Abstract

We show that a variety of quasi-phase-matched structures with engineered patterns can potentially be used for soliton control in quadratic nonlinear media. We study geometries with dislocations, tilts, and wells and predict spatial switching between different output soliton states. Experimental implementation conditions are discussed.

© 1999 Optical Society of America

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References

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  1. M. M. Fejer, in Beam Shaping and Control with Nonlinear Optics, F. Kajzar and R. Reinisch, eds. (Plenum, New York, 1998), pp. 375–406.
  2. L. M. Myers and W. R. Bosenberg, IEEE J. Quantum Electron. 33, 1663 (1997)J. Webjörn, S. Siala, D. W. Nam, R. G. Waarts, and R. J. Lang, IEEE J. Quantum Electron. 33, 1673 (1997).
    [CrossRef]
  3. M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, Opt. Lett. 22, 1341 (1997)G. Imeshev, A. Galvanauskas, D. Harter, M. A. Arbore, M. Proctor, and M. M. Fejer, Opt. Lett. 23, 864 (1998).
    [CrossRef]
  4. G. Imeshev, M. Proctor, and M. M. Fejer, Opt. Lett. 23, 673 (1998).
    [CrossRef]
  5. P. E. Powers, T. J. Kulp, and S. E. Bisson, Opt. Lett. 23, 159 (1998).
    [CrossRef]
  6. L. Torner, C. Balslev Clausen, and M. M. Fejer, Opt. Lett. 23, 903 (1998).
    [CrossRef]
  7. C. Balslev Clausen and L. Torner, Phys. Rev. Lett. 81, 790 (1998).
    [CrossRef]
  8. C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997)L. Torner and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3127 (1997).
    [CrossRef]
  9. A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Lett. A 129, 231 (1988)Phys. Rev. A 39, 1809, 1828 (1989)A. D. Capobianco, C. De Angelis, A. L. Palma, and G. F. Nalesso, J. Opt. Soc. Am. B 14, 1956 (1997).
    [CrossRef]
  10. A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995)L. Torner, Opt. Commun. 114, 136 (1995).
    [CrossRef]
  11. L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
    [CrossRef] [PubMed]
  12. Q. Chen and W. P. Risk, Electron. Lett. 32, 107 (1996)M. Oron, M. Katz, D. Eger, G. Rosenman, and A. Skliar, Electron. Lett. 33, 507 (1997)T. J. Edwards, G. A. Turnbull, M. H. Dunn, M. Ebrahimzadeh, H. Karlsson, G. Arvidsson, and F. Laurell, Opt. Lett. 23, 837 (1998).
    [CrossRef]

1998 (4)

1997 (3)

C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997)L. Torner and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3127 (1997).
[CrossRef]

L. M. Myers and W. R. Bosenberg, IEEE J. Quantum Electron. 33, 1663 (1997)J. Webjörn, S. Siala, D. W. Nam, R. G. Waarts, and R. J. Lang, IEEE J. Quantum Electron. 33, 1673 (1997).
[CrossRef]

M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, Opt. Lett. 22, 1341 (1997)G. Imeshev, A. Galvanauskas, D. Harter, M. A. Arbore, M. Proctor, and M. M. Fejer, Opt. Lett. 23, 864 (1998).
[CrossRef]

1996 (2)

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

Q. Chen and W. P. Risk, Electron. Lett. 32, 107 (1996)M. Oron, M. Katz, D. Eger, G. Rosenman, and A. Skliar, Electron. Lett. 33, 507 (1997)T. J. Edwards, G. A. Turnbull, M. H. Dunn, M. Ebrahimzadeh, H. Karlsson, G. Arvidsson, and F. Laurell, Opt. Lett. 23, 837 (1998).
[CrossRef]

1995 (1)

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

1988 (1)

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Lett. A 129, 231 (1988)Phys. Rev. A 39, 1809, 1828 (1989)A. D. Capobianco, C. De Angelis, A. L. Palma, and G. F. Nalesso, J. Opt. Soc. Am. B 14, 1956 (1997).
[CrossRef]

Aceves, A. B.

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Lett. A 129, 231 (1988)Phys. Rev. A 39, 1809, 1828 (1989)A. D. Capobianco, C. De Angelis, A. L. Palma, and G. F. Nalesso, J. Opt. Soc. Am. B 14, 1956 (1997).
[CrossRef]

Arbore, M. A.

Balslev Clausen, C.

C. Balslev Clausen and L. Torner, Phys. Rev. Lett. 81, 790 (1998).
[CrossRef]

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

C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997)L. Torner and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3127 (1997).
[CrossRef]

Bang, O.

C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997)L. Torner and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3127 (1997).
[CrossRef]

Bisson, S. E.

Bosenberg, W. R.

L. M. Myers and W. R. Bosenberg, IEEE J. Quantum Electron. 33, 1663 (1997)J. Webjörn, S. Siala, D. W. Nam, R. G. Waarts, and R. J. Lang, IEEE J. Quantum Electron. 33, 1673 (1997).
[CrossRef]

Buryak, A. V.

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

Chen, Q.

Q. Chen and W. P. Risk, Electron. Lett. 32, 107 (1996)M. Oron, M. Katz, D. Eger, G. Rosenman, and A. Skliar, Electron. Lett. 33, 507 (1997)T. J. Edwards, G. A. Turnbull, M. H. Dunn, M. Ebrahimzadeh, H. Karlsson, G. Arvidsson, and F. Laurell, Opt. Lett. 23, 837 (1998).
[CrossRef]

Chou, M. H.

Fejer, M. M.

Galvanauskas, A.

Harter, D.

Imeshev, G.

Kivshar, Yu. S.

C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997)L. Torner and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3127 (1997).
[CrossRef]

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

Kulp, T. J.

Mazilu, D.

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

Mihalache, D.

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

Moloney, J. V.

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Lett. A 129, 231 (1988)Phys. Rev. A 39, 1809, 1828 (1989)A. D. Capobianco, C. De Angelis, A. L. Palma, and G. F. Nalesso, J. Opt. Soc. Am. B 14, 1956 (1997).
[CrossRef]

Myers, L. M.

L. M. Myers and W. R. Bosenberg, IEEE J. Quantum Electron. 33, 1663 (1997)J. Webjörn, S. Siala, D. W. Nam, R. G. Waarts, and R. J. Lang, IEEE J. Quantum Electron. 33, 1673 (1997).
[CrossRef]

Newell, A. C.

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Lett. A 129, 231 (1988)Phys. Rev. A 39, 1809, 1828 (1989)A. D. Capobianco, C. De Angelis, A. L. Palma, and G. F. Nalesso, J. Opt. Soc. Am. B 14, 1956 (1997).
[CrossRef]

Powers, P. E.

Proctor, M.

Risk, W. P.

Q. Chen and W. P. Risk, Electron. Lett. 32, 107 (1996)M. Oron, M. Katz, D. Eger, G. Rosenman, and A. Skliar, Electron. Lett. 33, 507 (1997)T. J. Edwards, G. A. Turnbull, M. H. Dunn, M. Ebrahimzadeh, H. Karlsson, G. Arvidsson, and F. Laurell, Opt. Lett. 23, 837 (1998).
[CrossRef]

Torner, L.

C. Balslev Clausen and L. Torner, Phys. Rev. Lett. 81, 790 (1998).
[CrossRef]

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

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

Electron. Lett. (1)

Q. Chen and W. P. Risk, Electron. Lett. 32, 107 (1996)M. Oron, M. Katz, D. Eger, G. Rosenman, and A. Skliar, Electron. Lett. 33, 507 (1997)T. J. Edwards, G. A. Turnbull, M. H. Dunn, M. Ebrahimzadeh, H. Karlsson, G. Arvidsson, and F. Laurell, Opt. Lett. 23, 837 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. M. Myers and W. R. Bosenberg, IEEE J. Quantum Electron. 33, 1663 (1997)J. Webjörn, S. Siala, D. W. Nam, R. G. Waarts, and R. J. Lang, IEEE J. Quantum Electron. 33, 1673 (1997).
[CrossRef]

Opt. Lett. (4)

Phys. Lett. A (2)

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Lett. A 129, 231 (1988)Phys. Rev. A 39, 1809, 1828 (1989)A. D. Capobianco, C. De Angelis, A. L. Palma, and G. F. Nalesso, J. Opt. Soc. Am. B 14, 1956 (1997).
[CrossRef]

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

Phys. Rev. Lett. (3)

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

C. Balslev Clausen and L. Torner, Phys. Rev. Lett. 81, 790 (1998).
[CrossRef]

C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997)L. Torner and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3127 (1997).
[CrossRef]

Other (1)

M. M. Fejer, in Beam Shaping and Control with Nonlinear Optics, F. Kajzar and R. Reinisch, eds. (Plenum, New York, 1998), pp. 375–406.

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Figures (4)

Fig. 1
Fig. 1

Diagram of the three QPM structures: (a) dislocation, (b) tilt, and (c) well configurations.

Fig. 2
Fig. 2

Soliton switching in the dislocation configuration. The curves trace the peaks of the solitons. Δθ=2. (a) β=0. Input power I=40. The numbers indicate input velocity. (b) β=0. The input velocity is 0.9. The numbers indicate input power. (c) β=3. The Gaussian beam input is in the fundamental, and A=9. The numbers indicate input velocity. (d) β=3. The Gaussian beam input is in the fundamental, and the velocity is 0.9. The numbers indicate input amplitude A.

Fig. 3
Fig. 3

Switching in the title configuration. The circles (asterisks) are the results from numerical simulations with β=-3 β=3, and the solid (dashed) lines are corresponding estimates from H (see text). (a) Output velocity versus input soliton power in the tilt configuration. The input velocity is 0.42; Δθ=2. The insets show the FF (solid curves) and the SH (dashed curves) beam amplitudes at ξ=25. (b) Critical velocity at I=30. The dotted line is estimate when δ¯ and Imβ˜ are neglected.

Fig. 4
Fig. 4

Trapping of solitons in the well geometry. The numbers indicate soliton power. The width of the well is 3.0; β=3, v=0.15, and Δθ=4.0. The insets show the FF (solid curves) and the SH (dashed curves) beam amplitudes.

Equations (5)

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d¯z,x=dz-z0x=ndnexpinqz+z0x,
ia1ξ+122a1s2+a1*a2expiθ=0,ia2ξ+142a2s2+βa2+a12exp-iθ=0,
iA1ξ+122A1s2+A1*A2=0,iA2ξ+142A2s2-β˜A2-iδ˜A2sA12=0,
H=12-A1s2+14A2s2+Reβ˜A22+iδ˜2A2*A2s-A2A2*s-A12A2*+A1*2A2ds.
vc2=2IH>β˜,δ˜,v>=0,I-H0.

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