Abstract

The delay performance of slow light optical pulses inside photonic crystal slab waveguides is considered in the linear and nonlinear propagation regime from both a theoretical and an application point of view. The numerical model used relies on a nonlinear envelope propagation equation that includes the effects of second- and third-order dispersion, optical losses, and self-phase modulation. It is numerically shown that for rates of 40Gb/s and 100Gb/s, nonlinear solitary pulses experience less broadening than the linear case and can therefore be used to obtain larger delays. The influence of propagation losses on the soliton broadening factor is also incorporated and discussed. The results demonstrate the potential of implementing a variety of linear and nonlinear signal processing applications in photonic crystal waveguides including optical buffering.

© 2012 Optical Society of America

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    [CrossRef]
  37. S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenovic, L. Kuipers, D. M. Beggs, and T. F. Krauss, “Statistical fluctuations of transmission in slow light photonic-crystal waveguides,” Opt. Express 18, 14654–14663 (2010).
    [CrossRef]
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2012 (1)

C. Caer, X. Le Roux, D. Marris-Morrini, L. Vivien, and E. Cassan, “Slow light in slot photonic crystal waveguides by dispersion engineering,” Proc. SPIE 8425, 842504 (2012).
[CrossRef]

2011 (1)

2010 (7)

S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenovic, L. Kuipers, D. M. Beggs, and T. F. Krauss, “Statistical fluctuations of transmission in slow light photonic-crystal waveguides,” Opt. Express 18, 14654–14663 (2010).
[CrossRef]

M. Feng, K. L. Silverman, R. P. Mirin, and S. T. Cundiff, “Dark pulse quantum dot diode laser,” Opt. Express 18, 13385–13395(2010).
[CrossRef]

S. F. Hanim, J. Ali, and P. P. Yupapin, “Dark soliton generation using dual brillouin fiber laser in a fiber optic ring resonator,” Microw. Opt. Technol. Lett. 52, 881–883 (2010).
[CrossRef]

L. Lui, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low power, all-optical flip-flop memory on silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640  Gb/s using slow-light,” Opt. Express 18, 7770–7781 (2010).
[CrossRef]

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenovic, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
[CrossRef]

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

2009 (4)

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of fiber laser,” Phys. Rev. A 80, 045803 (2009).
[CrossRef]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17, 2944–2953 (2009).
[CrossRef]

S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. 103, 063903 (2009).
[CrossRef]

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80, 195305 (2009).
[CrossRef]

2008 (2)

B. Wang, S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Backscattering in monomode periodic waveguides,” Phys. Rev. B 78, 245108 (2008).
[CrossRef]

A. Theocharidis, T. Kamalakis, A. Chipouras, and T. Sphicopoulos, “Linear and nonlinear optical pulse propagation in photonic crystal waveguides near the band edge,” IEEE J. Quantum Electron. 44, 1020–1027 (2008).
[CrossRef]

2007 (6)

I. Neokosmidis, T. Kamalakis, and T. Sphicopoulos, “Optical delay lines based on soliton propagation in photonic crystal coupled resonator optical waveguides,” IEEE J. Quantum Electron. 43, 560–567 (2007).
[CrossRef]

L. C. Andreani and D. Gerace, “Light-matter interaction in photonic crystal slabs,” Phys. Status Solidi B 244, 3528–3539 (2007).
[CrossRef]

T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D 40, 2666–2670 (2007).
[CrossRef]

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observations of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express 15, 17458 (2007).
[CrossRef]

T. Kamalakis and T. Sphicopoulos, “A new formulation of coupled propagation equations in periodic nanophotonic waveguides for the treatment of Kerr-induced nonlinearities,” IEEE J. Quantum Electron. 43, 923–933 (2007).
[CrossRef]

2006 (1)

2005 (4)

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, 033903 (2005).
[CrossRef]

D. Gerace and L. C. Andreani, “Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs,” Photon. Nanostr. Fundam. Appl. 3, 120–128 (2005).
[CrossRef]

A. Petrov and M. Eich, “Dispersion compensation with photonic crystal line-defect waveguides,” IEEE J. Select. Areas Commun. Nanotech. Commun. 23, 1396–1401 (2005).
[CrossRef]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[CrossRef]

2004 (2)

N. Panoiu, M. Bahl, and R. Osgood, “All-optical tunability of a nonlinear photonic crystal channel drop filter,” Opt. Express 12, 1605–1610 (2004).
[CrossRef]

A. Yu. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
[CrossRef]

2001 (2)

2000 (2)

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

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Non-Linear Fiber Optics (Academic, 2001).

Ali, J.

S. F. Hanim, J. Ali, and P. P. Yupapin, “Dark soliton generation using dual brillouin fiber laser in a fiber optic ring resonator,” Microw. Opt. Technol. Lett. 52, 881–883 (2010).
[CrossRef]

Amiranashvili, S.

J. Bethge, C. Bree, S. Amiranashvili, F. Noack, G. Steinmeyer, and A. Demircan, “All-optical transistor using an optical event horizon,” in CLEO/Europe and EQEC 2011 Conference DigestOSA Technical Digest (CD) (Optical Society of America, 2011), paper CF4_1.

Andreani, L. C.

L. C. Andreani and D. Gerace, “Light-matter interaction in photonic crystal slabs,” Phys. Status Solidi B 244, 3528–3539 (2007).
[CrossRef]

D. Gerace and L. C. Andreani, “Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs,” Photon. Nanostr. Fundam. Appl. 3, 120–128 (2005).
[CrossRef]

Arakawa, S.

K. Kitayama, T. Kubo, R. Takahashi, S. Matsuo, S. Arakawa, M. Murata, M. Notomi, K. Nozaki, and K. Kato, “All-optical RAM buffer subsystem demonstrator,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2011), paper OMK.

Asakawa, K.

Baba, T.

Baets, R.

L. Lui, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low power, all-optical flip-flop memory on silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Bahl, M.

Beggs, D. M.

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenovic, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
[CrossRef]

S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenovic, L. Kuipers, D. M. Beggs, and T. F. Krauss, “Statistical fluctuations of transmission in slow light photonic-crystal waveguides,” Opt. Express 18, 14654–14663 (2010).
[CrossRef]

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80, 195305 (2009).
[CrossRef]

I. H. Rey, D. M. Beggs, T. Kampfrath, L. Kuipers, and T. F. Krauss, “Ultrafast tunable optical delay in slow light photonic crystal waveguides,” Group IV Photonics (GFP), 8th IEEE International Conference (2011).

Bethge, J.

J. Bethge, C. Bree, S. Amiranashvili, F. Noack, G. Steinmeyer, and A. Demircan, “All-optical transistor using an optical event horizon,” in CLEO/Europe and EQEC 2011 Conference DigestOSA Technical Digest (CD) (Optical Society of America, 2011), paper CF4_1.

Bree, C.

J. Bethge, C. Bree, S. Amiranashvili, F. Noack, G. Steinmeyer, and A. Demircan, “All-optical transistor using an optical event horizon,” in CLEO/Europe and EQEC 2011 Conference DigestOSA Technical Digest (CD) (Optical Society of America, 2011), paper CF4_1.

Caer, C.

C. Caer, X. Le Roux, D. Marris-Morrini, L. Vivien, and E. Cassan, “Slow light in slot photonic crystal waveguides by dispersion engineering,” Proc. SPIE 8425, 842504 (2012).
[CrossRef]

Cassan, E.

C. Caer, X. Le Roux, D. Marris-Morrini, L. Vivien, and E. Cassan, “Slow light in slot photonic crystal waveguides by dispersion engineering,” Proc. SPIE 8425, 842504 (2012).
[CrossRef]

Chipouras, A.

A. Theocharidis, T. Kamalakis, A. Chipouras, and T. Sphicopoulos, “Linear and nonlinear optical pulse propagation in photonic crystal waveguides near the band edge,” IEEE J. Quantum Electron. 44, 1020–1027 (2008).
[CrossRef]

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves, 2nd ed. (IEEE, 1990).

Colman, P.

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Combrie, S.

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Corcoran, B.

Cundiff, S. T.

De Rossi, A.

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

de Vries, T.

L. Lui, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low power, all-optical flip-flop memory on silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Demircan, A.

J. Bethge, C. Bree, S. Amiranashvili, F. Noack, G. Steinmeyer, and A. Demircan, “All-optical transistor using an optical event horizon,” in CLEO/Europe and EQEC 2011 Conference DigestOSA Technical Digest (CD) (Optical Society of America, 2011), paper CF4_1.

Doran, N. J.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

Ebnali-Heidari, M.

Eggleton, B. J.

Eich, M.

A. Petrov and M. Eich, “Dispersion compensation with photonic crystal line-defect waveguides,” IEEE J. Select. Areas Commun. Nanotech. Commun. 23, 1396–1401 (2005).
[CrossRef]

A. Yu. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
[CrossRef]

Engelen, R. J. P.

Fan, S.

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

Feng, M.

Forysiak, W.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

Geluk, E.

L. Lui, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low power, all-optical flip-flop memory on silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Gerace, D.

L. C. Andreani and D. Gerace, “Light-matter interaction in photonic crystal slabs,” Phys. Status Solidi B 244, 3528–3539 (2007).
[CrossRef]

D. Gerace and L. C. Andreani, “Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs,” Photon. Nanostr. Fundam. Appl. 3, 120–128 (2005).
[CrossRef]

Grillet, C.

Hama, Y.

Hanim, S. F.

S. F. Hanim, J. Ali, and P. P. Yupapin, “Dark soliton generation using dual brillouin fiber laser in a fiber optic ring resonator,” Microw. Opt. Technol. Lett. 52, 881–883 (2010).
[CrossRef]

Hughes, S.

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80, 195305 (2009).
[CrossRef]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[CrossRef]

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, 033903 (2005).
[CrossRef]

Hugonin, J. P.

Husko, C.

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Huybrechts, K.

L. Lui, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low power, all-optical flip-flop memory on silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Ikeda, N.

Ilic, B.

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observations of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Ishikura, N.

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef]

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

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed.(Princeton University, 2008).

Johnson, S. G.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef]

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

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed.(Princeton University, 2008).

Kamalakis, T.

A. Theocharidis, T. Kamalakis, A. Chipouras, and T. Sphicopoulos, “Linear and nonlinear optical pulse propagation in photonic crystal waveguides near the band edge,” IEEE J. Quantum Electron. 44, 1020–1027 (2008).
[CrossRef]

I. Neokosmidis, T. Kamalakis, and T. Sphicopoulos, “Optical delay lines based on soliton propagation in photonic crystal coupled resonator optical waveguides,” IEEE J. Quantum Electron. 43, 560–567 (2007).
[CrossRef]

T. Kamalakis and T. Sphicopoulos, “A new formulation of coupled propagation equations in periodic nanophotonic waveguides for the treatment of Kerr-induced nonlinearities,” IEEE J. Quantum Electron. 43, 923–933 (2007).
[CrossRef]

Kampfrath, T.

I. H. Rey, D. M. Beggs, T. Kampfrath, L. Kuipers, and T. F. Krauss, “Ultrafast tunable optical delay in slow light photonic crystal waveguides,” Group IV Photonics (GFP), 8th IEEE International Conference (2011).

Kato, K.

K. Kitayama, T. Kubo, R. Takahashi, S. Matsuo, S. Arakawa, M. Murata, M. Notomi, K. Nozaki, and K. Kato, “All-optical RAM buffer subsystem demonstrator,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2011), paper OMK.

Kitayama, K.

K. Kitayama, T. Kubo, R. Takahashi, S. Matsuo, S. Arakawa, M. Murata, M. Notomi, K. Nozaki, and K. Kato, “All-optical RAM buffer subsystem demonstrator,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2011), paper OMK.

Korterik, J. P.

Krauss, T. F.

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenovic, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
[CrossRef]

B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640  Gb/s using slow-light,” Opt. Express 18, 7770–7781 (2010).
[CrossRef]

S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenovic, L. Kuipers, D. M. Beggs, and T. F. Krauss, “Statistical fluctuations of transmission in slow light photonic-crystal waveguides,” Opt. Express 18, 14654–14663 (2010).
[CrossRef]

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80, 195305 (2009).
[CrossRef]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17, 2944–2953 (2009).
[CrossRef]

T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D 40, 2666–2670 (2007).
[CrossRef]

I. H. Rey, D. M. Beggs, T. Kampfrath, L. Kuipers, and T. F. Krauss, “Ultrafast tunable optical delay in slow light photonic crystal waveguides,” Group IV Photonics (GFP), 8th IEEE International Conference (2011).

Kubo, T.

K. Kitayama, T. Kubo, R. Takahashi, S. Matsuo, S. Arakawa, M. Murata, M. Notomi, K. Nozaki, and K. Kato, “All-optical RAM buffer subsystem demonstrator,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2011), paper OMK.

Kuipers, L.

Kumar, R.

L. Lui, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low power, all-optical flip-flop memory on silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Kuramochi, E.

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express 15, 17458 (2007).
[CrossRef]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[CrossRef]

Lalanne, P.

Le Roux, X.

C. Caer, X. Le Roux, D. Marris-Morrini, L. Vivien, and E. Cassan, “Slow light in slot photonic crystal waveguides by dispersion engineering,” Proc. SPIE 8425, 842504 (2012).
[CrossRef]

Lui, L.

L. Lui, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low power, all-optical flip-flop memory on silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Marris-Morrini, D.

C. Caer, X. Le Roux, D. Marris-Morrini, L. Vivien, and E. Cassan, “Slow light in slot photonic crystal waveguides by dispersion engineering,” Proc. SPIE 8425, 842504 (2012).
[CrossRef]

Matsuo, S.

K. Kitayama, T. Kubo, R. Takahashi, S. Matsuo, S. Arakawa, M. Murata, M. Notomi, K. Nozaki, and K. Kato, “All-optical RAM buffer subsystem demonstrator,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2011), paper OMK.

Mazoyer, S.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed.(Princeton University, 2008).

Melloni, A.

Mirin, R. P.

Mitsugi, S.

Monat, C.

Morichetti, F.

Morita, M.

Morthier, G.

L. Lui, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low power, all-optical flip-flop memory on silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Moss, D. J.

Murata, M.

K. Kitayama, T. Kubo, R. Takahashi, S. Matsuo, S. Arakawa, M. Murata, M. Notomi, K. Nozaki, and K. Kato, “All-optical RAM buffer subsystem demonstrator,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2011), paper OMK.

Neokosmidis, I.

I. Neokosmidis, T. Kamalakis, and T. Sphicopoulos, “Optical delay lines based on soliton propagation in photonic crystal coupled resonator optical waveguides,” IEEE J. Quantum Electron. 43, 560–567 (2007).
[CrossRef]

Nijhof, J. H. B.

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

Noack, F.

J. Bethge, C. Bree, S. Amiranashvili, F. Noack, G. Steinmeyer, and A. Demircan, “All-optical transistor using an optical event horizon,” in CLEO/Europe and EQEC 2011 Conference DigestOSA Technical Digest (CD) (Optical Society of America, 2011), paper CF4_1.

Notomi, M.

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express 15, 17458 (2007).
[CrossRef]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[CrossRef]

K. Kitayama, T. Kubo, R. Takahashi, S. Matsuo, S. Arakawa, M. Murata, M. Notomi, K. Nozaki, and K. Kato, “All-optical RAM buffer subsystem demonstrator,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2011), paper OMK.

Nozaki, K.

K. Kitayama, T. Kubo, R. Takahashi, S. Matsuo, S. Arakawa, M. Murata, M. Notomi, K. Nozaki, and K. Kato, “All-optical RAM buffer subsystem demonstrator,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2011), paper OMK.

O’Faolain, L.

Osgood, R.

Panoiu, N.

Patterson, M.

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80, 195305 (2009).
[CrossRef]

Pelusi, M.

Petrov, A.

A. Petrov and M. Eich, “Dispersion compensation with photonic crystal line-defect waveguides,” IEEE J. Select. Areas Commun. Nanotech. Commun. 23, 1396–1401 (2005).
[CrossRef]

Petrov, A. Yu.

A. Yu. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
[CrossRef]

Ramaswami, R.

R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Prespective (Morgan Kaufman, 1998).

Ramunno, L.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[CrossRef]

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, 033903 (2005).
[CrossRef]

Regreny, P.

L. Lui, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low power, all-optical flip-flop memory on silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Rey, I. H.

I. H. Rey, D. M. Beggs, T. Kampfrath, L. Kuipers, and T. F. Krauss, “Ultrafast tunable optical delay in slow light photonic crystal waveguides,” Group IV Photonics (GFP), 8th IEEE International Conference (2011).

Rodier, J. C.

Roelkens, G.

L. Lui, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low power, all-optical flip-flop memory on silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Sagnes, I.

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Schulz, S.

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80, 195305 (2009).
[CrossRef]

Schulz, S. A.

Shinkawa, M.

Shinya, A.

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express 15, 17458 (2007).
[CrossRef]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[CrossRef]

Silverman, K. L.

Sipe, J. E.

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, 033903 (2005).
[CrossRef]

Sivarajan, K. N.

R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Prespective (Morgan Kaufman, 1998).

Spasenovic, M.

Sphicopoulos, T.

A. Theocharidis, T. Kamalakis, A. Chipouras, and T. Sphicopoulos, “Linear and nonlinear optical pulse propagation in photonic crystal waveguides near the band edge,” IEEE J. Quantum Electron. 44, 1020–1027 (2008).
[CrossRef]

I. Neokosmidis, T. Kamalakis, and T. Sphicopoulos, “Optical delay lines based on soliton propagation in photonic crystal coupled resonator optical waveguides,” IEEE J. Quantum Electron. 43, 560–567 (2007).
[CrossRef]

T. Kamalakis and T. Sphicopoulos, “A new formulation of coupled propagation equations in periodic nanophotonic waveguides for the treatment of Kerr-induced nonlinearities,” IEEE J. Quantum Electron. 43, 923–933 (2007).
[CrossRef]

Spuesens, T.

L. Lui, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low power, all-optical flip-flop memory on silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Steinmeyer, G.

J. Bethge, C. Bree, S. Amiranashvili, F. Noack, G. Steinmeyer, and A. Demircan, “All-optical transistor using an optical event horizon,” in CLEO/Europe and EQEC 2011 Conference DigestOSA Technical Digest (CD) (Optical Society of America, 2011), paper CF4_1.

Sugimoto, Y.

Suzuki, K.

Takahashi, R.

K. Kitayama, T. Kubo, R. Takahashi, S. Matsuo, S. Arakawa, M. Murata, M. Notomi, K. Nozaki, and K. Kato, “All-optical RAM buffer subsystem demonstrator,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2011), paper OMK.

Tanabe, T.

Tang, D. Y.

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of fiber laser,” Phys. Rev. A 80, 045803 (2009).
[CrossRef]

Taniyama, H.

Theocharidis, A.

A. Theocharidis, T. Kamalakis, A. Chipouras, and T. Sphicopoulos, “Linear and nonlinear optical pulse propagation in photonic crystal waveguides near the band edge,” IEEE J. Quantum Electron. 44, 1020–1027 (2008).
[CrossRef]

Topolancik, J.

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observations of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Tucker, R. S.

van Hulst, N. F.

Van Thourhout, D.

L. Lui, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low power, all-optical flip-flop memory on silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

Villeneuve, P. R.

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

Vivien, L.

C. Caer, X. Le Roux, D. Marris-Morrini, L. Vivien, and E. Cassan, “Slow light in slot photonic crystal waveguides by dispersion engineering,” Proc. SPIE 8425, 842504 (2012).
[CrossRef]

Vollmer, F.

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observations of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Wang, B.

B. Wang, S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Backscattering in monomode periodic waveguides,” Phys. Rev. B 78, 245108 (2008).
[CrossRef]

Watanabe, T.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[CrossRef]

Watanabe, Y.

White, T. P.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Molding the Flow of Light, 2nd ed.(Princeton University, 2008).

Wong, C. W.

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Wu, X.

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of fiber laser,” Phys. Rev. A 80, 045803 (2009).
[CrossRef]

Young, J. F.

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, 033903 (2005).
[CrossRef]

Yupapin, P. P.

S. F. Hanim, J. Ali, and P. P. Yupapin, “Dark soliton generation using dual brillouin fiber laser in a fiber optic ring resonator,” Microw. Opt. Technol. Lett. 52, 881–883 (2010).
[CrossRef]

Zhang, H.

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of fiber laser,” Phys. Rev. A 80, 045803 (2009).
[CrossRef]

Zhao, L. M.

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of fiber laser,” Phys. Rev. A 80, 045803 (2009).
[CrossRef]

Zhong, W. D.

Appl. Phys. Lett. (1)

A. Yu. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
[CrossRef]

IEEE J. Quantum Electron. (3)

A. Theocharidis, T. Kamalakis, A. Chipouras, and T. Sphicopoulos, “Linear and nonlinear optical pulse propagation in photonic crystal waveguides near the band edge,” IEEE J. Quantum Electron. 44, 1020–1027 (2008).
[CrossRef]

I. Neokosmidis, T. Kamalakis, and T. Sphicopoulos, “Optical delay lines based on soliton propagation in photonic crystal coupled resonator optical waveguides,” IEEE J. Quantum Electron. 43, 560–567 (2007).
[CrossRef]

T. Kamalakis and T. Sphicopoulos, “A new formulation of coupled propagation equations in periodic nanophotonic waveguides for the treatment of Kerr-induced nonlinearities,” IEEE J. Quantum Electron. 43, 923–933 (2007).
[CrossRef]

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

J. H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330–336 (2000).
[CrossRef]

IEEE J. Select. Areas Commun. Nanotech. Commun. (1)

A. Petrov and M. Eich, “Dispersion compensation with photonic crystal line-defect waveguides,” IEEE J. Select. Areas Commun. Nanotech. Commun. 23, 1396–1401 (2005).
[CrossRef]

J. Lightwave Technol. (1)

J. Phys. D (1)

T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D 40, 2666–2670 (2007).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

S. F. Hanim, J. Ali, and P. P. Yupapin, “Dark soliton generation using dual brillouin fiber laser in a fiber optic ring resonator,” Microw. Opt. Technol. Lett. 52, 881–883 (2010).
[CrossRef]

Nat. Photonics (2)

L. Lui, R. Kumar, K. Huybrechts, T. Spuesens, G. Roelkens, E. Geluk, T. de Vries, P. Regreny, D. Van Thourhout, R. Baets, and G. Morthier, “An ultra-small, low power, all-optical flip-flop memory on silicon chip,” Nat. Photonics 4, 182–187 (2010).
[CrossRef]

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[CrossRef]

Opt. Express (10)

N. Panoiu, M. Bahl, and R. Osgood, “All-optical tunability of a nonlinear photonic crystal channel drop filter,” Opt. Express 12, 1605–1610 (2004).
[CrossRef]

R. J. P. Engelen, Y. Sugimoto, Y. Watanabe, J. P. Korterik, N. Ikeda, N. F. van Hulst, K. Asakawa, and L. Kuipers, “The effect of higher-order dispersion on slow light propagation in photonic crystal waveguides,” Opt. Express 14, 1658–1672 (2006).
[CrossRef]

M. Notomi, T. Tanabe, A. Shinya, E. Kuramochi, H. Taniyama, S. Mitsugi, and M. Morita, “Nonlinear and adiabatic control of high-Q photonic crystal nanocavities,” Opt. Express 15, 17458 (2007).
[CrossRef]

C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17, 2944–2953 (2009).
[CrossRef]

B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640  Gb/s using slow-light,” Opt. Express 18, 7770–7781 (2010).
[CrossRef]

M. Feng, K. L. Silverman, R. P. Mirin, and S. T. Cundiff, “Dark pulse quantum dot diode laser,” Opt. Express 18, 13385–13395(2010).
[CrossRef]

S. Mazoyer, P. Lalanne, J. C. Rodier, J. P. Hugonin, M. Spasenovic, L. Kuipers, D. M. Beggs, and T. F. Krauss, “Statistical fluctuations of transmission in slow light photonic-crystal waveguides,” Opt. Express 18, 14654–14663 (2010).
[CrossRef]

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenovic, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
[CrossRef]

M. Shinkawa, N. Ishikura, Y. Hama, K. Suzuki, and T. Baba, “Nonlinear enhancement in photonic crystal slow light waveguides fabricated using CMOS-compatible process,” Opt. Express 19, 22208–22218 (2011).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef]

Photon. Nanostr. Fundam. Appl. (1)

D. Gerace and L. C. Andreani, “Effects of disorder on propagation losses and cavity Q-factors in photonic crystal slabs,” Photon. Nanostr. Fundam. Appl. 3, 120–128 (2005).
[CrossRef]

Phys. Rev. A (1)

H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of fiber laser,” Phys. Rev. A 80, 045803 (2009).
[CrossRef]

Phys. Rev. B (4)

B. Wang, S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Backscattering in monomode periodic waveguides,” Phys. Rev. B 78, 245108 (2008).
[CrossRef]

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

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72, 161318 (2005).
[CrossRef]

M. Patterson, S. Hughes, S. Schulz, D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Disorder-induced incoherent scattering losses in photonic crystal waveguides: Bloch mode reshaping, multiple scattering, and breakdown of the Beer-Lambert law,” Phys. Rev. B 80, 195305 (2009).
[CrossRef]

Phys. Rev. Lett. (3)

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental observations of strong photon localization in disordered photonic crystal waveguides,” Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

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Figures (12)

Fig. 1.
Fig. 1.

Illustration of some of the PCSW designs considered in this paper: (a) a standard W1 air membrane PCSW formed in a triangular lattice of air holes embedded in a high-index material (e.g., Si) ( a = 410 nm , r a = 0.27 a , d = 0.5366 a ). (b) Horizontal cross section of an LE PCSW where an intentional dislocation is introduced on the holes situated closest to the line defect. The dislocations along the y -axis are assumed s 1 = 0.1171 a and s 2 = 0.039 a [18]. (c) A W1.1 waveguide, where the defect gap width is intentionally increased to 1.1 3 a , and (d) a W0.9 waveguide where the gap width is reduced to 0.9 3 a .

Fig. 2.
Fig. 2.

(a) Dispersion relation curves of the defect mode for the standard W1 and the LE-PCSWs, (b) the GVD coefficient β 2 , and (c) the TOD coefficient β 3 for the various waveguide designs introduced in Fig. 1.

Fig. 3.
Fig. 3.

(a) Backscattering coefficients ρ BS for the standard W1 and the LE-PCSWs, and (b) propagation loss coefficient for the waveguide designs in Fig. 1 assuming that the coefficient of the standard W1 waveguide at the fast light regime ( n g 0 5 ) is Γ ( n g 0 ) Γ ( 5 ) = 2 dB / cm .

Fig. 4.
Fig. 4.

(a) Broadening factor in the linear regime for a standard W1 and the LE-PCSW assuming that n g is varied and the length of the waveguide is chosen so that L = min ( L 1 , L 2 ) for (a)  40 Gb / s (the arrows indicate the direction of increasing n g , corresponding to a normalized frequency range of (A) 0.2648 a / λ 0.268 and (B) 0.2583 a / λ 0.2590 , in the case of the LE-PCSW), and (b)  100 Gb / s data rates where the broadening factor in the case of the LE-PCSW is not displayed because for this type of waveguide we always have BF > 1.3 if the waveguide length is selected as L = min ( L 1 , L 2 ) . (c) corresponds to the broadening factor obtained for the LEPCSW assuming for a fixed value of n g = 37 and various propagation lengths L chosen from 0 L min ( L 1 , L 2 ) . Also shown in all figures is the contribution of TOD.

Fig. 5.
Fig. 5.

Fundamental soliton peak power P 0 corresponding to a data rate of 40 Gb / s of the standard W1 and the LE-PCSWs.

Fig. 6.
Fig. 6.

Broadening factor for 40 Gb / s data rates of (a) a standard W1 waveguide, (b) an LE-PCSW (the arrows indicate the direction of increasing n g , corresponding to a normalized frequency range (A) and (B) mentioned in Fig. 4(a), while (C) is 0.2614 a / λ 0.2648 and (D) is 0.2583 a / λ 0.2609 ), and (c) the W1.1 and a W0.9 waveguides where n g is varied and the length of the waveguide is chosen so that L = min ( L 1 , L 2 ) . (d) shows the case of an LE-PCSW operated at n g = 37 and the propagation length L varies in 0 L min ( L 1 , L 2 ) . The figure assumes 2 dB / cm propagation losses at the fast light regime for the standard W1 waveguide and a maximum allowable loss limit of 20 dB . The arrows in (b) show the direction of increasing n g .

Fig. 7.
Fig. 7.

(a) Broadening factors obtained with both the RMS and the FWHM pulsewidths, and (b) the initial and the final intensity of the pulse at 40 Gbps of a standard W1 waveguide, where gray pulses appear adjacent to the central dark soliton.

Fig. 8.
Fig. 8.

Broadening factor for a 100 Gb / s data rate for (a) a standard W1 and the LE waveguide 100 Gb / s data rates where the broadening factor in the case of the LE-PCSW is not displayed because for this type of waveguide we always have BF > 1.3 if the waveguide length is selected as L = min ( L 1 , L 2 ) , (b) the W1.1 and W0.9 waveguides, and (c) the LE waveguide operating at n g = 37 .

Fig. 9.
Fig. 9.

Broadening factor of 40 Gb / s soliton pulses in the case of the LE-PCSW operating at n g = 37 , when the loss coefficient is increased by 20%.

Fig. 10.
Fig. 10.

Broadening factor of a LE-PCSW waveguide operated at n g = 37 obtained for (a)  40 Gb / s for a 5 dB / cm fast light loss of the standard W1 and (b)  40 Gb / s for a 1 dB / cm fast light loss of the standard W1 and (c)  100 Gb / s .

Fig. 11.
Fig. 11.

(a) Spectrum of a Gaussian pulse corresponding to R b = 40 Gb / s and a randomly fluctuating transfer function H ( f ), and (b) the power | A | 2 of the initial pulse and the pulse corresponding to the Gaussian spectrum multiplied by H ( f ) .

Fig. 12.
Fig. 12.

(a) Electric field intensity in alternative waveguide designs discussed in the text obtained at n g = 15 , and (b) estimated broadening factors for 100 Gb / s data rates assuming 2 dB / cm fast light losses for each waveguide design.

Equations (12)

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A x + Γ 2 A + j β 2 2 2 A T 2 β 3 6 3 A T 3 = j γ | A | 2 A ,
γ ( ω ) = 2 ω ε 0 a V ε NL | E ( r , ω ) | 4 d V .
ε NL = ε L ( r ) n 2 ( r ) Z 0 .
Γ = c 1 ρ OP n g + c 2 ρ BS n g 2 .
ρ BS = n | L c E T E T + ( ε 1 ε 2 ) 1 D N D N d r | 2 ,
ρ OP = n | L c E T + ε 1 1 D N d r | 2 .
Γ ( n g ) = Γ ( n g 0 ) ( n g n g 0 ) 2 ρ BS ( n g ) ρ BS ( n g 0 ) ,
BF = σ ( L ) σ ( 0 ) ,
σ 2 ( x ) = ( T T ¯ ) 2 | A ( x , T ) | 2 d T | A ( x , T ) | 2 d T .
A ( 0 , T ) = exp ( T 2 2 T 0 2 ) ,
BF LINEAR = ( 1 + ( L / L D 2 ) 2 + 1 4 ( L / L D 3 ) 2 ) 1 / 2 .
P 0 = | β 2 | γ T 0 2 .

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