Abstract

We put forward a method for generating engineerable competing quadratic and cubic nonlinearities in suitable settings in which frequency generation is accompanied by optical rectification. The novel scheme is based on the full exploitation of the geometrical conditions that determine the magnitude of the rectified fields and translates the different orientations of an elliptical pump beam into tunable nonlinearities, which can be used to act on the spectral composition and overall features of optical solitons.

© 2002 Optical Society of America

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  1. G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
    [CrossRef]
  2. L. Torner and A. P. Sukhorukov, Opt. Photon. News 12(2), 42 (2002).
    [CrossRef]
  3. A. V. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. (to be published).
  4. A. V. Buryak, Y. S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995).
    [CrossRef] [PubMed]
  5. S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Commun. 122, 200 (1996).
    [CrossRef]
  6. O. Bang, J. Opt. Soc. Am. B 14, 51 (1997).
    [CrossRef]
  7. L. Berge, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
    [CrossRef]
  8. O. Bang, Y. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
    [CrossRef]
  9. T. K. Gustafson, J. P. E. Taran, P. L. Kelley, and R. Y. Chiao, Opt. Commun. 2, 17 (1970).
    [CrossRef]
  10. Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, Phys. Rev. Lett. 74, 2816 (1995).
    [CrossRef] [PubMed]
  11. V. V. Steblina, A. V. Buryak, R. Sammut, D. Zhou, M. Segev, and P. Prucnal, J. Opt. Soc. Am. B 17, 2026 (2000).
    [CrossRef]
  12. D. Bedeaux and N. Bloembergen, Physica 69, 57 (1973).
    [CrossRef]
  13. M. Zgonik and P. Gunter, J. Opt. Soc. Am. B 13, 570 (1996).
    [CrossRef]
  14. I. Biaggio, Phys. Rev. Lett. 82, 193 (1999).
    [CrossRef]
  15. I. Biaggio, Appl. Phys. Lett. 78, 1861 (2001).
    [CrossRef]
  16. Ch. Bosshard, I. Biaggio, St. Fischer, S. Follonier, and P. Gunter, Opt. Lett. 24, 196 (1999).
    [CrossRef]
  17. R. Spreiter, Ch. Bosshard, and P. Gunter, J. Opt. Soc. Am. B 18, 1311 (2001).
    [CrossRef]
  18. Chr. Flytzanis and N. Bloembergen, Prog. Quantum Electron. 4, 271 (1976).
    [CrossRef]
  19. L. Torner, Opt. Commun. 114, 136 (1995).
    [CrossRef]
  20. L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, Opt. Lett. 20, 2183 (1995).
    [CrossRef]
  21. T. J. Alexander, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 23, 670 (1998).
    [CrossRef]
  22. I. Towers, A. V. Buryak, R. A. Sammut, and B. A. Malomed, Phys. Rev. E 63, 055601 (2001).
    [CrossRef]

2002 (1)

L. Torner and A. P. Sukhorukov, Opt. Photon. News 12(2), 42 (2002).
[CrossRef]

2001 (3)

I. Biaggio, Appl. Phys. Lett. 78, 1861 (2001).
[CrossRef]

R. Spreiter, Ch. Bosshard, and P. Gunter, J. Opt. Soc. Am. B 18, 1311 (2001).
[CrossRef]

I. Towers, A. V. Buryak, R. A. Sammut, and B. A. Malomed, Phys. Rev. E 63, 055601 (2001).
[CrossRef]

2000 (1)

1999 (2)

1998 (2)

T. J. Alexander, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 23, 670 (1998).
[CrossRef]

O. Bang, Y. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

1997 (2)

O. Bang, J. Opt. Soc. Am. B 14, 51 (1997).
[CrossRef]

L. Berge, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
[CrossRef]

1996 (3)

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Commun. 122, 200 (1996).
[CrossRef]

M. Zgonik and P. Gunter, J. Opt. Soc. Am. B 13, 570 (1996).
[CrossRef]

1995 (4)

1976 (1)

Chr. Flytzanis and N. Bloembergen, Prog. Quantum Electron. 4, 271 (1976).
[CrossRef]

1973 (1)

D. Bedeaux and N. Bloembergen, Physica 69, 57 (1973).
[CrossRef]

1970 (1)

T. K. Gustafson, J. P. E. Taran, P. L. Kelley, and R. Y. Chiao, Opt. Commun. 2, 17 (1970).
[CrossRef]

Akhmediev, N. N.

Alexander, T. J.

Bang, O.

O. Bang, Y. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

L. Berge, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
[CrossRef]

O. Bang, J. Opt. Soc. Am. B 14, 51 (1997).
[CrossRef]

Bedeaux, D.

D. Bedeaux and N. Bloembergen, Physica 69, 57 (1973).
[CrossRef]

Berge, L.

L. Berge, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
[CrossRef]

Biaggio, I.

I. Biaggio, Appl. Phys. Lett. 78, 1861 (2001).
[CrossRef]

Ch. Bosshard, I. Biaggio, St. Fischer, S. Follonier, and P. Gunter, Opt. Lett. 24, 196 (1999).
[CrossRef]

I. Biaggio, Phys. Rev. Lett. 82, 193 (1999).
[CrossRef]

Bloembergen, N.

Chr. Flytzanis and N. Bloembergen, Prog. Quantum Electron. 4, 271 (1976).
[CrossRef]

D. Bedeaux and N. Bloembergen, Physica 69, 57 (1973).
[CrossRef]

Bosshard, Ch.

Buryak, A. V.

I. Towers, A. V. Buryak, R. A. Sammut, and B. A. Malomed, Phys. Rev. E 63, 055601 (2001).
[CrossRef]

V. V. Steblina, A. V. Buryak, R. Sammut, D. Zhou, M. Segev, and P. Prucnal, J. Opt. Soc. Am. B 17, 2026 (2000).
[CrossRef]

O. Bang, Y. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

T. J. Alexander, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 23, 670 (1998).
[CrossRef]

S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Commun. 122, 200 (1996).
[CrossRef]

A. V. Buryak, Y. S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995).
[CrossRef] [PubMed]

A. V. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. (to be published).

Chiao, R. Y.

T. K. Gustafson, J. P. E. Taran, P. L. Kelley, and R. Y. Chiao, Opt. Commun. 2, 17 (1970).
[CrossRef]

De Rossi, A.

O. Bang, Y. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

Di Trapani, P.

A. V. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. (to be published).

Fischer, St.

Flytzanis, Chr.

Chr. Flytzanis and N. Bloembergen, Prog. Quantum Electron. 4, 271 (1976).
[CrossRef]

Follonier, S.

Gunter, P.

Gustafson, T. K.

T. K. Gustafson, J. P. E. Taran, P. L. Kelley, and R. Y. Chiao, Opt. Commun. 2, 17 (1970).
[CrossRef]

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Kelley, P. L.

T. K. Gustafson, J. P. E. Taran, P. L. Kelley, and R. Y. Chiao, Opt. Commun. 2, 17 (1970).
[CrossRef]

Kivshar, Y. S.

O. Bang, Y. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

T. J. Alexander, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 23, 670 (1998).
[CrossRef]

S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Commun. 122, 200 (1996).
[CrossRef]

A. V. Buryak, Y. S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995).
[CrossRef] [PubMed]

Malomed, B. A.

I. Towers, A. V. Buryak, R. A. Sammut, and B. A. Malomed, Phys. Rev. E 63, 055601 (2001).
[CrossRef]

Mazilu, D.

Mezentsev, V. K.

L. Berge, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
[CrossRef]

Mihalache, D.

Prucnal, P.

Rasmussen, J. J.

L. Berge, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
[CrossRef]

Sammut, R.

Sammut, R. A.

I. Towers, A. V. Buryak, R. A. Sammut, and B. A. Malomed, Phys. Rev. E 63, 055601 (2001).
[CrossRef]

Segev, M.

Skryabin, D.

A. V. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. (to be published).

Spreiter, R.

R. Spreiter, Ch. Bosshard, and P. Gunter, J. Opt. Soc. Am. B 18, 1311 (2001).
[CrossRef]

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, Phys. Rev. Lett. 74, 2816 (1995).
[CrossRef] [PubMed]

Steblina, V. V.

Stegeman, G. I.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Sukhorukov, A. P.

L. Torner and A. P. Sukhorukov, Opt. Photon. News 12(2), 42 (2002).
[CrossRef]

Taran, J. P. E.

T. K. Gustafson, J. P. E. Taran, P. L. Kelley, and R. Y. Chiao, Opt. Commun. 2, 17 (1970).
[CrossRef]

Torner, L.

L. Torner and A. P. Sukhorukov, Opt. Photon. News 12(2), 42 (2002).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

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

L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, Opt. Lett. 20, 2183 (1995).
[CrossRef]

Towers, I.

I. Towers, A. V. Buryak, R. A. Sammut, and B. A. Malomed, Phys. Rev. E 63, 055601 (2001).
[CrossRef]

Trillo, S.

O. Bang, Y. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Commun. 122, 200 (1996).
[CrossRef]

A. V. Buryak, Y. S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995).
[CrossRef] [PubMed]

A. V. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. (to be published).

Zgonik, M.

M. Zgonik and P. Gunter, J. Opt. Soc. Am. B 13, 570 (1996).
[CrossRef]

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, Phys. Rev. Lett. 74, 2816 (1995).
[CrossRef] [PubMed]

Zhou, D.

Appl. Phys. Lett. (1)

I. Biaggio, Appl. Phys. Lett. 78, 1861 (2001).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (3)

T. K. Gustafson, J. P. E. Taran, P. L. Kelley, and R. Y. Chiao, Opt. Commun. 2, 17 (1970).
[CrossRef]

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

S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Commun. 122, 200 (1996).
[CrossRef]

Opt. Lett. (4)

Opt. Photon. News (1)

L. Torner and A. P. Sukhorukov, Opt. Photon. News 12(2), 42 (2002).
[CrossRef]

Opt. Quantum Electron. (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Phys. Rev. E (3)

L. Berge, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
[CrossRef]

O. Bang, Y. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
[CrossRef]

I. Towers, A. V. Buryak, R. A. Sammut, and B. A. Malomed, Phys. Rev. E 63, 055601 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, Phys. Rev. Lett. 74, 2816 (1995).
[CrossRef] [PubMed]

I. Biaggio, Phys. Rev. Lett. 82, 193 (1999).
[CrossRef]

Physica (1)

D. Bedeaux and N. Bloembergen, Physica 69, 57 (1973).
[CrossRef]

Prog. Quantum Electron. (1)

Chr. Flytzanis and N. Bloembergen, Prog. Quantum Electron. 4, 271 (1976).
[CrossRef]

Other (1)

A. V. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. (to be published).

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Figures (3)

Fig. 1
Fig. 1

Fraction of energy flow carried by each wave that forms the solitons as a function of the strength of cubic nonlinearity α, and hence of orientation φ, for a fixed value of the total energy flow I=20. (a) γ=1, (b) γ=2.

Fig. 2
Fig. 2

Width of solitons as a function of amplitude for α=0.2. (a) γ=1, (b) γ=2. Insets, field profiles that correspond to two points (A and B) of the corresponding existence curves for solitons. Solid curves, fundamental frequency beam; dashed curves, SH beam.

Fig. 3
Fig. 3

Excitation of two solitons with different energies sharing the same input conditions: U=800/π1/4 exp-s2 and V=0. (a) α=0, (b) α=0.2. Solid curves, fundamental frequency beams; dashed curves, SH beams. The output beam is plotted at ξ=50.

Equations (10)

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2ik1A1y+12A1+k02ϵ0PNLωexp-ik1y=0,
2ik2A2y+12A2+4k02ϵ0PNL2ωexp-ik2y=0,
PORω=ϵ0nx4nx4rxxz24ϵzz+2A12+nz4rxxzrzzz4ϵzz+2A22-rxxz2EzA1,
POR2ω=ϵ0nz4nz4rxxzrzzz4ϵzz+2A12+nz4rzzz24ϵzz+2A22-rzzz2EzA2,
Ez=14sin2φnx4rxxzA12+nz4rzzzA22ϵzz sin2φ+ϵxx cos2φ.
P3ω=34χxxxx3-ω,-ω,ω,ω×A1+2ρ1A22A1,
P32ω=34χzzzz3-2ω,-2ω,2ω,2ω×A2+2ρ2A12A2,
iUξ-α122Us2+U*V exp-iβξ+αU2+γV2U=0,
iVξ-α222Us2+U2 expiβξ+2αγU2+V2V=0,
ν=ν01ϵzz+2-sin2φϵzz sin2φ+ϵxx cos2φ,

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