Abstract

We study the spatiotemporal dynamics of ultrashort pulses close to a point of zero group-velocity dispersion in planar waveguides with focusing nonlinearities. We find that the process of pulse collapse enhances the emission of so-called resonant radiation, providing an efficient mechanism of energy transfer from solitonic to dispersive waves and leading to suppression of the collapse.

© 2005 Optical Society of America

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References

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  1. Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, New York, 2003), Chap. 7 and references therein.
  2. X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
    [CrossRef]
  3. P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
    [CrossRef]
  4. H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
    [CrossRef]
  5. K. D. Moll and A. L. Gaeta, Opt. Lett. 29, 995 (2004).
    [CrossRef] [PubMed]
  6. D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
    [CrossRef]
  7. G. Fibich and B. Ilan, Opt. Lett. 29, 887 (2004).
    [CrossRef] [PubMed]
  8. V. I. Karpman, Phys. Rev. E 53, 1336 (1996).
    [CrossRef]
  9. N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
    [CrossRef] [PubMed]
  10. F. Biancalana, D. V. Skryabin, and A. V. Yulin, Phys. Rev. E 70, 016615 (2004).
    [CrossRef]
  11. M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
    [CrossRef]
  12. M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
    [CrossRef]
  13. L. Berge, Phys. Rep. 303, 259 (1998).
    [CrossRef]
  14. E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, Opt. Lett. 21, 62 (1996).
    [CrossRef] [PubMed]

2004 (4)

K. D. Moll and A. L. Gaeta, Opt. Lett. 29, 995 (2004).
[CrossRef] [PubMed]

G. Fibich and B. Ilan, Opt. Lett. 29, 887 (2004).
[CrossRef] [PubMed]

F. Biancalana, D. V. Skryabin, and A. V. Yulin, Phys. Rev. E 70, 016615 (2004).
[CrossRef]

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef]

2003 (3)

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef]

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

2001 (1)

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

1999 (1)

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

1998 (1)

L. Berge, Phys. Rep. 303, 259 (1998).
[CrossRef]

1996 (2)

1995 (1)

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, New York, 2003), Chap. 7 and references therein.

Aitchison, J. S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

Akhmediev, N.

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

Bar-Ad, S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

Berge, L.

L. Berge, Phys. Rep. 303, 259 (1998).
[CrossRef]

Biancalana, F.

F. Biancalana, D. V. Skryabin, and A. V. Yulin, Phys. Rev. E 70, 016615 (2004).
[CrossRef]

Cheskis, D.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

Conti, C.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Curley, P. F.

Di Trapani, P.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Eisenberg, H. S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

Fibich, G.

Franco, M. A.

Gaeta, A. L.

Grillon, G.

Ilan, B.

Jedrkiewicz, O.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Karlsson, M.

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

Karpman, V. I.

V. I. Karpman, Phys. Rev. E 53, 1336 (1996).
[CrossRef]

Katona, G.

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, New York, 2003), Chap. 7 and references therein.

Kolesik, M.

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef]

Liu, X.

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

Moll, K. D.

Moloney, J. V.

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef]

Morandotti, R.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

Mysyrowicz, A.

Nibbering, E. T. J.

Piskarskas, A.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Prade, B. S.

Qian, L. J.

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

Ross, D.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

Salin, F.

Silberberg, Y.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

Skryabin, D. V.

F. Biancalana, D. V. Skryabin, and A. V. Yulin, Phys. Rev. E 70, 016615 (2004).
[CrossRef]

Trillo, S.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Trull, J.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Valiulis, G.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Wise, F. W.

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

Wright, E. M.

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef]

Yulin, A. V.

F. Biancalana, D. V. Skryabin, and A. V. Yulin, Phys. Rev. E 70, 016615 (2004).
[CrossRef]

Opt. Lett. (3)

Phys. Rep. (1)

L. Berge, Phys. Rep. 303, 259 (1998).
[CrossRef]

Phys. Rev. A (1)

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (2)

F. Biancalana, D. V. Skryabin, and A. V. Yulin, Phys. Rev. E 70, 016615 (2004).
[CrossRef]

V. I. Karpman, Phys. Rev. E 53, 1336 (1996).
[CrossRef]

Phys. Rev. Lett. (6)

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef]

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef]

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef]

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, Phys. Rev. Lett. 87, 043902 (2001).
[CrossRef]

Other (1)

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, New York, 2003), Chap. 7 and references therein.

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Figures (2)

Fig. 1
Fig. 1

Spectral profiles of the Gaussian pulse after propagation distance z=0.2. (a) is calculated from Eq. (1) and (b) from Eq. (2). Normalized initial conditions given in the text correspond to the initial pulse with a duration of 53 fs, an aperture of 60 µm and a peak power of 180 kW. Thin dashed lines show the zero-GVD frequency. The solid curves are calculated from the approximate conditions of resonance: κΔ,Kx0 for (a) and δ2δ-1kx2 with =0.24 for (b).

Fig. 2
Fig. 2

Changes in the temporal profiles of the Gaussian pulse at x=0 as it propagates inside the waveguide, calculated from (a) Eq. (1) and (b) Eq. (2). The vertical panel in (b) shows the evolution of the Hamiltonian integral calculated over only the localized part of the field. All the parameters are the same as in Fig. 1.

Equations (2)

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iZE+dTdXLX,TEX-X,T-T+γ1+iωpTEdTRTEX,T-T2=0.
izA+12x2+t2-it3-istx2A+A2A=0,

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