Abstract

We report what is believed to be the first experimental demonstration of soliton content as a function of the intensity of input light for multicolor quadratic solitons. Experiments were conducted with spatial solitons excited with Gaussian beams in a bulk crystal cut for second-harmonic generation. The effects introduced by the finite crystal length and by the scheme employed to elucidate the soliton energy are highlighted.

© 2001 Optical Society of America

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References

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  1. G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980).
  2. N. N. Akhmediev and A. Ankiewicz, Solitons (Chapman & Hall, London, 1997).
  3. L. Torner and G. I. Stegeman, Opt. Photon. News 12(6), 36 (2001).
    [CrossRef]
  4. Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1975).
  5. A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).
    [CrossRef]
  6. L. Torner, Opt. Commun. 114, 136 (1995).
    [CrossRef]
  7. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef] [PubMed]
  8. R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. A 53, 1138 (1996).
  9. P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarkas, Phys. Rev. Lett. 81, 570 (1998).
    [CrossRef]
  10. X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
    [CrossRef]
  11. B. Bourliaguet, V. Couderc, A. Barthelemy, G. W. Ross, P. G. R. Smith, D. C. Hanna, and C. De Angelis, Opt. Lett. 24, 1410 (1999).
    [CrossRef]
  12. L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 153 (1999).
    [CrossRef]
  13. R. A. Fuerst, M. T. G. Canva, D. Baboiu, and G. I. Stegeman, Opt. Lett. 22, 1748 (1997).
    [CrossRef]
  14. R. A. Fuerst, M. T. G. Canva, G. I. Stegeman, G. Leo, and G. Assanto, Opt. Quantum Electron. 30, 907 (1998).
    [CrossRef]
  15. A. Barthelemy, B. Bourliaguet, C. De Angelis, F. Gringoli, and G. Nalesso, Opt. Commun. 171, 345 (1999).
    [CrossRef]

2001 (1)

L. Torner and G. I. Stegeman, Opt. Photon. News 12(6), 36 (2001).
[CrossRef]

1999 (4)

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

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 153 (1999).
[CrossRef]

A. Barthelemy, B. Bourliaguet, C. De Angelis, F. Gringoli, and G. Nalesso, Opt. Commun. 171, 345 (1999).
[CrossRef]

B. Bourliaguet, V. Couderc, A. Barthelemy, G. W. Ross, P. G. R. Smith, D. C. Hanna, and C. De Angelis, Opt. Lett. 24, 1410 (1999).
[CrossRef]

1998 (2)

R. A. Fuerst, M. T. G. Canva, G. I. Stegeman, G. Leo, and G. Assanto, Opt. Quantum Electron. 30, 907 (1998).
[CrossRef]

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarkas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

1997 (1)

1996 (1)

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. A 53, 1138 (1996).

1995 (3)

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).
[CrossRef]

L. Torner, Opt. Commun. 114, 136 (1995).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

1975 (1)

Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1975).

Akhmediev, N. N.

N. N. Akhmediev and A. Ankiewicz, Solitons (Chapman & Hall, London, 1997).

Ankiewicz, A.

N. N. Akhmediev and A. Ankiewicz, Solitons (Chapman & Hall, London, 1997).

Artigas, D.

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 153 (1999).
[CrossRef]

Assanto, G.

R. A. Fuerst, M. T. G. Canva, G. I. Stegeman, G. Leo, and G. Assanto, Opt. Quantum Electron. 30, 907 (1998).
[CrossRef]

Baboiu, D.

Baek, Y.

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. A 53, 1138 (1996).

Barthelemy, A.

B. Bourliaguet, V. Couderc, A. Barthelemy, G. W. Ross, P. G. R. Smith, D. C. Hanna, and C. De Angelis, Opt. Lett. 24, 1410 (1999).
[CrossRef]

A. Barthelemy, B. Bourliaguet, C. De Angelis, F. Gringoli, and G. Nalesso, Opt. Commun. 171, 345 (1999).
[CrossRef]

Bourliaguet, B.

A. Barthelemy, B. Bourliaguet, C. De Angelis, F. Gringoli, and G. Nalesso, Opt. Commun. 171, 345 (1999).
[CrossRef]

B. Bourliaguet, V. Couderc, A. Barthelemy, G. W. Ross, P. G. R. Smith, D. C. Hanna, and C. De Angelis, Opt. Lett. 24, 1410 (1999).
[CrossRef]

Buryak, A. V.

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).
[CrossRef]

Caironi, D.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarkas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Canva, M. T. G.

R. A. Fuerst, M. T. G. Canva, G. I. Stegeman, G. Leo, and G. Assanto, Opt. Quantum Electron. 30, 907 (1998).
[CrossRef]

R. A. Fuerst, M. T. G. Canva, D. Baboiu, and G. I. Stegeman, Opt. Lett. 22, 1748 (1997).
[CrossRef]

Couderc, V.

Danielius, R.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarkas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

De Angelis, C.

A. Barthelemy, B. Bourliaguet, C. De Angelis, F. Gringoli, and G. Nalesso, Opt. Commun. 171, 345 (1999).
[CrossRef]

B. Bourliaguet, V. Couderc, A. Barthelemy, G. W. Ross, P. G. R. Smith, D. C. Hanna, and C. De Angelis, Opt. Lett. 24, 1410 (1999).
[CrossRef]

Di Trapani, P.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarkas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Dubietis, A.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarkas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Fuerst, R. A.

R. A. Fuerst, M. T. G. Canva, G. I. Stegeman, G. Leo, and G. Assanto, Opt. Quantum Electron. 30, 907 (1998).
[CrossRef]

R. A. Fuerst, M. T. G. Canva, D. Baboiu, and G. I. Stegeman, Opt. Lett. 22, 1748 (1997).
[CrossRef]

Gringoli, F.

A. Barthelemy, B. Bourliaguet, C. De Angelis, F. Gringoli, and G. Nalesso, Opt. Commun. 171, 345 (1999).
[CrossRef]

Hagan, D. J.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Hanna, D. C.

Karamzin, Yu. N.

Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1975).

Kivshar, Yu. S.

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).
[CrossRef]

Lamb, G. L.

G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980).

Leo, G.

R. A. Fuerst, M. T. G. Canva, G. I. Stegeman, G. Leo, and G. Assanto, Opt. Quantum Electron. 30, 907 (1998).
[CrossRef]

Liu, X.

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

Mazilu, D.

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 153 (1999).
[CrossRef]

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Mihalache, D.

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 153 (1999).
[CrossRef]

Nalesso, G.

A. Barthelemy, B. Bourliaguet, C. De Angelis, F. Gringoli, and G. Nalesso, Opt. Commun. 171, 345 (1999).
[CrossRef]

Piskarkas, A.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarkas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Qian, L. J.

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

Ross, G. W.

Schiek, R.

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. A 53, 1138 (1996).

Smith, P. G. R.

Stegeman, G. I.

L. Torner and G. I. Stegeman, Opt. Photon. News 12(6), 36 (2001).
[CrossRef]

R. A. Fuerst, M. T. G. Canva, G. I. Stegeman, G. Leo, and G. Assanto, Opt. Quantum Electron. 30, 907 (1998).
[CrossRef]

R. A. Fuerst, M. T. G. Canva, D. Baboiu, and G. I. Stegeman, Opt. Lett. 22, 1748 (1997).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. A 53, 1138 (1996).

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Sukhorukov, A. P.

Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1975).

Torner, L.

L. Torner and G. I. Stegeman, Opt. Photon. News 12(6), 36 (2001).
[CrossRef]

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 153 (1999).
[CrossRef]

L. Torner, Opt. Commun. 114, 136 (1995).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Torres, J. P.

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 153 (1999).
[CrossRef]

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Valiulis, G.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarkas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Van Stryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Wise, F. W.

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

Opt. Commun. (3)

L. Torner, Opt. Commun. 114, 136 (1995).
[CrossRef]

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 153 (1999).
[CrossRef]

A. Barthelemy, B. Bourliaguet, C. De Angelis, F. Gringoli, and G. Nalesso, Opt. Commun. 171, 345 (1999).
[CrossRef]

Opt. Lett. (2)

Opt. Photon. News (1)

L. Torner and G. I. Stegeman, Opt. Photon. News 12(6), 36 (2001).
[CrossRef]

Opt. Quantum Electron. (1)

R. A. Fuerst, M. T. G. Canva, G. I. Stegeman, G. Leo, and G. Assanto, Opt. Quantum Electron. 30, 907 (1998).
[CrossRef]

Phys. Lett. A (1)

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).
[CrossRef]

Phys. Rev. A (1)

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. A 53, 1138 (1996).

Phys. Rev. Lett. (3)

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarkas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

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

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1975).

Other (2)

G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980).

N. N. Akhmediev and A. Ankiewicz, Solitons (Chapman & Hall, London, 1997).

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. M, mirror; F1, F2, postive lenses. Other abbreviations are defined in text.

Fig. 2
Fig. 2

(a) Measured energy versus blade position. Diamonds and solid curve, a spatial soliton is excited; dotted curve, quasi-linear diffraction. (b) Profiles of the soliton (diamonds) and of the diffracted beam (open triangles). Solid and dotted curves, the respective Gaussian fits.

Fig. 3
Fig. 3

Measured soliton content as a function of the input peak power. Filled points, experimental data; solid curve, theoretical cw value for an infinite sample. (a) Exact phase matching, (b) outside phase matching. Dotted curves are drawn as an aid to the eye.

Fig. 4
Fig. 4

Calculated fraction of input power remaining inside pinholes of different sizes as functions of input peak intensity. Numbers with arrows are the pinhole diameters δx2-δx1 in micrometers. Crystal lengths, (a) L=2 cm (as in the experiment) and (b) L=4 cm.

Fig. 5
Fig. 5

Calculated widths (FWHM) of the output beams as a function of the input peak intensity. Dotted curves, values for an infinite crystal. (a) L=2 cm, (b) L=4 cm.

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