Abstract

We present approximate analytical expressions for the estimation of the degenerate four-wave mixing conversion efficiency in slow-light photonic crystal waveguides (PCWs). The derived formulas incorporate the different effective modal areas and the frequency-dependent linear and nonlinear parameters of the pump, signal, and idler waves. The influence of linear loss, two-photon absorption, and free-carrier generation is also accounted for. Numerical solution of the coupled propagation equations is used to verify the validity of the proposed expressions under different values of the linear and nonlinear parameters of the waveguide. It is shown that the derived expressions provide an accurate estimation of the conversion efficiency and are thus expected to be useful in the design of PCWs for nonlinear signal-processing applications.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Gong, J. Huang, K. Li, N. Copner, J. J. Martinez, L. Wang, T. Duan, W. Zhang, and W. H. Loh, “Spoof four wave mixing for all-optical wavelength conversion,” Opt. Express 20, 24030–24037 (2012).
    [CrossRef]
  2. R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
    [CrossRef]
  3. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007).
    [CrossRef]
  4. R. Salem, M. A. Foster, A. C. Turner, D. F. Geragthy, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2007).
    [CrossRef]
  5. S. Rawal, R. K. Sinha, and R. M. De La Rue, “Silicon-on-insulator photonic miniature devices with slow light enhanced third-order nonlinearities,” J. Nanophoton. 6, 063504 (2012).
    [CrossRef]
  6. B. Corcoran, M. D. Pelusi, C. Monat, J. Li, L. O’Faolain, T. F. Krauss, and B. J. Eggleton, “Ultracompact 160  Gbaud all-optical demultiplexing exploiting slow light in a engineered silicon photonic crystal waveguide,” Opt. Lett. 36, 1728–1730 (2011).
    [CrossRef]
  7. F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, “Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion,” Nat. Commun. 2, 296 (2011).
    [CrossRef]
  8. J. Li, L. O’Faolain, and T. F. Krauss, “Four-wave mixing in slow light photonic crystal waveguides with very high group index,” Opt. Express 20, 17474–17479 (2012).
    [CrossRef]
  9. J. Li, L. O’Faolain, S. A. Schulz, and T. F. Krauss, “Low loss propagation in slow light photonic crystal waveguides at group indices up to 60,” Photon. Nanostr. Fundam. Appl. 10, 589–593 (2012).
    [CrossRef]
  10. G. P. Agrawal, NonLinear Fiber Optics, 4th ed. (Academic, 2007).
  11. T. Chen, J. Sun, and L. Li, “Modal theory of slow light enhanced third-order nonlinear effects in photonic crystal waveguides,” Opt. Express 20, 20043–20058 (2012).
    [CrossRef]
  12. S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010).
    [CrossRef]
  13. S. Roy, M. Santagiustina, P. Colman, S. Combrie, and A. De Rossi, “Modeling the dispersion of the nonlinearity in slow mode photonic crystal waveguides,” IEEE Photon. J. 4, 224–233 (2012).
    [CrossRef]
  14. P. Kanakis, T. Kamalakis, and T. Sphicopoulos, “Optimization of the storage capacity of slow light photonic crystal waveguides,” Opt. Lett. 37, 4585–4587 (2012).
    [CrossRef]
  15. 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]
  16. P. Kanakis, T. Kamalakis, and T. Sphicopoulos, “Numerical analysis of soliton propagation in photonic crystal slab waveguides for signal processing application,” J. Opt. Soc. Am. B 29, 2787–2796 (2012).
    [CrossRef]
  17. L. Yin and G. Agrawal, “Impact of two photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. 32, 2031–2033 (2007).
    [CrossRef]
  18. 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]
  19. B. Corcoran, C. Monat, D. Pudo, B. J. Eggleton, T. F. Krauss, D. J. Moss, L. O’Faolain, M. Pelusi, and T. P. White, “Nonlinear loss dynamics in a silicon slow-light photonic crystal waveguide,” Opt. Lett. 35, 1073–1075 (2010).
    [CrossRef]
  20. J. F. McMillan, M. Yu, D. Kwong, and C. Wong, “Observation of four-wave mixing in slow light silicon photonic crystal wavguides,” Opt. Express 18, 15484–15497 (2010).
    [CrossRef]
  21. C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010).
    [CrossRef]
  22. M. Santagiustina, C. G. Someda, G. Vadala, S. Combrie, and A. De Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express 18, 21024–21029 (2010).
    [CrossRef]
  23. K. Lengle, L. Bramerie, M. Gay, M. Costa e Silva, S. Lobo, J. Simon, P. Colman, S. Combrie, and A. de Rossi, “Investigation of FWM in dispersion-engineered GaInP photonic crystal waveguides,” Opt. Express 20, 16154–16165 (2012).
    [CrossRef]
  24. T. Vallaitis, S. Bogatscher, L. Alloatti, P. Dumon, R. Baets, M. L. Scimeca, I. Biaggio, F. Diederich, C. Koos, W. Freude, and J. Leuthold, “Optical properties of highly nonlinear silicon-organic hybrid (SOH) waveguide geometries,” Opt. Express 17, 17357–17368 (2009).
    [CrossRef]
  25. K. Suzuki and T. Baba, “Nonlinear light propagation in chalcogenide photonic crystal slow light waveguides,” Opt. Express 18, 26675–26685 (2010).
    [CrossRef]
  26. S. Roy, A. Willinger, S. Combrie, A. De Rossi, G. Eisenstein, and M. Santaguistina, “Narrowband optical parametric gain in slow mode engineered GaInP photonic crystal waveguides,” Opt. Lett. 37, 2919–2921 (2012).
    [CrossRef]
  27. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
    [CrossRef]
  28. A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
    [CrossRef]
  29. J. R. Dormand and P. J. Prince, “A family of embedded Runge-Kutta formulae,” J. Comput. Appl. Math. 6, 19–26 (1980).
    [CrossRef]
  30. 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, 7206–7216 (2009).
    [CrossRef]
  31. B. Corcoran, T. D. Vo, M. D. Pelusi, C. Monat, D. Xu, A. Densmore, R. Ma, S. Janz, D. J. Moss, and B. J. Eggleton, “Silicon nanowire based radio-frequency spectrum analyzer,” Opt. Express 18, 20190–20200 (2010).
    [CrossRef]
  32. I. D. Rukhlenko, M. Premarante, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. 16, 200–215 (2010).
    [CrossRef]
  33. 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, 6227–6232 (2008).
    [CrossRef]

2012 (10)

Y. Gong, J. Huang, K. Li, N. Copner, J. J. Martinez, L. Wang, T. Duan, W. Zhang, and W. H. Loh, “Spoof four wave mixing for all-optical wavelength conversion,” Opt. Express 20, 24030–24037 (2012).
[CrossRef]

J. Li, L. O’Faolain, and T. F. Krauss, “Four-wave mixing in slow light photonic crystal waveguides with very high group index,” Opt. Express 20, 17474–17479 (2012).
[CrossRef]

J. Li, L. O’Faolain, S. A. Schulz, and T. F. Krauss, “Low loss propagation in slow light photonic crystal waveguides at group indices up to 60,” Photon. Nanostr. Fundam. Appl. 10, 589–593 (2012).
[CrossRef]

T. Chen, J. Sun, and L. Li, “Modal theory of slow light enhanced third-order nonlinear effects in photonic crystal waveguides,” Opt. Express 20, 20043–20058 (2012).
[CrossRef]

S. Rawal, R. K. Sinha, and R. M. De La Rue, “Silicon-on-insulator photonic miniature devices with slow light enhanced third-order nonlinearities,” J. Nanophoton. 6, 063504 (2012).
[CrossRef]

S. Roy, M. Santagiustina, P. Colman, S. Combrie, and A. De Rossi, “Modeling the dispersion of the nonlinearity in slow mode photonic crystal waveguides,” IEEE Photon. J. 4, 224–233 (2012).
[CrossRef]

P. Kanakis, T. Kamalakis, and T. Sphicopoulos, “Optimization of the storage capacity of slow light photonic crystal waveguides,” Opt. Lett. 37, 4585–4587 (2012).
[CrossRef]

P. Kanakis, T. Kamalakis, and T. Sphicopoulos, “Numerical analysis of soliton propagation in photonic crystal slab waveguides for signal processing application,” J. Opt. Soc. Am. B 29, 2787–2796 (2012).
[CrossRef]

K. Lengle, L. Bramerie, M. Gay, M. Costa e Silva, S. Lobo, J. Simon, P. Colman, S. Combrie, and A. de Rossi, “Investigation of FWM in dispersion-engineered GaInP photonic crystal waveguides,” Opt. Express 20, 16154–16165 (2012).
[CrossRef]

S. Roy, A. Willinger, S. Combrie, A. De Rossi, G. Eisenstein, and M. Santaguistina, “Narrowband optical parametric gain in slow mode engineered GaInP photonic crystal waveguides,” Opt. Lett. 37, 2919–2921 (2012).
[CrossRef]

2011 (2)

B. Corcoran, M. D. Pelusi, C. Monat, J. Li, L. O’Faolain, T. F. Krauss, and B. J. Eggleton, “Ultracompact 160  Gbaud all-optical demultiplexing exploiting slow light in a engineered silicon photonic crystal waveguide,” Opt. Lett. 36, 1728–1730 (2011).
[CrossRef]

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, “Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion,” Nat. Commun. 2, 296 (2011).
[CrossRef]

2010 (11)

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, D. Pudo, B. J. Eggleton, T. F. Krauss, D. J. Moss, L. O’Faolain, M. Pelusi, and T. P. White, “Nonlinear loss dynamics in a silicon slow-light photonic crystal waveguide,” Opt. Lett. 35, 1073–1075 (2010).
[CrossRef]

J. F. McMillan, M. Yu, D. Kwong, and C. Wong, “Observation of four-wave mixing in slow light silicon photonic crystal wavguides,” Opt. Express 18, 15484–15497 (2010).
[CrossRef]

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010).
[CrossRef]

M. Santagiustina, C. G. Someda, G. Vadala, S. Combrie, and A. De Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express 18, 21024–21029 (2010).
[CrossRef]

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010).
[CrossRef]

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

K. Suzuki and T. Baba, “Nonlinear light propagation in chalcogenide photonic crystal slow light waveguides,” Opt. Express 18, 26675–26685 (2010).
[CrossRef]

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

B. Corcoran, T. D. Vo, M. D. Pelusi, C. Monat, D. Xu, A. Densmore, R. Ma, S. Janz, D. J. Moss, and B. J. Eggleton, “Silicon nanowire based radio-frequency spectrum analyzer,” Opt. Express 18, 20190–20200 (2010).
[CrossRef]

I. D. Rukhlenko, M. Premarante, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. 16, 200–215 (2010).
[CrossRef]

2009 (3)

2008 (1)

2007 (3)

2005 (1)

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
[CrossRef]

1980 (1)

J. R. Dormand and P. J. Prince, “A family of embedded Runge-Kutta formulae,” J. Comput. Appl. Math. 6, 19–26 (1980).
[CrossRef]

Agrawal, G.

Agrawal, G. P.

I. D. Rukhlenko, M. Premarante, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. 16, 200–215 (2010).
[CrossRef]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007).
[CrossRef]

G. P. Agrawal, NonLinear Fiber Optics, 4th ed. (Academic, 2007).

Alloatti, L.

Andrekson, P. A.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Asakawa, K.

Baba, T.

Baets, R.

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. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010).
[CrossRef]

Biaggio, I.

Bogatscher, S.

Bogris, A.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Bramerie, L.

Canciamilla, A.

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, “Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion,” Nat. Commun. 2, 296 (2011).
[CrossRef]

Chen, T.

Cohen, O.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
[CrossRef]

Colman, P.

K. Lengle, L. Bramerie, M. Gay, M. Costa e Silva, S. Lobo, J. Simon, P. Colman, S. Combrie, and A. de Rossi, “Investigation of FWM in dispersion-engineered GaInP photonic crystal waveguides,” Opt. Express 20, 16154–16165 (2012).
[CrossRef]

S. Roy, M. Santagiustina, P. Colman, S. Combrie, and A. De Rossi, “Modeling the dispersion of the nonlinearity in slow mode photonic crystal waveguides,” IEEE Photon. J. 4, 224–233 (2012).
[CrossRef]

Combrie, S.

Copner, N.

Corcoran, B.

Costa e Silva, M.

Dasgupta, S.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

De La Rue, R. M.

S. Rawal, R. K. Sinha, and R. M. De La Rue, “Silicon-on-insulator photonic miniature devices with slow light enhanced third-order nonlinearities,” J. Nanophoton. 6, 063504 (2012).
[CrossRef]

de Rossi, A.

Densmore, A.

Diederich, F.

Dormand, J. R.

J. R. Dormand and P. J. Prince, “A family of embedded Runge-Kutta formulae,” J. Comput. Appl. Math. 6, 19–26 (1980).
[CrossRef]

Duan, T.

Dumon, P.

Ebnali-Heidari, M.

Eggleton, B. J.

Eisenstein, G.

Ellis, A. D.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Fang, A.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
[CrossRef]

Ferrari, C.

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, “Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion,” Nat. Commun. 2, 296 (2011).
[CrossRef]

Foster, M. A.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

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

Freude, W.

Gaeta, A. L.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

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

Gay, M.

Geragthy, D. F.

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

Gomez-Iglesias, A.

Gong, Y.

Grillet, C.

Gruner-Nielsen, L.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Hak, D.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
[CrossRef]

Herstrom, S.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Huang, J.

Hugonin, J. P.

Ikeda, N.

Inoue, K.

Jakobsen, D.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Janz, S.

Jones, R.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
[CrossRef]

Kakande, J.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Kamalakis, T.

Kanakis, P.

Koos, C.

Krauss, T. F.

J. Li, L. O’Faolain, S. A. Schulz, and T. F. Krauss, “Low loss propagation in slow light photonic crystal waveguides at group indices up to 60,” Photon. Nanostr. Fundam. Appl. 10, 589–593 (2012).
[CrossRef]

J. Li, L. O’Faolain, and T. F. Krauss, “Four-wave mixing in slow light photonic crystal waveguides with very high group index,” Opt. Express 20, 17474–17479 (2012).
[CrossRef]

B. Corcoran, M. D. Pelusi, C. Monat, J. Li, L. O’Faolain, T. F. Krauss, and B. J. Eggleton, “Ultracompact 160  Gbaud all-optical demultiplexing exploiting slow light in a engineered silicon photonic crystal waveguide,” Opt. Lett. 36, 1728–1730 (2011).
[CrossRef]

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010).
[CrossRef]

B. Corcoran, C. Monat, D. Pudo, B. J. Eggleton, T. F. Krauss, D. J. Moss, L. O’Faolain, M. Pelusi, and T. P. White, “Nonlinear loss dynamics in a silicon slow-light photonic crystal waveguide,” Opt. Lett. 35, 1073–1075 (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]

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010).
[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]

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, 6227–6232 (2008).
[CrossRef]

Kuipers, L.

Kwong, D.

Lalanne, P.

Lengle, K.

Leuthold, J.

Levy, J. S.

Li, J.

Li, K.

Li, L.

Lin, Q.

Lipson, M.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

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

Liu, A.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
[CrossRef]

Lobo, S.

Loh, W. H.

Lundstrom, C.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Ma, R.

Martinez, J. J.

Mazoyer, S.

McMillan, J. F.

Melloni, A.

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, “Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion,” Nat. Commun. 2, 296 (2011).
[CrossRef]

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (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]

Monat, C.

Morichetti, F.

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, “Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion,” Nat. Commun. 2, 296 (2011).
[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]

Moss, D. J.

O’Faolain, L.

J. Li, L. O’Faolain, and T. F. Krauss, “Four-wave mixing in slow light photonic crystal waveguides with very high group index,” Opt. Express 20, 17474–17479 (2012).
[CrossRef]

J. Li, L. O’Faolain, S. A. Schulz, and T. F. Krauss, “Low loss propagation in slow light photonic crystal waveguides at group indices up to 60,” Photon. Nanostr. Fundam. Appl. 10, 589–593 (2012).
[CrossRef]

B. Corcoran, M. D. Pelusi, C. Monat, J. Li, L. O’Faolain, T. F. Krauss, and B. J. Eggleton, “Ultracompact 160  Gbaud all-optical demultiplexing exploiting slow light in a engineered silicon photonic crystal waveguide,” Opt. Lett. 36, 1728–1730 (2011).
[CrossRef]

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010).
[CrossRef]

B. Corcoran, C. Monat, D. Pudo, B. J. Eggleton, T. F. Krauss, D. J. Moss, L. O’Faolain, M. Pelusi, and T. P. White, “Nonlinear loss dynamics in a silicon slow-light photonic crystal waveguide,” Opt. Lett. 35, 1073–1075 (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]

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010).
[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]

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, 6227–6232 (2008).
[CrossRef]

O’Gorman, J.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Oda, H.

Painter, O. J.

Paniccia, M.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
[CrossRef]

Parmigiani, F.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Pelusi, M.

Pelusi, M. D.

Petropoulos, P.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Phelan, R.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Poitras, C. B.

Premarante, M.

I. D. Rukhlenko, M. Premarante, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. 16, 200–215 (2010).
[CrossRef]

Prince, P. J.

J. R. Dormand and P. J. Prince, “A family of embedded Runge-Kutta formulae,” J. Comput. Appl. Math. 6, 19–26 (1980).
[CrossRef]

Pudo, D.

Rawal, S.

S. Rawal, R. K. Sinha, and R. M. De La Rue, “Silicon-on-insulator photonic miniature devices with slow light enhanced third-order nonlinearities,” J. Nanophoton. 6, 063504 (2012).
[CrossRef]

Richardson, D. J.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Rong, H.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
[CrossRef]

Roy, S.

S. Roy, A. Willinger, S. Combrie, A. De Rossi, G. Eisenstein, and M. Santaguistina, “Narrowband optical parametric gain in slow mode engineered GaInP photonic crystal waveguides,” Opt. Lett. 37, 2919–2921 (2012).
[CrossRef]

S. Roy, M. Santagiustina, P. Colman, S. Combrie, and A. De Rossi, “Modeling the dispersion of the nonlinearity in slow mode photonic crystal waveguides,” IEEE Photon. J. 4, 224–233 (2012).
[CrossRef]

Rukhlenko, I. D.

I. D. Rukhlenko, M. Premarante, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. 16, 200–215 (2010).
[CrossRef]

Salem, R.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[CrossRef]

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

Samarelli, A.

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, “Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion,” Nat. Commun. 2, 296 (2011).
[CrossRef]

Santagiustina, M.

S. Roy, M. Santagiustina, P. Colman, S. Combrie, and A. De Rossi, “Modeling the dispersion of the nonlinearity in slow mode photonic crystal waveguides,” IEEE Photon. J. 4, 224–233 (2012).
[CrossRef]

M. Santagiustina, C. G. Someda, G. Vadala, S. Combrie, and A. De Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express 18, 21024–21029 (2010).
[CrossRef]

Santaguistina, M.

Schulz, S. A.

J. Li, L. O’Faolain, S. A. Schulz, and T. F. Krauss, “Low loss propagation in slow light photonic crystal waveguides at group indices up to 60,” Photon. Nanostr. Fundam. Appl. 10, 589–593 (2012).
[CrossRef]

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (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]

Scimeca, M. L.

Simon, J.

Sinha, R. K.

S. Rawal, R. K. Sinha, and R. M. De La Rue, “Silicon-on-insulator photonic miniature devices with slow light enhanced third-order nonlinearities,” J. Nanophoton. 6, 063504 (2012).
[CrossRef]

Sjodin, M.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Slavik, R.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Someda, C. G.

Sorel, M.

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, “Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion,” Nat. Commun. 2, 296 (2011).
[CrossRef]

Spasenovic, M.

Sphicopoulos, T.

Sun, J.

Suzuki, K.

Sygletos, S.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Syvridis, D.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

Turner, A. C.

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

Turner-Foster, A. C.

Vadala, G.

Vallaitis, T.

Vo, T. D.

Wang, L.

Weerasuriya, R.

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

White, T. P.

Willinger, A.

Wong, C.

Xu, D.

Yin, L.

Yu, M.

Zhang, W.

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

I. D. Rukhlenko, M. Premarante, and G. P. Agrawal, “Nonlinear silicon photonics: analytical tools,” IEEE J. Sel. Top. Quantum Electron. 16, 200–215 (2010).
[CrossRef]

IEEE Photon. J. (1)

S. Roy, M. Santagiustina, P. Colman, S. Combrie, and A. De Rossi, “Modeling the dispersion of the nonlinearity in slow mode photonic crystal waveguides,” IEEE Photon. J. 4, 224–233 (2012).
[CrossRef]

J. Comput. Appl. Math. (1)

J. R. Dormand and P. J. Prince, “A family of embedded Runge-Kutta formulae,” J. Comput. Appl. Math. 6, 19–26 (1980).
[CrossRef]

J. Nanophoton. (1)

S. Rawal, R. K. Sinha, and R. M. De La Rue, “Silicon-on-insulator photonic miniature devices with slow light enhanced third-order nonlinearities,” J. Nanophoton. 6, 063504 (2012).
[CrossRef]

J. Opt. (1)

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010).
[CrossRef]

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

Nat. Commun. (1)

F. Morichetti, A. Canciamilla, C. Ferrari, A. Samarelli, M. Sorel, and A. Melloni, “Travelling-wave resonant four-wave mixing breaks the limits of cavity-enhanced all-optical wavelength conversion,” Nat. Commun. 2, 296 (2011).
[CrossRef]

Nat. Photonics (2)

R. Slavik, F. Parmigiani, J. Kakande, C. Lundstrom, M. Sjodin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Gruner-Nielsen, D. Jakobsen, S. Herstrom, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, “All-optical phase and amplitude regenerator for next-generation telecommunications systems,” Nat. Photonics 4, 690–695 (2010).
[CrossRef]

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

Nature (1)

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433, 725–728 (2005).
[CrossRef]

Opt. Express (16)

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18, 3582–3591 (2010).
[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]

J. F. McMillan, M. Yu, D. Kwong, and C. Wong, “Observation of four-wave mixing in slow light silicon photonic crystal wavguides,” Opt. Express 18, 15484–15497 (2010).
[CrossRef]

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010).
[CrossRef]

M. Santagiustina, C. G. Someda, G. Vadala, S. Combrie, and A. De Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express 18, 21024–21029 (2010).
[CrossRef]

K. Lengle, L. Bramerie, M. Gay, M. Costa e Silva, S. Lobo, J. Simon, P. Colman, S. Combrie, and A. de Rossi, “Investigation of FWM in dispersion-engineered GaInP photonic crystal waveguides,” Opt. Express 20, 16154–16165 (2012).
[CrossRef]

T. Vallaitis, S. Bogatscher, L. Alloatti, P. Dumon, R. Baets, M. L. Scimeca, I. Biaggio, F. Diederich, C. Koos, W. Freude, and J. Leuthold, “Optical properties of highly nonlinear silicon-organic hybrid (SOH) waveguide geometries,” Opt. Express 17, 17357–17368 (2009).
[CrossRef]

K. Suzuki and T. Baba, “Nonlinear light propagation in chalcogenide photonic crystal slow light waveguides,” Opt. Express 18, 26675–26685 (2010).
[CrossRef]

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, 7206–7216 (2009).
[CrossRef]

B. Corcoran, T. D. Vo, M. D. Pelusi, C. Monat, D. Xu, A. Densmore, R. Ma, S. Janz, D. J. Moss, and B. J. Eggleton, “Silicon nanowire based radio-frequency spectrum analyzer,” Opt. Express 18, 20190–20200 (2010).
[CrossRef]

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, 6227–6232 (2008).
[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]

Y. Gong, J. Huang, K. Li, N. Copner, J. J. Martinez, L. Wang, T. Duan, W. Zhang, and W. H. Loh, “Spoof four wave mixing for all-optical wavelength conversion,” Opt. Express 20, 24030–24037 (2012).
[CrossRef]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007).
[CrossRef]

J. Li, L. O’Faolain, and T. F. Krauss, “Four-wave mixing in slow light photonic crystal waveguides with very high group index,” Opt. Express 20, 17474–17479 (2012).
[CrossRef]

T. Chen, J. Sun, and L. Li, “Modal theory of slow light enhanced third-order nonlinear effects in photonic crystal waveguides,” Opt. Express 20, 20043–20058 (2012).
[CrossRef]

Opt. Lett. (5)

Photon. Nanostr. Fundam. Appl. (1)

J. Li, L. O’Faolain, S. A. Schulz, and T. F. Krauss, “Low loss propagation in slow light photonic crystal waveguides at group indices up to 60,” Photon. Nanostr. Fundam. Appl. 10, 589–593 (2012).
[CrossRef]

Other (1)

G. P. Agrawal, NonLinear Fiber Optics, 4th ed. (Academic, 2007).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1.

(a) Horizontal cross section of a PCW formed in a triangular lattice of air holes embedded in a high index material (e.g., Si) with lattice constant a0=412nm, slab height h=220nm, and hole radius 0.2913a0. Introducing a horizontal dislocation of the holes closest to the line defect (first neighbors) by s1=0.1019a0 and the second neighbors by s2=0.0485a0, results in a flat dispersion relation near 1.55 μm, corresponding to a group index ng60. (b) Dispersion relation of the defect mode is shown. The inset shows the variation of the mode group index with respect to the wavelength. The thick portion of the curves corresponds to the flatband region where ng does not change more than ±10% from its specified value, ng=60.

Fig. 2.
Fig. 2.

(a) Various effective modal areas with respect to the pump-signal detuning. The rectangles correspond to XPM where we assume that all three modal fields in Eq. (6) are located at a wavelength satisfying the expression λψ=λκ=λρ+Δλ, and we vary λρ. The circles correspond to FWM, i.e., λψ=λρ+Δλ, λκ=λρΔλ, and we again vary λρ. The effective modal area for SPM is shown with a plain line for fixed λκ, and we vary λψ. (b) The linear loss coefficient in dB/cm inside the flatband region.

Fig. 3.
Fig. 3.

Wavelength dependence of FWM conversion efficiency (a) numerically calculated and (b) estimated using Eq. (22), assuming Pp(0)=2W and L=200μm.

Fig. 4.
Fig. 4.

FWM conversion efficiency with respect to the waveguide length and the incident pump power calculated (a) numerically and (b) analytically using Eq. (22). The wavelength of the signal and the idler waves are considered fixed at λs=1553.6nm and λi=1549.3nm, respectively.

Fig. 5.
Fig. 5.

Wavelength dependence of FWM conversion efficiency when the FC effects are included: (a) numerically calculated, (b) by treating the three loss mechanisms independently, and (c) by ignoring the TPA loss term. The waveguide length is L=200μm, and the incident pump power Pp(0)=2W.

Fig. 6.
Fig. 6.

FWM conversion efficiency with respect to the waveguide length, L and the incident pump power, Pp(0) incorporating the FC effects is calculated (a) numerically, (b) by treating the three loss mechanisms independently, and (c) by ignoring the TPA loss term. The wavelength of the signal and the idler waves are considered fixed at λs=1553.6 and λi=1549.3nm, respectively.

Fig. 7.
Fig. 7.

FWM conversion efficiency assuming that the three loss mechanisms have comparable impact to the propagating light with respect to the waveguide length, L and the incident pump power, Pp(0) calculated (a) numerically, (b) by treating the three loss mechanisms independently, and (c) by ignoring the TPA loss term.

Fig. 8.
Fig. 8.

FWM conversion efficiency of a rectangular pulse train with T1=50ps with respect to the pulse repetition rate by applying Eqs. (37) and (22).

Tables (2)

Tables Icon

Table 1. Impact of TPA and FCA on the FWM at Various ng

Tables Icon

Table 2. Impact of Detuning on the FWM Penalty (with and without FC Effects) at Various ng

Equations (41)

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

ηPi(L)Ps(0),
dBpdz=ap2Bp+Tp|Bp|2Bp+Fp|Bp|4Bp,
dBsdz=as2Bs+Ts|Bp|2Bs+Fs|Bp|4Bs+jMsBp2Bi*ejΔkz,
dBidz=ai2Bi+Ti|Bp|2Bi+Fi|Bp|4Bi+jMiBp2Bs*ejΔkz.
Tp=(jn2ωpc112βTPA)Sp2Appp1,
Aρκψ=(V|Eρ|2dVV|Eρ|2dVV|Eκ|2dVV|Eψ|2dV)1/2a0VEρ*Eρ*EκEψdV.
Ts=(2jn2ωsc1βTPA)SpSsApss1,
Ti=(2jn2ωic1βTPA)SpSiApii1.
FμNcPp2(j2πλμC1C22)(λμλ0)2,
Mx=n2ωxc1Apsi1SpSsSi.
η=ωiωs(1+κ24g2)sinh2(gL)eaiL.
κ=Δk+2n2cP¯p(ωsApss+ωiApiiωpAppp),
g=(n2SpcApsi)2SiSpωiωsP¯p2κ2/4.
P¯p1L0LPp(z)dz=Pp(0)1eaLaL.
dPpdz=[ap+2Re{Tp}Pp]Pp.
Pp(z)=Pp(0)eapz1+Pp(0)βTPASp2(1eapz)/(apAppp),
P¯p=ApppβTPASp2Lln(1+βTPASp2Pp(0)apAppp[1eapL]).
dBsdz=jIm{Ts}|Bp|2Bs+jMsP¯pBi*ejΔkz,
dBidz=jIm{Ti}|Bp|2Bi+jMiP¯pBs*ejΔkz.
η0=ωiωs(1+κ24g2)sinh2(gL).
dPidz=(ai+2Re{Ti}Pp)Pi.
η=(ωiωs)(1+κ24g2)sinh2(gL)eaiL2Re{Ti}P¯pL.
dPpdz=(ap+2Re{Tp}Pp+2Re{Fp}Pp2)Pp.
Pp(z)=Pp(0)eapz(1+K1z)(1+K2z)1/2,
e0=2l01[(el0+2)+3l01(el01)],
e1=6l01L1[(el0+1)+2l01(el01)],
P¯p=[2(e1e0K1)LK13/2K1K2tanh1(K11+K2zK1K2)+2e11+K2zLK1K2]0L,
P¯p2=1L[(e1e0K1)2K12(K1z+1)(K1K2)+{(e0K1e1)[e1(2K1K2)e0K1K2]K12+(e1e0K2)2K2}ln(1+K1z)(K1K2)2]0L.
dPpdz(ap+2Re{Fp}Pp2)Pp.
Pp(z)=Pp(0)eapz(1+δ(1e2apz))1/2,
δ=2ap1Re{Fp}Pp(0)2.
P¯p=Pp(0)apLδ{sin1(eapLδ1+1)sin1(1δ1+1)},
P¯p2=Pp(0)22apδln(1+δ(1e2apL)).
κtot=κ+Im{Fs+Fi2Fp}P¯p2,
dPidz=(ai+2Re{Ti}Pp+2Re{Fi}Pp2)Pi.
li=Pi(L)Pi(0)=exp(aiL+2LRe{Tp}P¯p+2LRe{Fi}P¯p2).
η=li(ωiωs)(1+κtot24g2)sinh2(gL),
NCt=N0NCτC,
NC(z,t)=NC(z,tn)e(ttn)/τC+N0{etn/τCe(ttn)/τC}
NC(z,t)=NC(z,tn+T1)e(ttnT1)/τC,
Nc(z,tn)=N0{etn/τceT1/τc}e(TT1)/τc1eT/τc.

Metrics