Abstract

We present a theoretical analysis supported by comprehensive numerical simulations of quasi-phase-matched four-wave mixing (FWM) of ultrashort optical pulses that propagate in weakly width-modulated silicon photonic nanowire gratings. Our study reveals that, by properly designing the optical waveguide such that the interacting pulses copropagate with the same group velocity, a conversion efficiency enhancement of more than 15 dB, as compared to a uniform waveguide, can readily be achieved. We also analyze the dependence of the conversion efficiency and FWM gain on the pulse width, time delay, walk-off parameter, and grating modulation depth.

© 2014 Optical Society of America

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  1. R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, Appl. Phys. Lett. 24, 308 (1974).
    [CrossRef]
  2. K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
    [CrossRef]
  3. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, Opt. Express 11, 2862 (2003).
    [CrossRef]
  4. D. Dimitropoulos, V. Raghunathan, R. Claps, and B. Jalali, Opt. Express 12, 149 (2004).
    [CrossRef]
  5. H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, Opt. Express 13, 4629 (2005).
    [CrossRef]
  6. R. Espinola, J. Dadap, R. M. Osgood, S. McNab, and Y. Vlasov, Opt. Express 13, 4341 (2005).
    [CrossRef]
  7. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, Nature 441, 960 (2006).
    [CrossRef]
  8. Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, Opt. Express 14, 4786 (2006).
    [CrossRef]
  9. N. C. Panoiu, X. Chen, and R. M. Osgood, Opt. Lett. 31, 3609 (2006).
    [CrossRef]
  10. K. Yamada, H. Fukuda, T. Tsuchizawa, T. Watanabe, T. Shoji, and S. Itabashi, IEEE Photon. Technol. Lett. 18, 1046 (2006).
    [CrossRef]
  11. Y.-H. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia, and O. Cohen, Opt. Express 14, 11721 (2006).
    [CrossRef]
  12. M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, Opt. Express 15, 12949 (2007).
    [CrossRef]
  13. X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, Nat. Photonics 4, 557 (2010).
    [CrossRef]
  14. S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, Nat. Photonics 4, 561 (2010).
    [CrossRef]
  15. B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. Green, Opt. Express 19, 20172 (2011).
    [CrossRef]
  16. X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, Nat. Photonics 6, 667 (2012).
    [CrossRef]
  17. J. B. Driscoll, N. Ophir, R. R. Grote, J. I. Dadap, N. C. Panoiu, K. Bergman, and R. M. Osgood, Opt. Express 20, 9227 (2012).
    [CrossRef]
  18. Q. Lin, O. J. Painter, and G. P. Agrawal, Opt. Express 15, 16604 (2007).
    [CrossRef]
  19. R. M. Osgood, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I.-W. Hsieh, E. Dulkeith, W. M. J. Green, and Y. A. Vlasov, Adv. Opt. Photon. 1, 162 (2009).
    [CrossRef]
  20. Q. Lin and G. P. Agrawal, Opt. Lett. 31, 3140 (2006).
    [CrossRef]
  21. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
    [CrossRef]
  22. X. Chen, N. C. Panoiu, and R. M. Osgood, IEEE J. Quantum Electron. 42, 160 (2006).
    [CrossRef]
  23. N. C. Panoiu, X. Liu, and R. M. Osgood, Opt. Lett. 34, 947 (2009).
    [CrossRef]
  24. S. Lavdas, J. B. Driscoll, H. Jiang, R. R. Grote, R. M. Osgood, and N. C. Panoiu, Opt. Lett. 38, 3953 (2013).
    [CrossRef]
  25. R. A. Soref and B. R. Bennett, IEEE J. Quantum Electron. 23, 123 (1987).
    [CrossRef]
  26. M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, Phys. Rev. Lett. 100, 183601 (2008).
    [CrossRef]
  27. O. Yaakobi and L. Friedland, Phys. Rev. A 82, 023820 (2010).
    [CrossRef]

2013 (1)

2012 (2)

J. B. Driscoll, N. Ophir, R. R. Grote, J. I. Dadap, N. C. Panoiu, K. Bergman, and R. M. Osgood, Opt. Express 20, 9227 (2012).
[CrossRef]

X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, Nat. Photonics 6, 667 (2012).
[CrossRef]

2011 (1)

2010 (3)

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, Nat. Photonics 4, 557 (2010).
[CrossRef]

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, Nat. Photonics 4, 561 (2010).
[CrossRef]

O. Yaakobi and L. Friedland, Phys. Rev. A 82, 023820 (2010).
[CrossRef]

2009 (2)

2008 (2)

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, Phys. Rev. Lett. 100, 183601 (2008).
[CrossRef]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

2007 (2)

2006 (7)

Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, Opt. Express 14, 4786 (2006).
[CrossRef]

Q. Lin and G. P. Agrawal, Opt. Lett. 31, 3140 (2006).
[CrossRef]

N. C. Panoiu, X. Chen, and R. M. Osgood, Opt. Lett. 31, 3609 (2006).
[CrossRef]

Y.-H. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia, and O. Cohen, Opt. Express 14, 11721 (2006).
[CrossRef]

X. Chen, N. C. Panoiu, and R. M. Osgood, IEEE J. Quantum Electron. 42, 160 (2006).
[CrossRef]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, Nature 441, 960 (2006).
[CrossRef]

K. Yamada, H. Fukuda, T. Tsuchizawa, T. Watanabe, T. Shoji, and S. Itabashi, IEEE Photon. Technol. Lett. 18, 1046 (2006).
[CrossRef]

2005 (2)

2004 (1)

2003 (1)

1987 (1)

R. A. Soref and B. R. Bennett, IEEE J. Quantum Electron. 23, 123 (1987).
[CrossRef]

1978 (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

1974 (1)

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, Appl. Phys. Lett. 24, 308 (1974).
[CrossRef]

Agrawal, G. P.

Alic, N.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, Nat. Photonics 4, 561 (2010).
[CrossRef]

Ashkin, A.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, Appl. Phys. Lett. 24, 308 (1974).
[CrossRef]

Baets, R.

X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, Nat. Photonics 6, 667 (2012).
[CrossRef]

B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. Green, Opt. Express 19, 20172 (2011).
[CrossRef]

Bennett, B. R.

R. A. Soref and B. R. Bennett, IEEE J. Quantum Electron. 23, 123 (1987).
[CrossRef]

Bergman, K.

Bjorkholm, J. E.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, Appl. Phys. Lett. 24, 308 (1974).
[CrossRef]

Boggio, J. M. C.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, Nat. Photonics 4, 561 (2010).
[CrossRef]

Carrasco, S.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, Phys. Rev. Lett. 100, 183601 (2008).
[CrossRef]

Chen, X.

Claps, R.

Cohen, O.

Dadap, J.

Dadap, J. I.

Dimitropoulos, D.

Divliansky, I. B.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, Nat. Photonics 4, 561 (2010).
[CrossRef]

Driscoll, J. B.

Dulkeith, E.

Espinola, R.

Fauchet, P. M.

Fejer, M. M.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, Phys. Rev. Lett. 100, 183601 (2008).
[CrossRef]

Foster, M. A.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, Opt. Express 15, 12949 (2007).
[CrossRef]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, Nature 441, 960 (2006).
[CrossRef]

Friedland, L.

O. Yaakobi and L. Friedland, Phys. Rev. A 82, 023820 (2010).
[CrossRef]

Fukuda, H.

K. Yamada, H. Fukuda, T. Tsuchizawa, T. Watanabe, T. Shoji, and S. Itabashi, IEEE Photon. Technol. Lett. 18, 1046 (2006).
[CrossRef]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, Opt. Express 13, 4629 (2005).
[CrossRef]

Gaeta, A. L.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, Opt. Express 15, 12949 (2007).
[CrossRef]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, Nature 441, 960 (2006).
[CrossRef]

Geraghty, D. F.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

Green, W.

Green, W. M. J.

X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, Nat. Photonics 6, 667 (2012).
[CrossRef]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, Nat. Photonics 4, 557 (2010).
[CrossRef]

R. M. Osgood, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I.-W. Hsieh, E. Dulkeith, W. M. J. Green, and Y. A. Vlasov, Adv. Opt. Photon. 1, 162 (2009).
[CrossRef]

Grote, R. R.

Hill, K. O.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

Hsieh, I.-W.

Hum, D. S.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, Phys. Rev. Lett. 100, 183601 (2008).
[CrossRef]

Itabashi, S.

K. Yamada, H. Fukuda, T. Tsuchizawa, T. Watanabe, T. Shoji, and S. Itabashi, IEEE Photon. Technol. Lett. 18, 1046 (2006).
[CrossRef]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, Opt. Express 13, 4629 (2005).
[CrossRef]

Jalali, B.

Jiang, H.

Johnson, D. C.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

Kawasaki, B. S.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

Kuo, Y.-H.

Kuyken, B.

X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, Nat. Photonics 6, 667 (2012).
[CrossRef]

B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. Green, Opt. Express 19, 20172 (2011).
[CrossRef]

Lavdas, S.

Lin, Q.

Lipson, M.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, Opt. Express 15, 12949 (2007).
[CrossRef]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, Nature 441, 960 (2006).
[CrossRef]

Liu, X.

MacDonald, R. I.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

McNab, S.

Mookherjea, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, Nat. Photonics 4, 561 (2010).
[CrossRef]

Moro, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, Nat. Photonics 4, 561 (2010).
[CrossRef]

Nasr, M. B.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, Phys. Rev. Lett. 100, 183601 (2008).
[CrossRef]

Ophir, N.

Osgood, R. M.

Painter, O. J.

Paniccia, M.

Panoiu, N. C.

Park, J. S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, Nat. Photonics 4, 561 (2010).
[CrossRef]

Radic, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, Nat. Photonics 4, 561 (2010).
[CrossRef]

Raghunathan, V.

Roelkens, G.

X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, Nat. Photonics 6, 667 (2012).
[CrossRef]

B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. Green, Opt. Express 19, 20172 (2011).
[CrossRef]

Rong, H.

Saleh, B. E. A.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, Phys. Rev. Lett. 100, 183601 (2008).
[CrossRef]

Salem, R.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, Opt. Express 15, 12949 (2007).
[CrossRef]

Schmidt, B. S.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, Nature 441, 960 (2006).
[CrossRef]

Sergienko, A. V.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, Phys. Rev. Lett. 100, 183601 (2008).
[CrossRef]

Sharping, J. E.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, Nature 441, 960 (2006).
[CrossRef]

Shoji, T.

K. Yamada, H. Fukuda, T. Tsuchizawa, T. Watanabe, T. Shoji, and S. Itabashi, IEEE Photon. Technol. Lett. 18, 1046 (2006).
[CrossRef]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, Opt. Express 13, 4629 (2005).
[CrossRef]

Sih, V.

Soref, R. A.

R. A. Soref and B. R. Bennett, IEEE J. Quantum Electron. 23, 123 (1987).
[CrossRef]

Stolen, R. H.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, Appl. Phys. Lett. 24, 308 (1974).
[CrossRef]

Takahashi, J.

Takahashi, M.

Teich, M. C.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, Phys. Rev. Lett. 100, 183601 (2008).
[CrossRef]

Torner, L.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, Phys. Rev. Lett. 100, 183601 (2008).
[CrossRef]

Torres, J. P.

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, Phys. Rev. Lett. 100, 183601 (2008).
[CrossRef]

Tsuchizawa, T.

K. Yamada, H. Fukuda, T. Tsuchizawa, T. Watanabe, T. Shoji, and S. Itabashi, IEEE Photon. Technol. Lett. 18, 1046 (2006).
[CrossRef]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, Opt. Express 13, 4629 (2005).
[CrossRef]

Turner, A. C.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, Opt. Express 15, 12949 (2007).
[CrossRef]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, Nature 441, 960 (2006).
[CrossRef]

Vlasov, Y.

Vlasov, Y. A.

Watanabe, T.

K. Yamada, H. Fukuda, T. Tsuchizawa, T. Watanabe, T. Shoji, and S. Itabashi, IEEE Photon. Technol. Lett. 18, 1046 (2006).
[CrossRef]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, Opt. Express 13, 4629 (2005).
[CrossRef]

Xu, S.

Yaakobi, O.

O. Yaakobi and L. Friedland, Phys. Rev. A 82, 023820 (2010).
[CrossRef]

Yamada, K.

K. Yamada, H. Fukuda, T. Tsuchizawa, T. Watanabe, T. Shoji, and S. Itabashi, IEEE Photon. Technol. Lett. 18, 1046 (2006).
[CrossRef]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, Opt. Express 13, 4629 (2005).
[CrossRef]

Zhang, J.

Zlatanovic, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, Nat. Photonics 4, 561 (2010).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (1)

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, Appl. Phys. Lett. 24, 308 (1974).
[CrossRef]

IEEE J. Quantum Electron. (2)

X. Chen, N. C. Panoiu, and R. M. Osgood, IEEE J. Quantum Electron. 42, 160 (2006).
[CrossRef]

R. A. Soref and B. R. Bennett, IEEE J. Quantum Electron. 23, 123 (1987).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. Yamada, H. Fukuda, T. Tsuchizawa, T. Watanabe, T. Shoji, and S. Itabashi, IEEE Photon. Technol. Lett. 18, 1046 (2006).
[CrossRef]

J. Appl. Phys. (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

Nat. Photonics (4)

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, Nat. Photonics 4, 557 (2010).
[CrossRef]

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, Nat. Photonics 4, 561 (2010).
[CrossRef]

X. Liu, B. Kuyken, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, Nat. Photonics 6, 667 (2012).
[CrossRef]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

Nature (1)

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, Nature 441, 960 (2006).
[CrossRef]

Opt. Express (10)

Opt. Lett. (4)

Phys. Rev. A (1)

O. Yaakobi and L. Friedland, Phys. Rev. A 82, 023820 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, Phys. Rev. Lett. 100, 183601 (2008).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic showing a periodically width-modulated Si-PNW and the configuration of a pulsed, seeded degenerate FWM setup. Dispersion maps are shown of dispersion coefficients (b) β1, (c) β2, and (d) β4.

Fig. 2.
Fig. 2.

Wavelength diagrams defined by the phase-matching conditions in (a) Eq. (2) and (b) Eq. (3). Solid (dashed) lines correspond to the signal (idler) and green (blue) lines to Λ=2mm (Λ=6mm). Dashed–dotted lines correspond to λp=λs=λi and vertical dotted lines mark β2(λ)=0. z dependence of (c) Δneff and (d) β2 and γ are shown for one period, Λ. In (c) and (d), the lines correspond to Δw=10nm (dashed–dotted), Δw=20nm (dashed), and Δw=30nm (solid). In all panels, w0=740nm.

Fig. 3.
Fig. 3.

Left (right) panels show the evolution of an optical pulse in a uniform (quasi-phase-matched Bragg) waveguide (see the text for the values of the pulse and waveguide parameters). Top, second, and third row panels show the z dependence of the temporal pulse profile, its spectrum, and FC density, respectively. (g) Input (green) and output pulse spectra corresponding to the uniform (blue) and Bragg (red) waveguides. In the inset are the signal and pump regions of the spectra. (h) Variation N(z) for uniform (solid) and Bragg (dotted) waveguides. In the inset is the dependence Δnfc(z) for Δw=10nm (brown), Δw=20nm (blue), and Δw=30nm (red).

Fig. 4.
Fig. 4.

(a), (b) CE η(z), calculated for different α and Δw, respectively; α=0 in (b). (c) CE calculated for different T0, for Bragg (solid) and uniform (dotted) waveguides. Pulse and waveguide parameters in (a)–(c) are the same as in Fig. 3. (d) FWM gain versus z (the values of pulse and waveguide parameters are given in the text).

Fig. 5.
Fig. 5.

(a) Pulse evolution for λs=2181nm and λi=2066nm. (b) CE dependence on z. Green and blue lines correspond to the pulse in (a), and λs=2066nm and λi=2181nm, respectively. The other parameters in (a) and (b) are w0=600nm, Λ=6mm, λp=2122nm, T0=500fs, Pp=200mW, and Ps=20mW.

Equations (4)

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iuz+n=1n=4inβn(z)n!nutn=i[cκ(z)2nvg(z)αfc(z)+α]u,ωκ(z)nvg(z)δnfc(z)uγ(z)[1+iτ(z)t]|u|2u,
Nt=Ntc+3Γ(z)4ε0A2(z)vg2(z)|u|4,
|2(βpγPp)βsβi|=Kg,
|2γPp+β2,pΔω2+β4,pΔω4/12|=Kg.

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