. Appl. 4, 1-11 (2006).
[CrossRef]

S. Combrié, E. Weidner, A. De Rossi, S. Bansropun, S. Cassette, A. Talneau, and H. Benisty, “Detailed analysis by Fabry-Perot method of slab photonic crystal line-defect waveguides and cavities in aluminium-free material system,” Opt. Express 14, 7353-7361 (2006).
[CrossRef] [PubMed]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement at a photonic wire miniband edge,” Opt. Lett. 26, 2113-2115 (2005).
[CrossRef]

S. Olivier, H. Benisty, C. Weisbuch, C. J. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 11, 1490-1496 (2003).
[CrossRef] [PubMed]

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one-dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 79, 7483-7492 (1996).
[CrossRef]

J.-M. Lourtioz, H. Benisty, V. Berger, J. M. Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer, 2005).

Berger, V.

J.-M. Lourtioz, H. Benisty, V. Berger, J. M. Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer, 2005).

Bogaerts, W.

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

Booruang, S.

Brenot, H.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, and G. H. Duan, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Cambournac, C.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, and G. H. Duan, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

Cassette, S.

Coldren, L. A.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

Combrié, S.

Corzine, S. W.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

Cuisin, C.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

David, A.

H. Benisty, A. David, L. Martinelli, E. Viasnoff-Schwoob, C. Weisbuch, G.-H. Duan, K. Janiak, and H. Heidrich, “From modal control to spontaneous emission and gain in photonic crystal waveguides,” Photonics Nanostruct. Fundam. Appl. 4, 1-11 (2006).
[CrossRef]

De La Rue, R. M.

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one-dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

De Rossi, A.

Derouin, E.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

Drisse, O.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

Duan, G. H.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, and G. H. Duan, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

L. Martinelli, H. Benisty, O. Khayam, G. H. Duan, H. Heidrich, and K. Janiak, “Analysis and optimization of compact demultiplexer monitor based on photonic crystal waveguide,” J. Lightwave Technol. 25, 2385-2394 (2007).
[CrossRef]

Duan, G.-H.

H. Benisty, A. David, L. Martinelli, E. Viasnoff-Schwoob, C. Weisbuch, G.-H. Duan, K. Janiak, and H. Heidrich, “From modal control to spontaneous emission and gain in photonic crystal waveguides,” Photonics Nanostruct. Fundam. Appl. 4, 1-11 (2006).
[CrossRef]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

Dunbar, L. A.

Dutta, N. K.

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).

Engelen, J. P.

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

Engelen, R. J. P.

Fellow, L.

Ferrand, P.

P. Ferrand, R. Romestain, and J. C. Vial, “Photonic band-gap properties of a porous silicon periodic planar waveguide,” Phys. Rev. B 63, 115106 (2001).
[CrossRef]

Ferrini, R.

Friesem, A. A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038-2059 (1997).
[CrossRef]

Froufe-Pérez, L. S.

S. Albaledejo, J. J. Saenz, M. Lester, L. S. Froufe-Pérez, and A. Garcia-Martin, “Optical conductance of waveguides built into finite photonic crystals,” Appl. Phys. Lett. 91, 061107 (2007).
[CrossRef]

Gaburro, Z.

M. Ghulinyan, Z. Gaburro, D. S. Wiersma, and L. Pavesi, “Tuning of resonant Zener tunneling by vapor diffusion and condensation in porous optical superlattices,” Phys. Rev. B 74, 045118 (2006).
[CrossRef]

Garcia-Martin, A.

S. Albaledejo, J. J. Saenz, M. Lester, L. S. Froufe-Pérez, and A. Garcia-Martin, “Optical conductance of waveguides built into finite photonic crystals,” Appl. Phys. Lett. 91, 061107 (2007).
[CrossRef]

Garmire, E.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

Garvin, H. L.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

Gérard, J. M.

J.-M. Lourtioz, H. Benisty, V. Berger, J. M. Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer, 2005).

Gersen, H.

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

Ghulinyan, M.

M. Ghulinyan, Z. Gaburro, D. S. Wiersma, and L. Pavesi, “Tuning of resonant Zener tunneling by vapor diffusion and condensation in porous optical superlattices,” Phys. Rev. B 74, 045118 (2006).
[CrossRef]

Golka, S.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

Greenwell, A. B.

Hamman, H. F.

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

Handmer, C. J.

Heidrich, H.

L. Martinelli, H. Benisty, O. Khayam, G. H. Duan, H. Heidrich, and K. Janiak, “Analysis and optimization of compact demultiplexer monitor based on photonic crystal waveguide,” J. Lightwave Technol. 25, 2385-2394 (2007).
[CrossRef]

H. Benisty, A. David, L. Martinelli, E. Viasnoff-Schwoob, C. Weisbuch, G.-H. Duan, K. Janiak, and H. Heidrich, “From modal control to spontaneous emission and gain in photonic crystal waveguides,” Photonics Nanostruct. Fundam. Appl. 4, 1-11 (2006).
[CrossRef]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

Hensel, H. J.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

Houdré, R.

B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdré, “Fourier analysis of Bloch wave propagation in photonic crystals,” J. Opt. Soc. Am. B 22, 1179-1190 (2005).
[CrossRef]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement at a photonic wire miniband edge,” Opt. Lett. 26, 2113-2115 (2005).
[CrossRef]

S. Olivier, H. Benisty, C. Weisbuch, C. J. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 11, 1490-1496 (2003).
[CrossRef] [PubMed]

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one-dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

Hunsperger, R. G.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

Inoshita, K.

T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, “Light localizations in photonic crystal line defect waveguides,” IEEE J. Sel. Top. Quantum Electron. 10, 484-491 (2004).
[CrossRef]

Janiak, K.

L. Martinelli, H. Benisty, O. Khayam, G. H. Duan, H. Heidrich, and K. Janiak, “Analysis and optimization of compact demultiplexer monitor based on photonic crystal waveguide,” J. Lightwave Technol. 25, 2385-2394 (2007).
[CrossRef]

H. Benisty, A. David, L. Martinelli, E. Viasnoff-Schwoob, C. Weisbuch, G.-H. Duan, K. Janiak, and H. Heidrich, “From modal control to spontaneous emission and gain in photonic crystal waveguides,” Photonics Nanostruct. Fundam. Appl. 4, 1-11 (2006).
[CrossRef]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

Joannopoulos, J. D.

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

Karle, T. J.

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

Khayam, O.

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, and G. H. Duan, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

L. Martinelli, H. Benisty, O. Khayam, G. H. Duan, H. Heidrich, and K. Janiak, “Analysis and optimization of compact demultiplexer monitor based on photonic crystal waveguide,” J. Lightwave Technol. 25, 2385-2394 (2007).
[CrossRef]

Korterik, J. P.

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

Krauss, T. F.

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15, 219-226 (2007).
[CrossRef] [PubMed]

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

S. Olivier, H. Benisty, C. Weisbuch, C. J. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 11, 1490-1496 (2003).
[CrossRef] [PubMed]

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one-dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

Kuipers, L.

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15, 219-226 (2007).
[CrossRef] [PubMed]

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

Kuroki, Y.

T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, “Light localizations in photonic crystal line defect waveguides,” IEEE J. Sel. Top. Quantum Electron. 10, 484-491 (2004).
[CrossRef]

Lederer, F.

Legouézigou, L.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

Legouézigou, O.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

Lester, M.

S. Albaledejo, J. J. Saenz, M. Lester, L. S. Froufe-Pérez, and A. Garcia-Martin, “Optical conductance of waveguides built into finite photonic crystals,” Appl. Phys. Lett. 91, 061107 (2007).
[CrossRef]

Lombardet, B.

Lourtioz, J.-M.

J.-M. Lourtioz, H. Benisty, V. Berger, J. M. Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer, 2005).

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).

Martijn de Sterke, C.

Martinelli, L.

L. Martinelli, H. Benisty, O. Khayam, G. H. Duan, H. Heidrich, and K. Janiak, “Analysis and optimization of compact demultiplexer monitor based on photonic crystal waveguide,” J. Lightwave Technol. 25, 2385-2394 (2007).
[CrossRef]

H. Benisty, A. David, L. Martinelli, E. Viasnoff-Schwoob, C. Weisbuch, G.-H. Duan, K. Janiak, and H. Heidrich, “From modal control to spontaneous emission and gain in photonic crystal waveguides,” Photonics Nanostruct. Fundam. Appl. 4, 1-11 (2006).
[CrossRef]

Maystre, D.

J.-M. Lourtioz, H. Benisty, V. Berger, J. M. Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer, 2005).

McNab, S. J.

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

Meade, R. D.

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

Michaeli, A.

Moharam, M. G.

Moiseyev, N.

I. Vorobeichikh, E. Narevicius, G. Rosenblum, M. Orenstein, and N. Moiseyev, “Electromagnetic realization of orders-of-magnitude tunneling enhancement in a double well system,” Phys. Rev. Lett. 90, 176806 (2003).
[CrossRef]

Mori, D.

T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, “Light localizations in photonic crystal line defect waveguides,” IEEE J. Sel. Top. Quantum Electron. 10, 484-491 (2004).
[CrossRef]

Nakamura, M.

A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. 13, 233-253 (1977).
[CrossRef]

Narevicius, E.

I. Vorobeichikh, E. Narevicius, G. Rosenblum, M. Orenstein, and N. Moiseyev, “Electromagnetic realization of orders-of-magnitude tunneling enhancement in a double well system,” Phys. Rev. Lett. 90, 176806 (2003).
[CrossRef]

O'Boyle, M.

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

Oesterle, U.

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one-dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

Olivier, S.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement at a photonic wire miniband edge,” Opt. Lett. 26, 2113-2115 (2005).
[CrossRef]

S. Olivier, H. Benisty, C. Weisbuch, C. J. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 11, 1490-1496 (2003).
[CrossRef] [PubMed]

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one-dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

Orenstein, M.

I. Vorobeichikh, E. Narevicius, G. Rosenblum, M. Orenstein, and N. Moiseyev, “Electromagnetic realization of orders-of-magnitude tunneling enhancement in a double well system,” Phys. Rev. Lett. 90, 176806 (2003).
[CrossRef]

Pavesi, L.

M. Ghulinyan, Z. Gaburro, D. S. Wiersma, and L. Pavesi, “Tuning of resonant Zener tunneling by vapor diffusion and condensation in porous optical superlattices,” Phys. Rev. B 74, 045118 (2006).
[CrossRef]

Peral, E.

Pertsch, T.

Peschel, U.

Pommereau, F.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

Rattier, M.

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one-dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

Romestain, R.

P. Ferrand, R. Romestain, and J. C. Vial, “Photonic band-gap properties of a porous silicon periodic planar waveguide,” Phys. Rev. B 63, 115106 (2001).
[CrossRef]

Rosenblatt, D.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038-2059 (1997).
[CrossRef]

Rosenblum, G.

I. Vorobeichikh, E. Narevicius, G. Rosenblum, M. Orenstein, and N. Moiseyev, “Electromagnetic realization of orders-of-magnitude tunneling enhancement in a double well system,” Phys. Rev. Lett. 90, 176806 (2003).
[CrossRef]

Saenz, J. J.

S. Albaledejo, J. J. Saenz, M. Lester, L. S. Froufe-Pérez, and A. Garcia-Martin, “Optical conductance of waveguides built into finite photonic crystals,” Appl. Phys. Lett. 91, 061107 (2007).
[CrossRef]

Salib, M.

Settle, M. D.

Sharon, A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038-2059 (1997).
[CrossRef]

Smith, C. J.

Smith, C. J. M.

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement at a photonic wire miniband edge,” Opt. Lett. 26, 2113-2115 (2005).
[CrossRef]

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one-dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

Somekh, S.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

Steel, M. J.

Sukhorukov, A. A.

Talneau, A.

Tamir, T.

T. Tamir, Guided Wave Optoelectronics (Springer-Verlag, 1990).
[CrossRef]

Tchelnokov, A.

J.-M. Lourtioz, H. Benisty, V. Berger, J. M. Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer, 2005).

van Huslt, N. F.

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

Vial, J. C.

P. Ferrand, R. Romestain, and J. C. Vial, “Photonic band-gap properties of a porous silicon periodic planar waveguide,” Phys. Rev. B 63, 115106 (2001).
[CrossRef]

Viasnoff-Schwoob, E.

H. Benisty, A. David, L. Martinelli, E. Viasnoff-Schwoob, C. Weisbuch, G.-H. Duan, K. Janiak, and H. Heidrich, “From modal control to spontaneous emission and gain in photonic crystal waveguides,” Photonics Nanostruct. Fundam. Appl. 4, 1-11 (2006).
[CrossRef]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement at a photonic wire miniband edge,” Opt. Lett. 26, 2113-2115 (2005).
[CrossRef]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

Vlasov, Y. A.

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

Vorobeichikh, I.

I. Vorobeichikh, E. Narevicius, G. Rosenblum, M. Orenstein, and N. Moiseyev, “Electromagnetic realization of orders-of-magnitude tunneling enhancement in a double well system,” Phys. Rev. Lett. 90, 176806 (2003).
[CrossRef]

Weidner, E.

Weisbuch, C.

H. Benisty, A. David, L. Martinelli, E. Viasnoff-Schwoob, C. Weisbuch, G.-H. Duan, K. Janiak, and H. Heidrich, “From modal control to spontaneous emission and gain in photonic crystal waveguides,” Photonics Nanostruct. Fundam. Appl. 4, 1-11 (2006).
[CrossRef]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, S. Olivier, R. Houdré, and C. J. M. Smith, “Spontaneous emission enhancement at a photonic wire miniband edge,” Opt. Lett. 26, 2113-2115 (2005).
[CrossRef]

S. Olivier, H. Benisty, C. Weisbuch, C. J. Smith, T. F. Krauss, and R. Houdré, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 11, 1490-1496 (2003).
[CrossRef] [PubMed]

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one-dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

Wiersma, D. S.

M. Ghulinyan, Z. Gaburro, D. S. Wiersma, and L. Pavesi, “Tuning of resonant Zener tunneling by vapor diffusion and condensation in porous optical superlattices,” Phys. Rev. B 74, 045118 (2006).
[CrossRef]

Winn, J. N.

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

Yariv, A.

E. Peral, A. Yariv, and L. Fellow, “Supermodes of grating-coupled multimode waveguides and application to mode conversion between copropagating modes mediated by backward Bragg scattering,” J. Lightwave Technol. 17, 942-947 (1999).
[CrossRef]

A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. 13, 233-253 (1977).
[CrossRef]

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

A. Yariv, “Coupled mode theory for guided wave optics,” IEEE J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

A. Yariv, Quantum Electronics (Wiley, 1989).

Appl. Phys. Lett.

S. Albaledejo, J. J. Saenz, M. Lester, L. S. Froufe-Pérez, and A. Garcia-Martin, “Optical conductance of waveguides built into finite photonic crystals,” Appl. Phys. Lett. 91, 061107 (2007).
[CrossRef]

E. Viasnoff-Schwoob, C. Weisbuch, H. Benisty, C. Cuisin, E. Derouin, O. Drisse, G.-H. Duan, L. Legouézigou, O. Legouézigou, F. Pommereau, S. Golka, H. Heidrich, H. J. Hensel, and K. Janiak, “Compact wavelength monitoring by lateral outcoupling in wedged photonic crystal multimode waveguides,” Appl. Phys. Lett. 86, 101107 (2005).
[CrossRef]

O. Khayam, C. Cambournac, H. Benisty, M. Ayre, H. Brenot, and G. H. Duan, “In-plane Littrow lasing of broad photonic crystal waveguides,” Appl. Phys. Lett. 91, 041111 (2007).
[CrossRef]

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46-47 (1973).
[CrossRef]

IEEE J. Quantum Electron.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33, 2038-2059 (1997).
[CrossRef]

A. Yariv, “Coupled mode theory for guided wave optics,” IEEE J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum Electron. 13, 233-253 (1977).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

T. Baba, D. Mori, K. Inoshita, and Y. Kuroki, “Light localizations in photonic crystal line defect waveguides,” IEEE J. Sel. Top. Quantum Electron. 10, 484-491 (2004).
[CrossRef]

J. Appl. Phys.

H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 79, 7483-7492 (1996).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Nature

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

Opt. Express

Opt. Lett.

Photonics Nanostruct. Fundam. Appl.

H. Benisty, A. David, L. Martinelli, E. Viasnoff-Schwoob, C. Weisbuch, G.-H. Duan, K. Janiak, and H. Heidrich, “From modal control to spontaneous emission and gain in photonic crystal waveguides,” Photonics Nanostruct. Fundam. Appl. 4, 1-11 (2006).
[CrossRef]

Phys. Rev. B

P. Ferrand, R. Romestain, and J. C. Vial, “Photonic band-gap properties of a porous silicon periodic planar waveguide,” Phys. Rev. B 63, 115106 (2001).
[CrossRef]

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. De La Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one-dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

M. Ghulinyan, Z. Gaburro, D. S. Wiersma, and L. Pavesi, “Tuning of resonant Zener tunneling by vapor diffusion and condensation in porous optical superlattices,” Phys. Rev. B 74, 045118 (2006).
[CrossRef]

Phys. Rev. Lett.

I. Vorobeichikh, E. Narevicius, G. Rosenblum, M. Orenstein, and N. Moiseyev, “Electromagnetic realization of orders-of-magnitude tunneling enhancement in a double well system,” Phys. Rev. Lett. 90, 176806 (2003).
[CrossRef]

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

Other

We believe that the extent of slowdown in (k,ω) space is akin to the issue of the natural radius of Fabry-Perot modes (rFP~λ×thickness×finesse), which is itself tightly related to Fresnel zones (r~λ×distance), that is, to the generic quadratic transverse behavior of transverse phase lags off an unfolded reference path). We may, along the same line, conjecture that thickness tolerances would be similar to those of high-finesse Fabry-Perot resonators, demanding thickness variations of less than δW=λ/2/finesse but with a precise finesse definition depending on the frequency span and thus on the number of oscillations being exploited.

J.-M. Lourtioz, H. Benisty, V. Berger, J. M. Gérard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices (Springer, 2005).

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

T. Tamir, Guided Wave Optoelectronics (Springer-Verlag, 1990).
[CrossRef]

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993).

A. Yariv, Quantum Electronics (Wiley, 1989).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).

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Figures (12)

Fig. 1
Fig. 1

(a) Generic broad waveguide with a side corrugation. The z-periodic dielectric component ϵ ̂ ( x ) = FT [ ϵ ( x , z ) ] G o z is sketched together with the electric field profile E m ( x ) of a higher-order transverse mode. (b) The case of a photonic-crystal waveguide is similar, even though the cladding is extended.

Fig. 2
Fig. 2

(a) Dispersion relation of a slab waveguide with artificial folding at the Brillouin zone edge. (b) Locally, branches of higher-order modes cross each other along a regular net and are equidistant. Their FSR is defined, as well as the phase detuning from the Bragg condition.

Fig. 3
Fig. 3

(a) Typical dispersion diagram for a coupling constant still small compared with the FSR. Blue, real part of the dispersion; red, imaginary part added to the real part (see inset). (b) Same as (a) for a case where parity (see inset) splits the interaction with the grating into two independent subsets, whose branches cross each other, thus doubling their frequency separation in the interaction region.

Fig. 4
Fig. 4

Lowest two bands of the positive frequency half-plane of Fig. 3a (a) at critical coupling and (b) above critical coupling.

Fig. 5
Fig. 5

Imaginary eigenvalues for (a) a generic case for increasing the coupling constant up to κ = 0.6 . (b) Generic sketch of the band structure above the critical coupling with the two superlocalized states appearing with their high imaginary wave vector (all imaginary values are plotted with respect to the zero abscissa here); the dashed line shows the point used in (a). (c) Same as (a) but for the case of Fig. 3b where symmetry selection rules apply. (d) Enlarged band structure of (b) close to zero detuning. The inset shows that local stop bands are somewhat dispersed, as an effect of the finite number of modes.

Fig. 6
Fig. 6

Semilog plots of the slopes of the first bands in Figs. 3a, 5 as a measure of group velocity, v g = ω k z , within a normalization factor. The three cases correspond to (a) below, (b) at, and (c) above the critical coupling. The order of magnitude of slowdown (around a decade) and its extent (spanning a few oscillations) are seen in (b).

Fig. 7
Fig. 7

Study of eigenmode decomposition: (a) the branches associated with selected coupling constants and the points b–e chosen for the plots below. (b) Real part of the forward (blue) and backward (magenta) coefficients for the modes near the origin. The two modes give the same distribution, with just backward and forward swapped. An imaginary part also exists, with rather more mode mixing, but no large coefficients. (c) Appearance of more mixing near critical coupling. (d) Disappearance of the latter strong mixing above the critical coupling. (e) Strongly mixed nature of the superimaginary modes above critical coupling.

Fig. 8
Fig. 8

Study of transmission along a section of given length L, without or with gain. Here, one of the higher-lying interacting bands is studied. (a) Peaks spanning a transmission window defined by the band limits are similar to those of a 1D DBR for a low coupling constant. (b) For a coupling constant above the critical value, a complex pattern occurs, with transmission peaks not reaching unity. (c) In the presence of gain, the narrower peaks associated with the slower local group velocities have the larger gain. (d) Same effect for a large coupling constant, with more contrast as some peaks are quite narrow. The dashed curve is a guide to the eye.

Fig. 9
Fig. 9

Real broad periodic waveguide with triangular corrugation for studies by PWE (band structure) and by FDTD (propagation). Indices are n 1 = n 3 = 1 and n 2 = 3.21 in our case.

Fig. 10
Fig. 10

(a) Bands of the system illustrated in Fig. 9 (E polarization), with h Λ = 1.0 and W Λ = 15 . (b) First magnification of the dotted box, with real and imaginary dispersion [same convention as Fig. 3a], showing the superimaginary modes. (c) Second magnification of the real dispersion only, highlighting the low group-velocity range attained, v g = c n g . (d) Band structure of the W2 photonic-crystal waveguide, showing slow modes of appreciable bandwidth. (d) Band structure of a corrugated guide with h Λ = 1.0 on both sides and W Λ = 1.5 for comparison.

Fig. 11
Fig. 11

(a) Analysis of flatbands around extrema of minibands and minigaps. Red/blue spacings increase/decrease along a vertical. (b) Plot of the extrema among two adjacent bands (for h Λ = 1.0 ) as a function of band frequency. The crossing is the flatband situation. Vertical dashes indicate the miniband location for W Λ = 6 . v g follows the trend of the gray “butterfly,” linear versus ( ω ω o ) . The crossing point evolves along the dotted curve for variable h. (c) Slow-light regions, primary and secondary, as deduced from a study at various corrugation heights (ellipses and lozenges). The Gaussian is the spectrum of the source pulse used for FDTD simulations in Fig. 12.

Fig. 12
Fig. 12

FDTD observation of light slowdown for waveguides with W Λ = 6 and variable corrugation depth. (a)–(d) Output power integrated along the cross section (see Fig. 9) and plotted as a function of simulation time. (e) Plot of cumulated signals showing the slower rise time. The corrugation depths h Λ are indicated. Cases (b) and (d) give the flattest rising edge, in agreement with the degree of coincidence of the pulse spectrum with the critical regions in Fig. 11c.

Equations (15)

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modulated region E m ( x ) E m ( x ) d x W modul E 0 2 W E 0 2 .
i d a n ( z ) d z = β n a n .
β n = v g 1 [ ω ω 0 Δ n × FSR ω ] .
( i d d z + β n ) a n ( z ) + j = 1 N κ n j b j ( z ) = 0 , with 1 n N ,
( i d d z + β n ) b n ( z ) + j = 1 N κ n j a j ( z ) = 0 , with 1 n N .
d d z M = i C M ,
π κ c FSR ω = 1.0 .
T ( ω ) = n = 1 N a n ( z = L ) 2 ,
R ( ω ) = n = 1 N b n ( z = 0 ) 2 .
( n core ω c ) 2 = k 2 + m 2 π 2 W 2 .
n core c ω n core c ω M 0 [ 1 + ( c n core ω M 0 ) 2 k 0 Δ k + ( c π n core ω M 0 W ) 2 M Δ m ] .
ω ω M 0 [ 1 + sin 2 ( θ ) ( Δ k k 0 ) + cos 2 ( θ ) ( Δ m M ) ] .
ω ω M 0 FSR ω Δ m + [ W π tan ( θ ) ] Δ k ,
E m 2 ε ̂ 1 ( x ) d x ε ̂ 1 max 0 W modul E 0 2 sin 2 ( m π W x ) d x = ε ̂ 1 max E 0 2 ( m π W ) 2 W modul 3 3 ,
Γ ( m ) Γ 1 ( m , m ) = E m 2 ε ̂ 1 ( x ) d x E m 2 d x m 2 W 2 W = m 2 W 3 .

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