A proposal for enhancing four-wave mixing in slow light engineered photonic crystal waveguides and its application to optical regeneration

M. Ebnali-Heidari; C. Monat; C. Grillet; M. K Moravvej-Farshi

doi:10.1364/OE.17.018340

A proposal for enhancing four-wave mixing in slow light engineered photonic crystal waveguides and its application to optical regeneration

M. Ebnali-Heidari, C. Monat, C. Grillet, and M. K Moravvej-Farshi

Optics Express
Vol. 17,
Issue 20,
pp. 18340-18353
(2009)
•https://doi.org/10.1364/OE.17.018340

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M. Ebnali-Heidari, C. Monat, C. Grillet, and M. K Moravvej-Farshi, "A proposal for enhancing four-wave mixing in slow light engineered photonic crystal waveguides and its application to optical regeneration," Opt. Express 17, 18340-18353 (2009)

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Related Topics
Table of Contents Category
- Nonlinear Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Photonic crystal waveguides (130.5296)
- Nonlinear optics, four-wave mixing (190.4380)
- Signal regeneration (200.6015)
- Dispersion (260.2030)

About this Article
History
- Original Manuscript: August 4, 2009
- Revised Manuscript: September 17, 2009
- Manuscript Accepted: September 18, 2009
- Published: September 25, 2009

Accessible

Open Access

Abstract

In this paper, we investigate both analytically and numerically four-wave mixing (FWM) in short (80 μm) dispersion engineered slow light photonic crystal waveguides. We demonstrate that both a larger FWM conversion efficiency and an increased FWM bandwidth (~10nm) can be achieved in these waveguides as compared to dispersive PhC waveguides. This improvement is achieved through the net slow light enhancement of the FWM efficiency (almost 30dB as compared to a fast nanowire of similar length), even in the presence of slow light increased linear and nonlinear losses, and the suitable dispersion profile of these waveguides. We show how such improved FWM operation can be advantageously exploited for designing a compact 2R and 3R regenerator with the appropriate nonlinear power transfer function.

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References

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Publication

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T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
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J. F. McMillan, X. D. Yang, N. C. Panoiu, R. M. Osgood, and C. W. Wong, “Enhanced stimulated Raman scattering in slow-light photonic crystal waveguides,” Opt. Lett. 31(9), 1235–1237 (2006).
[PubMed]
B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).
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(4), 2944–2953 (2009).
[PubMed]
K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009).
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M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16(2), 1300–1320 (2008).
[PubMed]
M. R. E. Lamont, B. T. Kuhlmey, and C. M. de Sterke, “Multi-order dispersion engineering for optimal four-wave mixing,” Opt. Express 16(10), 7551–7563 (2008).
[PubMed]
M. R. E. Lamont, B. Luther-Davies, D. Y. Choi, S. Madden, X. Gai, and B. J. Eggleton, “Net-gain from a parametric amplifier on a chalcogenide optical chip,” Opt. Express 16(25), 20374–20381 (2008).
[PubMed]
M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007).
[PubMed]
R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2007).
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[PubMed]
S. Kubo, D. Mori, and T. Baba, “Low-group-velocity and low-dispersion slow light in photonic crystal waveguides,” Opt. Lett. 32(20), 2981–2983 (2007).
[PubMed]
J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
[PubMed]
A. Säynätjoki, M. Mulot, J. Ahopelto, and H. Lipsanen, “Dispersion engineering of photonic crystal waveguides with ring-shaped holes,” Opt. Express 15(13), 8323–8328 (2007).
[PubMed]
M. Ebnali-Heidari, C. Grillet, C. Monat, and B. J. Eggleton, “Dispersion engineering of slow light photonic crystal waveguides using microfluidic infiltration,” Opt. Express 17(3), 1628–1635 (2009).
[PubMed]
G. P. Agrawal, “Nonlinear Fiber Optics, ” in Elsevier Inc, ed. Academic Press (2002).
L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32(4), 391–393 (2007).
[PubMed]
E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express 14(9), 3853–3863 (2006).
[PubMed]
T. Kapfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, “Ultrafast re-routing of light via slow modes in a nano-photonic directional coupler,” Appl. Phys. Lett. 94(24), 241119–241121 (2009).
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(3), 0339031–0339034 (2005).
L. C. Andreani and D. Gerace, “Light-matter interaction in photonic crystal slabs,” Phys. Status Solidi B 244(10), 3528–3539 (2007).
M. Patterson, S. Hughes, S. Combrié, N. V. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903–253906 (2009).
[PubMed]
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(16), 1613181–1613184 (2005).
R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008).
[PubMed]
N. Le Thomas, R. Houdré, L. H. Frandsen, J. Fage-Pedersen, A. Lavrinenko, and P. I. Borel, “Grating-assisted superresolution of slow waves in Fourier space,” Phys. Rev. B 76(3), 035103–035106 (2007).
M. W. Lee, C. Grillet, C. G. Poulton, C. Monat, C. L. Smith, E. Mägi, D. Freeman, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Characterizing photonic crystal waveguides with an expanded k-space evanescent coupling technique,” Opt. Express 16(18), 13800–13808 (2008).
[PubMed]
L. O’Faolain, T. P. White, D. O’Brien, X. D. Yuan, M. D. Settle, and T. F. Krauss, “Dependence of extrinsic loss on group velocity in photonic crystal waveguides,” Opt. Express 15(20), 13129–13138 (2007).
[PubMed]
L. O’Faolain, S. Schulz, D. M. Beggs, T. P. White, A. Samarelli, M. Sorel, R. M. de la Rue, and T. F. Krauss, “Losses in engineered slow light photonic crystal waveguides”, in Proc. European Conference on PECS-VIII,121, (2009)
L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).
M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogensilsequioxane electron-beam resist,” Electron. Lett. 44(2), 115–116 (2008).
W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De La Rue, “Solitons and spectral broadening in long silicon-on- insulator photonic wires,” Opt. Express 16(5), 3310–3319 (2008).
[PubMed]
V. G. Ta’eed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(3), 360–370 (2006).
M. Rochette, J. L. Blows, and B. J. Eggleton, “3R optical regeneration: an all-optical solution with BER improvement,” Opt. Express 14(14), 6414–6427 (2006).
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R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “All-optical regeneration on a silicon chip,” Opt. Express 15(12), 7802–7809 (2007).
[PubMed]
E. Ciaramella, F. Curti, and S. Trillo, “All-optical signal reshaping by means of four-wave mixing in optical fibers,” IEEE Photon. Technol. Lett. 13(2), 142–144 (2001).
A. Bogris and D. Syvridis, “Regenerative properties of a pump-modulated four-wave mixing scheme in dispersion-shifted fibers,” J. Lightwave Technol. 21(9), 1892–1902 (2003).

2009 (8)

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic crystal waveguides,” Nat. Photonics 3(4), 206–210 (2009).

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(4), 2944–2953 (2009).
[PubMed]

K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009).
[PubMed]

A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. Vy Tran, S. Combrié, A. de Rossi, R. Frey, and G. Roosen, “Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide,” Opt. Express 17(2), 552–557 (2009).
[PubMed]

Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009).
[PubMed]

M. Ebnali-Heidari, C. Grillet, C. Monat, and B. J. Eggleton, “Dispersion engineering of slow light photonic crystal waveguides using microfluidic infiltration,” Opt. Express 17(3), 1628–1635 (2009).
[PubMed]

T. Kapfrath, D. M. Beggs, T. P. White, M. Burresi, D. van Oosten, T. F. Krauss, and L. Kuipers, “Ultrafast re-routing of light via slow modes in a nano-photonic directional coupler,” Appl. Phys. Lett. 94(24), 241119–241121 (2009).

M. Patterson, S. Hughes, S. Combrié, N. V. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903–253906 (2009).
[PubMed]

2008 (10)

R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008).
[PubMed]

M. W. Lee, C. Grillet, C. G. Poulton, C. Monat, C. L. Smith, E. Mägi, D. Freeman, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Characterizing photonic crystal waveguides with an expanded k-space evanescent coupling technique,” Opt. Express 16(18), 13800–13808 (2008).
[PubMed]

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogensilsequioxane electron-beam resist,” Electron. Lett. 44(2), 115–116 (2008).

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorrel, and R. M. De La Rue, “Solitons and spectral broadening in long silicon-on- insulator photonic wires,” Opt. Express 16(5), 3310–3319 (2008).
[PubMed]

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16(2), 1300–1320 (2008).
[PubMed]

M. R. E. Lamont, B. T. Kuhlmey, and C. M. de Sterke, “Multi-order dispersion engineering for optimal four-wave mixing,” Opt. Express 16(10), 7551–7563 (2008).
[PubMed]

M. R. E. Lamont, B. Luther-Davies, D. Y. Choi, S. Madden, X. Gai, and B. J. Eggleton, “Net-gain from a parametric amplifier on a chalcogenide optical chip,” Opt. Express 16(25), 20374–20381 (2008).
[PubMed]

T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2(8), 448–450 (2008).

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
[PubMed]

2007 (9)

A. Säynätjoki, M. Mulot, J. Ahopelto, and H. Lipsanen, “Dispersion engineering of photonic crystal waveguides with ring-shaped holes,” Opt. Express 15(13), 8323–8328 (2007).
[PubMed]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007).
[PubMed]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2007).

L. O’Faolain, T. P. White, D. O’Brien, X. D. Yuan, M. D. Settle, and T. F. Krauss, “Dependence of extrinsic loss on group velocity in photonic crystal waveguides,” Opt. Express 15(20), 13129–13138 (2007).
[PubMed]

N. Le Thomas, R. Houdré, L. H. Frandsen, J. Fage-Pedersen, A. Lavrinenko, and P. I. Borel, “Grating-assisted superresolution of slow waves in Fourier space,” Phys. Rev. B 76(3), 035103–035106 (2007).

S. Kubo, D. Mori, and T. Baba, “Low-group-velocity and low-dispersion slow light in photonic crystal waveguides,” Opt. Lett. 32(20), 2981–2983 (2007).
[PubMed]

L. C. Andreani and D. Gerace, “Light-matter interaction in photonic crystal slabs,” Phys. Status Solidi B 244(10), 3528–3539 (2007).

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32(4), 391–393 (2007).
[PubMed]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “All-optical regeneration on a silicon chip,” Opt. Express 15(12), 7802–7809 (2007).
[PubMed]

2006 (6)

E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express 14(9), 3853–3863 (2006).
[PubMed]

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).

V. G. Ta’eed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(3), 360–370 (2006).

M. Rochette, J. L. Blows, and B. J. Eggleton, “3R optical regeneration: an all-optical solution with BER improvement,” Opt. Express 14(14), 6414–6427 (2006).
[PubMed]

J. F. McMillan, X. D. Yang, N. C. Panoiu, R. M. Osgood, and C. W. Wong, “Enhanced stimulated Raman scattering in slow-light photonic crystal waveguides,” Opt. Lett. 31(9), 1235–1237 (2006).
[PubMed]

L. H. Frandsen, A. V. Lavrinenko, J. Fage-Pedersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties,” Opt. Express 14(20), 9444–9450 (2006).
[PubMed]

2005 (2)

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(3), 0339031–0339034 (2005).

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(16), 1613181–1613184 (2005).

2004 (2)

A. Bogoni, P. Ghelfi, M. Scaffardi, and L. Poti, “All-optical regeneration and demultiplexing for 160-Gb/s transmission systems using a NOLM-based three-stage scheme,” J. Quantum Electron. 10, 192–196 (2004).

A. Yu. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85(21), 4866–4868 (2004).

2003 (1)

A. Bogris and D. Syvridis, “Regenerative properties of a pump-modulated four-wave mixing scheme in dispersion-shifted fibers,” J. Lightwave Technol. 21(9), 1892–1902 (2003).

2002 (1)

M. Soljačić, S. G. Johnson, S. H. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19(9), 2052–2059 (2002).

2001 (2)

N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 0566041–05660416 (2001).

E. Ciaramella, F. Curti, and S. Trillo, “All-optical signal reshaping by means of four-wave mixing in optical fibers,” IEEE Photon. Technol. Lett. 13(2), 142–144 (2001).

Agrawal, G. P.

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32(4), 391–393 (2007).
[PubMed]

Ahopelto, J.

A. Säynätjoki, M. Mulot, J. Ahopelto, and H. Lipsanen, “Dispersion engineering of photonic crystal waveguides with ring-shaped holes,” Opt. Express 15(13), 8323–8328 (2007).
[PubMed]

Andreani, L. C.

L. C. Andreani and D. Gerace, “Light-matter interaction in photonic crystal slabs,” Phys. Status Solidi B 244(10), 3528–3539 (2007).

Asakawa, K.

K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009).
[PubMed]

Baba, T.

Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009).
[PubMed]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).

R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008).
[PubMed]

S. Kubo, D. Mori, and T. Baba, “Low-group-velocity and low-dispersion slow light in photonic crystal waveguides,” Opt. Lett. 32(20), 2981–2983 (2007).
[PubMed]

Baron, A.

Beggs, D. M.

Benton, C.

Bhat, N. A. R.

N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 0566041–05660416 (2001).

Blows, J. L.

M. Rochette, J. L. Blows, and B. J. Eggleton, “3R optical regeneration: an all-optical solution with BER improvement,” Opt. Express 14(14), 6414–6427 (2006).
[PubMed]

Bogoni, A.

Bogris, A.

A. Bogris and D. Syvridis, “Regenerative properties of a pump-modulated four-wave mixing scheme in dispersion-shifted fibers,” J. Lightwave Technol. 21(9), 1892–1902 (2003).

Borel, P. I.

Burresi, M.

Choi, D. Y.

Chong, H.

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).

Ciaramella, E.

E. Ciaramella, F. Curti, and S. Trillo, “All-optical signal reshaping by means of four-wave mixing in optical fibers,” IEEE Photon. Technol. Lett. 13(2), 142–144 (2001).

Combrié, S.

Corcoran, B.

Curti, F.

E. Ciaramella, F. Curti, and S. Trillo, “All-optical signal reshaping by means of four-wave mixing in optical fibers,” IEEE Photon. Technol. Lett. 13(2), 142–144 (2001).

De La Rue, R. M.

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).

De Rossi, A.

de Sterke, C. M.

M. R. E. Lamont, B. T. Kuhlmey, and C. M. de Sterke, “Multi-order dispersion engineering for optimal four-wave mixing,” Opt. Express 16(10), 7551–7563 (2008).
[PubMed]

Delaye, P.

Ding, W.

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A. Yu. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85(21), 4866–4868 (2004).

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R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008).
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R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “All-optical regeneration on a silicon chip,” Opt. Express 15(12), 7802–7809 (2007).
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R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2007).

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R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “All-optical regeneration on a silicon chip,” Opt. Express 15(12), 7802–7809 (2007).
[PubMed]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2007).

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L. C. Andreani and D. Gerace, “Light-matter interaction in photonic crystal slabs,” Phys. Status Solidi B 244(10), 3528–3539 (2007).

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R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2007).

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J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
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Kubo, S.

Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009).
[PubMed]

S. Kubo, D. Mori, and T. Baba, “Low-group-velocity and low-dispersion slow light in photonic crystal waveguides,” Opt. Lett. 32(20), 2981–2983 (2007).
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M. R. E. Lamont, B. T. Kuhlmey, and C. M. de Sterke, “Multi-order dispersion engineering for optimal four-wave mixing,” Opt. Express 16(10), 7551–7563 (2008).
[PubMed]

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R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008).
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M. R. E. Lamont, B. T. Kuhlmey, and C. M. de Sterke, “Multi-order dispersion engineering for optimal four-wave mixing,” Opt. Express 16(10), 7551–7563 (2008).
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R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2007).

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Madden, S.

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L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).

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Monat, C.

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R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008).
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A. Säynätjoki, M. Mulot, J. Ahopelto, and H. Lipsanen, “Dispersion engineering of photonic crystal waveguides with ring-shaped holes,” Opt. Express 15(13), 8323–8328 (2007).
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J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
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K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009).
[PubMed]

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L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).

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Poti, L.

Poulton, C. G.

Ramunno, L.

Rochette, M.

M. Rochette, J. L. Blows, and B. J. Eggleton, “3R optical regeneration: an all-optical solution with BER improvement,” Opt. Express 14(14), 6414–6427 (2006).
[PubMed]

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Ruan, Y.

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R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “All-optical regeneration on a silicon chip,” Opt. Express 15(12), 7802–7809 (2007).
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A. Säynätjoki, M. Mulot, J. Ahopelto, and H. Lipsanen, “Dispersion engineering of photonic crystal waveguides with ring-shaped holes,” Opt. Express 15(13), 8323–8328 (2007).
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L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).

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M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16(2), 1300–1320 (2008).
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R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “All-optical regeneration on a silicon chip,” Opt. Express 15(12), 7802–7809 (2007).
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R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2007).

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Vy Tran, Q.

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J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
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L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).

Yuan, X. D.

Appl. Phys. Lett. (2)

A. Yu. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85(21), 4866–4868 (2004).

Electron. Lett. (2)

L. O'Faolain, X. Yuan, D. McIntyre, S. Thoms, H. Chong, R. M. De la Rue, and T. F. Krauss, “Low-loss propagation in photonic crystal waveguides,” Electron. Lett. 42(25), 1454–1455 (2006).

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

IEEE Photon. Technol. Lett. (1)

E. Ciaramella, F. Curti, and S. Trillo, “All-optical signal reshaping by means of four-wave mixing in optical fibers,” IEEE Photon. Technol. Lett. 13(2), 142–144 (2001).

J. Lightwave Technol. (1)

A. Bogris and D. Syvridis, “Regenerative properties of a pump-modulated four-wave mixing scheme in dispersion-shifted fibers,” J. Lightwave Technol. 21(9), 1892–1902 (2003).

J. Opt. Soc. Am. B (1)

J. Quantum Electron. (1)

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T. F. Krauss, “Why do we need slow light?” Nat. Photonics 2(8), 448–450 (2008).

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).

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Opt. Express (17)

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16(2), 1300–1320 (2008).
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M. R. E. Lamont, B. T. Kuhlmey, and C. M. de Sterke, “Multi-order dispersion engineering for optimal four-wave mixing,” Opt. Express 16(10), 7551–7563 (2008).
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K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express 17(9), 7206–7216 (2009).
[PubMed]

J. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16(9), 6227–6232 (2008).
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A. Säynätjoki, M. Mulot, J. Ahopelto, and H. Lipsanen, “Dispersion engineering of photonic crystal waveguides with ring-shaped holes,” Opt. Express 15(13), 8323–8328 (2007).
[PubMed]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “All-optical regeneration on a silicon chip,” Opt. Express 15(12), 7802–7809 (2007).
[PubMed]

M. Rochette, J. L. Blows, and B. J. Eggleton, “3R optical regeneration: an all-optical solution with BER improvement,” Opt. Express 14(14), 6414–6427 (2006).
[PubMed]

Opt. Lett. (4)

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32(4), 391–393 (2007).
[PubMed]

Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34(7), 1072–1074 (2009).
[PubMed]

S. Kubo, D. Mori, and T. Baba, “Low-group-velocity and low-dispersion slow light in photonic crystal waveguides,” Opt. Lett. 32(20), 2981–2983 (2007).
[PubMed]

Phys. Rev. B (2)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 0566041–05660416 (2001).

Phys. Rev. Lett. (3)

R. J. P. Engelen, D. Mori, T. Baba, and L. Kuipers, “Two regimes of slow-light losses revealed by adiabatic reduction of group velocity,” Phys. Rev. Lett. 101(10), 103901 (2008).
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Phys. Status Solidi B (1)

L. C. Andreani and D. Gerace, “Light-matter interaction in photonic crystal slabs,” Phys. Status Solidi B 244(10), 3528–3539 (2007).

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Fig. 1 (a) Schematic of the partially degenerate FWM configuration investigated here along with the probed planar PhC waveguide. (b-c) Group index of a conventional PhC waveguide (b) and a PhC waveguide engineered by local infiltration with a fluid (n_f = 1.85) (c).

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Fig. 2 (a-b) GVD (β₂ blue) and fourth order dispersion (β₄ green) of the fundamental mode sustained by (a) the conventional PhC waveguide and (b) the engineered PhC waveguide of Fig. 1(b-c). (c-d) Normalized (respectively to the maximum value) FWM conversion efficiency, G_idler as a function of the pump wavelength and the pump-probe detuning for (c) the conventional and (d) the engineered PhC waveguide.

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Fig. 3 Group index dispersion (left) and normalized FWM conversion efficiency (right), G_idler, as a function of the pump wavelength and the pump-probe detuning for three engineered PhC waveguides with (a-b) (r/a=0.31, n _f=1.8) (c-d), (r/a=0.32, n _f=1.75) and (e-f) (r/a=0.33, n _f=1.7).

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Fig. 4 (a) FWM conversion efficiency as a function of the pump-probe detuning for the 80μm engineered PhC waveguides with n _g=31, 40, 47, and 66, and the reference 80μm nanowire (n _g=4.25) and 3mm ridge waveguide (n _g=3.5). The peak power of the 12ps pump is 5W, and the power of the cw probe is 1mW. (b) Associated output spectra for the n _g=31 PhC waveguide

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Fig. 5 FWM conversion efficiency as a function of the peak pump power for the waveguides of Fig. 4 (same parameters) and two pump-probe detunings equal to (a) 2.5nm and (b) 4nm.

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Fig. 6 Principle of 2R regeneration based on FWM between a pulsed pump and a cw probe. The pump signal is regenerated by spectrally filtering the idler.

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Fig. 7 (a) FWM spectra at various pump powers (indicated on the right) for an 80µm long PhC waveguide with n _g=31, as probed by a pulsed pump (λ_pump=1565.8 nm) and a cw probe (λ_probe=1569.8nm) signal. (b) Corresponding power transfer function between the filtered idler and the pump power, as obtained by “numerically” filtering the idler using a Gaussian band-pass filter with different idler-filter detunings (Δλ_f) and a filter bandwidth BP _W equal to 0.3nm.

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Fig. 8 (a-b) Power transfer functions obtained for different waveguides with group index n_g=3.5, 31, and 66 by filtering the idler signal using a Gaussian band-pass filter with BP _W=0.3nm, and (a) Δλ_f variable or (b) constant and equal to 0.3nm. The pump and probe parameters are similar to that of Fig. 5(a).

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Fig. 9 (a) FWM spectra for various input pump power at λ_pump=1565.8 nm from the engineered PhC waveguide with n _g=31. The probe power is 1mw, and the pump-probe detuning is 4.2nm. Both pump and probe signals are pulsed with a duration of 12ps. (b) Power transfer function for the waveguide used in (a) along with corresponding curves obtained for the PhC waveguide with n _g=66, and the fast 3mm ridge waveguide for reference. The bandwidth of the filter used for these calculations is 0.3nm, and the detuning from the idler is indicated on the plot. The pump and probe wavelengths and powers are similar to that of Fig. 5(a).

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Tables (2)

Table 1 Summary of the parameters used in Eqs. (1) and (2) for silicon and the n_g dependence considered.

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Table 2 Summary of the characteristics of the various waveguides investigated here, regarding their flatband slow light window (characterized by its central wavelength λ_c, and its bandwidth BW) and the FWM operation calculated through the simulations. A nanowire and ridge waveguides are added for comparison.

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Equations (10)

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

P_{N L} = \frac{3}{2} ε_{0} χ^{(3)} E_{pump}^{2} E_{probe}^{*} e^{i (Δ k_{L} z - Δ ω t)}

Δ ω = 2 ω_{pump} - ω_{probe} - ω_{idler}

Δ k_{L} = 2 β_{pump} - β_{probe} - β_{idler}

G_{idler} (L) \equiv \frac{P_{idler} (L)}{P_{probe} (0)} = {(\frac{γ \bar{P_{pump}}}{g} \sin h (g L))}^{2} e^{- α L}

\bar{P_{p u m p} (L)} = P_{p u m p} (0) (\frac{1 - e^{- α L}}{α L})

g = \sqrt{{(γ {\bar{P}}_{p u m p})}^{2} - {(\frac{Δ k_{L} + Δ k_{N L}}{2})}^{2}}

Δ k_{N L} = 2 γ {\bar{P}}_{p u m p}

Δ k_{L} \approx Ω_{s}^{2} β_{2} + \frac{1}{12} Ω_{s}^{4} β_{4}

\begin{array}{l} \frac{\partial A}{\partial z} + \frac{α}{2} A - i \sum_{m = 2}^{4} \frac{i^{m} β_{m}}{m!} \frac{\partial^{m} A}{\partial t^{m}} = i (γ + \frac{β_{T P A}}{2 A_{e f f}}) (1 + \frac{i}{ω_{0}} \frac{\partial}{\partial t}) A (z, t) \int_{- \infty}^{t} R (t - t^{'}) {| A (z, t^{'}) |}^{2} d t^{'} \\ - N_{c} (\frac{σ}{2} + \frac{2 k_{c} i π}{λ_{0}}) A \end{array}

\frac{\partial N_{c} (t)}{\partial t} = \frac{β_{T P A}}{2 h ν_{0} A_{e f f}^{2}} {| A |}^{4} - \frac{N_{c}}{τ_{r e c o m b}}

WG / length (µm)	A_eff (µm²)	n_g	λ_c (nm)	BW (nm) (10%)	γ [m²/W]	FWM maximum Bandwidth (P_pump=5W)	FWM maximum efficiency (P_pump=5W)
PhC/ 80	0.547	31	1565.8	11.8	2887	14nm	−25dB
PhC/ 80	0.547	40	1549.5	8	4841	11nm	−21dB
PhC/ 80	0.547	47	1537.4	7.1	6736	10nm	−18.5dB
PhC/ 80	0.547	66	1519.6	4.6	13439	7nm	−13dB
Nanowire/ 80	0.12.	4.25	N/A	N/A	213	N/A	−44.6dB
Ridge/ 3000	0.66	3.5	N/A	N/A	31	N/A	−37dB

WG / length (µm)	A_eff (µm²)	n_g	λ_c (nm)	BW (nm) (10%)	γ [m²/W]	FWM maximum Bandwidth (P_pump=5W)	FWM maximum efficiency (P_pump=5W)
PhC/ 80	0.547	31	1565.8	11.8	2887	14nm	−25dB
PhC/ 80	0.547	40	1549.5	8	4841	11nm	−21dB
PhC/ 80	0.547	47	1537.4	7.1	6736	10nm	−18.5dB
PhC/ 80	0.547	66	1519.6	4.6	13439	7nm	−13dB
Nanowire/ 80	0.12.	4.25	N/A	N/A	213	N/A	−44.6dB
Ridge/ 3000	0.66	3.5	N/A	N/A	31	N/A	−37dB