Abstract

We demonstrate that strong modulation instability (MI) of copropagating optical waves can be observed in Si photonic nanowires with a length of only a few millimeters. We consider two distinct cases, namely one in which one wave propagates in the normal group-velocity dispersion (GVD) region and the other one experiences anomalous GVD, and a second case in which both waves propagate in the anomalous GVD region. In both cases we show that, for comparable optical powers, the peak value of the MI gain spectrum is 2 to 3 orders of magnitude larger than that achieved in optical fibers.

© 2006 Optical Society of America

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  1. J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, in Proc. SPIE 3007, 112 (1997).
    [CrossRef]
  2. R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 65 (2002).
    [CrossRef]
  3. Y. A. Vlasov and S. J. McNab, Opt. Express 12, 1622 (2004).
    [CrossRef] [PubMed]
  4. O. Boyraz and B. Jalali, Opt. Express 12, 5269 (2004).
    [CrossRef] [PubMed]
  5. H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, Nature 433, 294 (2005).
    [CrossRef]
  6. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, Opt. Express 11, 1731 (2003).
    [CrossRef] [PubMed]
  7. R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, Opt. Express 12, 3716 (2004).
    [CrossRef]
  8. J. I. Dadap, R. L. Espinola, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, Opt. Lett. 29, 2755 (2004).
    [CrossRef] [PubMed]
  9. Q. Xu, V. R. Almeida, and M. Lipson, Opt. Express 12, 4437 (2004).
    [CrossRef] [PubMed]
  10. X. Chen, N. C. Panoiu, and R. M. Osgood, IEEE J. Quantum Electron. 42, 160 (2006).
    [CrossRef]
  11. R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, Opt. Express 13, 4341 (2005).
    [CrossRef] [PubMed]
  12. H. Rong, Y. Kuo, A. Liu, M. Paniccia, and O. Cohen, Opt. Express 14, 1182 (2006).
    [CrossRef] [PubMed]
  13. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, Nature 441, 960 (2006).
    [CrossRef] [PubMed]
  14. O. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, Opt. Express 12, 4094 (2004).
    [CrossRef] [PubMed]
  15. J. J. Wynne, Phys. Rev. 178, 1295 (1969).
    [CrossRef]
  16. R. A. Soref and B. R. Bennett, IEEE J. Quantum Electron. 23, 123 (1987).
    [CrossRef]
  17. G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
    [CrossRef] [PubMed]
  18. J. A. Rothenberg, Phys. Rev. A 42, 682 (1990).
    [CrossRef] [PubMed]
  19. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  20. J. F. McMillan, X. Yang, N. C. Panoiu, R. M. Osgood, and C. W. Wong, Opt. Lett. 31, 1235 (2006).
    [CrossRef] [PubMed]

2006 (4)

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] [PubMed]

H. Rong, Y. Kuo, A. Liu, M. Paniccia, and O. Cohen, Opt. Express 14, 1182 (2006).
[CrossRef] [PubMed]

J. F. McMillan, X. Yang, N. C. Panoiu, R. M. Osgood, and C. W. Wong, Opt. Lett. 31, 1235 (2006).
[CrossRef] [PubMed]

2005 (2)

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, Nature 433, 294 (2005).
[CrossRef]

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, Opt. Express 13, 4341 (2005).
[CrossRef] [PubMed]

2004 (6)

2003 (1)

2002 (1)

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

1997 (1)

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, in Proc. SPIE 3007, 112 (1997).
[CrossRef]

1990 (1)

J. A. Rothenberg, Phys. Rev. A 42, 682 (1990).
[CrossRef] [PubMed]

1987 (2)

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

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef] [PubMed]

1969 (1)

J. J. Wynne, Phys. Rev. 178, 1295 (1969).
[CrossRef]

Agarwal, A. M.

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, in Proc. SPIE 3007, 112 (1997).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Ahmad, R. U.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

Almeida, V. R.

Bennett, B. R.

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

Boyraz, O.

Camarda, G. S.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

Chen, X.

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

Claps, R.

Cohen, O.

H. Rong, Y. Kuo, A. Liu, M. Paniccia, and O. Cohen, Opt. Express 14, 1182 (2006).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, Nature 433, 294 (2005).
[CrossRef]

Dadap, J. I.

Dimitropoulos, D.

Espinola, R. L.

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, Opt. Express 13, 4341 (2005).
[CrossRef] [PubMed]

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, Opt. Express 12, 3716 (2004).
[CrossRef]

J. I. Dadap, R. L. Espinola, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, Opt. Lett. 29, 2755 (2004).
[CrossRef] [PubMed]

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

Fang, A.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, Nature 433, 294 (2005).
[CrossRef]

Foresi, J. S.

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, in Proc. SPIE 3007, 112 (1997).
[CrossRef]

Foster, M. A.

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

Gaeta, A. L.

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

Hak, D.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, Nature 433, 294 (2005).
[CrossRef]

Han, Y.

Jalali, B.

Jones, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, Nature 433, 294 (2005).
[CrossRef]

Kimerling, L. C.

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, in Proc. SPIE 3007, 112 (1997).
[CrossRef]

Koonath, P.

Kuo, Y.

Liao, L.

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, in Proc. SPIE 3007, 112 (1997).
[CrossRef]

Lim, D. R.

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, in Proc. SPIE 3007, 112 (1997).
[CrossRef]

Lipson, M.

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

Q. Xu, V. R. Almeida, and M. Lipson, Opt. Express 12, 4437 (2004).
[CrossRef] [PubMed]

Liu, A.

H. Rong, Y. Kuo, A. Liu, M. Paniccia, and O. Cohen, Opt. Express 14, 1182 (2006).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, Nature 433, 294 (2005).
[CrossRef]

McMillan, J. F.

McNab, S. J.

Nicolaescu, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, Nature 433, 294 (2005).
[CrossRef]

Osgood, R. M.

J. F. McMillan, X. Yang, N. C. Panoiu, R. M. Osgood, and C. W. Wong, Opt. Lett. 31, 1235 (2006).
[CrossRef] [PubMed]

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

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, Opt. Express 13, 4341 (2005).
[CrossRef] [PubMed]

J. I. Dadap, R. L. Espinola, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, Opt. Lett. 29, 2755 (2004).
[CrossRef] [PubMed]

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, Opt. Express 12, 3716 (2004).
[CrossRef]

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

Paniccia, M.

H. Rong, Y. Kuo, A. Liu, M. Paniccia, and O. Cohen, Opt. Express 14, 1182 (2006).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, Nature 433, 294 (2005).
[CrossRef]

Panoiu, N. C.

Pizzuto, F.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

Raghunathan, V.

Rao, H.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

Rong, H.

H. Rong, Y. Kuo, A. Liu, M. Paniccia, and O. Cohen, Opt. Express 14, 1182 (2006).
[CrossRef] [PubMed]

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, Nature 433, 294 (2005).
[CrossRef]

Rothenberg, J. A.

J. A. Rothenberg, Phys. Rev. A 42, 682 (1990).
[CrossRef] [PubMed]

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] [PubMed]

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] [PubMed]

Soref, R. A.

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

Turner, A. C.

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

Vlasov, Y. A.

Wong, C. W.

Wynne, J. J.

J. J. Wynne, Phys. Rev. 178, 1295 (1969).
[CrossRef]

Xu, Q.

Yang, X.

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)

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

Nature (2)

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, Nature 433, 294 (2005).
[CrossRef]

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

Opt. Express (8)

Opt. Lett. (2)

Phys. Rev. (1)

J. J. Wynne, Phys. Rev. 178, 1295 (1969).
[CrossRef]

Phys. Rev. A (1)

J. A. Rothenberg, Phys. Rev. A 42, 682 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef] [PubMed]

Proc. SPIE (1)

J. S. Foresi, D. R. Lim, L. Liao, A. M. Agarwal, and L. C. Kimerling, in Proc. SPIE 3007, 112 (1997).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

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Figures (3)

Fig. 1
Fig. 1

Wavelength and frequency dependence of n eff , n g , and β 2 .

Fig. 2
Fig. 2

Calculated MI gain spectra for (a) case A and (b) case B. The powers of the signal wave in cases A and B are P s = 50 mW and P s = 10 mW , respectively.

Fig. 3
Fig. 3

Results of numerical simulation of MI. (a) Gain spectra for cases A (dashed curve) and B (solid curve); (b) and (c) correspond to case A, (d) and (e) correspond to case B and show the normalized temporal profiles of the signal pulses at z = 19.5 mm , z = 20 mm , and z = 20.5 mm (from bottom to top) and the spectra at z = 20 mm , respectively. For clarity, the temporal profiles are shifted by 1. The peak powers are P p = P s = 250 mW (case A) and P p = P s = 100 mW (case B).

Equations (4)

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

i u p z + i v g p u p t β 2 p 2 2 u p t 2 = i c κ p 2 n v g p ( α i n + α FC p ) u p ω p κ p n v g p δ n FC p u p 3 ω p ε 0 A 0 v g p ( P p Γ p v g p u p 2 + 2 P s Γ s p v g s u s 2 ) u p ,
i u s z + i v g s u s t β 2 s 2 2 u s t 2 = i c κ s 2 n v g s ( α i n + α FC s ) u s ω s κ s n v g s δ n FC s u s 3 ω s ε 0 A 0 v g s ( P s Γ s v g s u s 2 + 2 P p Γ p s v g p u p 2 ) u s ,
N t = N t c + 6 ε 0 A 0 2 [ P p 2 Γ p 2 v g p 2 u p 4 P s 2 Γ s 2 v g s 2 u s 4 + 2 ( ω p Γ s p + ω s Γ p s ) P p P s ( ω p + ω s ) v g p v g s u p 2 u s 2 ] ,
[ ( Λ Ω v g p ) 2 ϱ p ] [ ( Λ Ω v g s ) 2 ϱ s ] = η Ω 4 ,

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