Abstract

We show that the efficiency and the mismatch bandwidth of quadratic soliton formation under conditions of second-harmonic generation can be enhanced in an important way in synthetic phase-matching profiles. Soliton excitation in smooth but arbitrary profiles is shown to be well described by a reduced variational approach. The potential of abrupt, nonadiabatic profiles for improved soliton formation is numerically revealed.

© 2000 Optical Society of America

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References

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  1. G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
    [CrossRef]
  2. A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995); L. Torner, Opt. Commun. 114, 136 (1995).
    [CrossRef]
  3. L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 151 (1999).
    [CrossRef]
  4. M. Ohkawa, R. A. Fuerst, and G. I. Stegeman, J. Opt. Soc. Am. B 15, 2769 (1998).
    [CrossRef]
  5. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef] [PubMed]
  6. C. R. Menyuk, R. Schiek, and L. Torner, J. Opt. Soc. Am. B 11, 2434 (1994).
    [CrossRef]
  7. B. Bourliaguet, V. Couderc, A. Barthélémy, G. W. Ross, P. G. R. Smith, D. C. Hanna, and C. De Angelis, Opt. Lett. 24, 1410 (1999).
    [CrossRef]
  8. G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanaukas, M. Fermann, and D. Harter, J. Opt. Soc. Am. B 17, 304 (2000).
    [CrossRef]
  9. R. Schiek, Y. Baek, and G. I. Stegeman, J. Opt. Soc. Am. B 15, 2255 (1998).
    [CrossRef]
  10. L. Torner, C. B. Clausen, and M. M. Fejer, Opt. Lett. 23, 903 (1998).
    [CrossRef]
  11. V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
    [CrossRef]
  12. C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
    [CrossRef]
  13. D. Artigas, L. Torner, and N. N. Akhmediev, Opt. Commun. 162, 347 (1999).
    [CrossRef]

2000 (1)

1999 (3)

D. Artigas, L. Torner, and N. N. Akhmediev, Opt. Commun. 162, 347 (1999).
[CrossRef]

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 151 (1999).
[CrossRef]

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

1998 (3)

1996 (2)

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

1995 (3)

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995); L. Torner, Opt. Commun. 114, 136 (1995).
[CrossRef]

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

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

1994 (1)

Akhmediev, N. N.

D. Artigas, L. Torner, and N. N. Akhmediev, Opt. Commun. 162, 347 (1999).
[CrossRef]

Arbore, M. A.

Artigas, D.

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 151 (1999).
[CrossRef]

D. Artigas, L. Torner, and N. N. Akhmediev, Opt. Commun. 162, 347 (1999).
[CrossRef]

Baek, Y.

Barthélémy, A.

Bourliaguet, B.

Buryak, A. V.

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995); L. Torner, Opt. Commun. 114, 136 (1995).
[CrossRef]

Clausen, C. B.

Couderc, V.

De Angelis, C.

Etrich, C.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

Fejer, M. M.

Fermann, M.

Fuerst, R. A.

Galvanaukas, A.

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

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

Hanna, D. C.

Harter, D.

Imeshev, G.

Kivshar, Y. S.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

Kivshar, Yu. S.

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995); L. Torner, Opt. Commun. 114, 136 (1995).
[CrossRef]

Lederer, F.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

Lisak, M.

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

Malomed, B. A.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

Mazilu, D.

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 151 (1999).
[CrossRef]

Menyuk, C. R.

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

C. R. Menyuk, R. Schiek, and L. Torner, J. Opt. Soc. Am. B 11, 2434 (1994).
[CrossRef]

Mihalache, D.

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 151 (1999).
[CrossRef]

Ohkawa, M.

Peschel, U.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

Ross, G. W.

Schiek, R.

Smith, P. G. R.

Steblina, V. V.

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

Stegeman, G. I.

M. Ohkawa, R. A. Fuerst, and G. I. Stegeman, J. Opt. Soc. Am. B 15, 2769 (1998).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, J. Opt. Soc. Am. B 15, 2255 (1998).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

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

Torner, L.

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 151 (1999).
[CrossRef]

D. Artigas, L. Torner, and N. N. Akhmediev, Opt. Commun. 162, 347 (1999).
[CrossRef]

L. Torner, C. B. Clausen, and M. M. Fejer, Opt. Lett. 23, 903 (1998).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

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

C. R. Menyuk, R. Schiek, and L. Torner, J. Opt. Soc. Am. B 11, 2434 (1994).
[CrossRef]

Torres, J. P.

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 151 (1999).
[CrossRef]

Torruellas, W. E.

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

VanStryland, E. W.

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

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

Opt. Commun. (3)

L. Torner, J. P. Torres, D. Artigas, D. Mihalache, and D. Mazilu, Opt. Commun. 164, 151 (1999).
[CrossRef]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

D. Artigas, L. Torner, and N. N. Akhmediev, Opt. Commun. 162, 347 (1999).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

Phys. Lett. A (1)

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995); L. Torner, Opt. Commun. 114, 136 (1995).
[CrossRef]

Phys. Rev. E (1)

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

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

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Figures (4)

Fig. 1
Fig. 1

Variation of the fraction of the total energy flow carried by the FF and the SH signals as a function of propagation length, for two different mismatch profiles.

Fig. 2
Fig. 2

Analogous to Fig. 1(a) but for shorter profile lengths. (a) L=2, (b) L=1.

Fig. 3
Fig. 3

Detailed evolution in selected cases: (a), (b) I=50, L=2, βL=-5; (c), (d) I=100, L=5, βL=-10. In both cases β0=25 and βξ varies linearly in the range 0<ξ<L and is constant for ξ>L. Only the FF is input with a Gaussian shape.

Fig. 4
Fig. 4

Soliton content with only FF input with a Gaussian shape, as a function of βL, for two different input energy flows: (a) I=50, (b) I=100. β0=25, and L=2. The mismatch varies linearly in the range 0<ξ<L and is constant for ξ>L. Filled circles, with βξ profile; open circles, without βξ profile. Dashed lines, minimum mismatch for the existence of solitons with the value of I.

Equations (9)

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ia1ξ-α122a1s2+a1*a2 exp-iβξξ=0,
ia1ξ-α222a2s2+a12 expiβξξ=0,
L=dsiA1A1ξ*-A1*A1ξ+i2A2A2ξ*-A2*A2ξ-α1A1s2-α22A2s2+βA22-A12A2*-A12*A2,
B=2a1/2a+b/23/2b cosϕ2-2ϕ1,
A2=-B2b3/22a1/2b-2a
dϕ1dξ=a21+4ab,
dϕ2dξ=-β-3b2+2ab4b-8a,
dA2/a1/2dξ=-4A2Bb+2asinϕ2-2ϕ1,
dB2/b1/2dξ=-dA2/a1/2dξ.

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