Abstract

We show the principle of operation of a setup to adiabatically shape solitons in quadratic nonlinear media to different beam profiles and widths or different fractions of energy carried by the second-harmonic wave. The shaping mechanism is based on soliton generation and propagation in chirped, quasi-phase-matched samples.

© 1998 Optical Society of America

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Errata

Lluis Torner, Carl Balslev Clausen, and Martin M. Fejer, "Adiabatic shaping of quadratic solitons:?errata," Opt. Lett. 24, 1077-1077 (1999)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-24-15-1077

References

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  1. Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).
  2. For reviews, see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); K. Blow and G. Stegeman, eds., feature on nonlinear guided waves: physics and applications, J. Opt. Soc. Am. B 14, 2950–3260 (1997).
    [CrossRef]
  3. 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); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
    [CrossRef] [PubMed]
  4. C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
    [CrossRef]
  5. C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997); H. He and P. Drummond, Phys. Rev. Lett. 78, 4311 (1997); T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).
    [CrossRef]
  6. P. D. Drummond and H. He, Phys. Rev. A 56, R1107 (1997); M. J. Werner and P. D. Drummond, Phys. Rev. A 56, 1508 (1997).
    [CrossRef]
  7. L. Torner, C. R. Menyuk, and G. I. Stegeman, Opt. Lett. 19, 1615 (1994); Opt. Commun. 114, 136 (1995).
    [CrossRef] [PubMed]
  8. A. V. Buryak and Y. S. Kivshar, Opt. Lett. 19, 1612 (1994); Phys. Lett. A 197, 407 (1995).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  10. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
    [CrossRef]
  11. M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, Opt. Lett. 22, 1341 (1997).
    [CrossRef]
  12. L. Torner and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3127 (1997).
    [CrossRef]
  13. C. B. Clausen, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
    [CrossRef]

1997

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997); H. He and P. Drummond, Phys. Rev. Lett. 78, 4311 (1997); T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).
[CrossRef]

P. D. Drummond and H. He, Phys. Rev. A 56, R1107 (1997); M. J. Werner and P. D. Drummond, Phys. Rev. A 56, 1508 (1997).
[CrossRef]

M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, Opt. Lett. 22, 1341 (1997).
[CrossRef]

L. Torner and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3127 (1997).
[CrossRef]

C. B. Clausen, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

1996

For reviews, see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); K. Blow and G. Stegeman, eds., feature on nonlinear guided waves: physics and applications, J. Opt. Soc. Am. B 14, 2950–3260 (1997).
[CrossRef]

1995

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); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef] [PubMed]

1994

1992

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

1988

1976

Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Arbore, M. A.

Assanto, G.

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997); H. He and P. Drummond, Phys. Rev. Lett. 78, 4311 (1997); T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).
[CrossRef]

Bang, O.

C. B. Clausen, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

Buryak, A. V.

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Chou, M. H.

Clausen, C. B.

C. B. Clausen, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

Conti, C.

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997); H. He and P. Drummond, Phys. Rev. Lett. 78, 4311 (1997); T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).
[CrossRef]

Drummond, P. D.

P. D. Drummond and H. He, Phys. Rev. A 56, R1107 (1997); M. J. Werner and P. D. Drummond, Phys. Rev. A 56, 1508 (1997).
[CrossRef]

Etrich, C.

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

Fejer, M. M.

M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, Opt. Lett. 22, 1341 (1997).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Galvanauskas, A.

Hagan, D. J.

For reviews, see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); K. Blow and G. Stegeman, eds., feature on nonlinear guided waves: physics and applications, J. Opt. Soc. Am. B 14, 2950–3260 (1997).
[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); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef] [PubMed]

Harter, D.

He, H.

P. D. Drummond and H. He, Phys. Rev. A 56, R1107 (1997); M. J. Werner and P. D. Drummond, Phys. Rev. A 56, 1508 (1997).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Karamzin, Yu. N.

Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Kivshar, Y. S.

Kuehl, H. H.

Lederer, F.

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[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); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef] [PubMed]

L. Torner, C. R. Menyuk, and G. I. Stegeman, Opt. Lett. 19, 1615 (1994); Opt. Commun. 114, 136 (1995).
[CrossRef] [PubMed]

Peschel, U.

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

Stegeman, G. I.

L. Torner and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3127 (1997).
[CrossRef]

For reviews, see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); K. Blow and G. Stegeman, eds., feature on nonlinear guided waves: physics and applications, J. Opt. Soc. Am. B 14, 2950–3260 (1997).
[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); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef] [PubMed]

L. Torner, C. R. Menyuk, and G. I. Stegeman, Opt. Lett. 19, 1615 (1994); Opt. Commun. 114, 136 (1995).
[CrossRef] [PubMed]

Sukhorukov, A. P.

Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Torner, L.

L. Torner and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3127 (1997).
[CrossRef]

For reviews, see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); K. Blow and G. Stegeman, eds., feature on nonlinear guided waves: physics and applications, J. Opt. Soc. Am. B 14, 2950–3260 (1997).
[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); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef] [PubMed]

L. Torner, C. R. Menyuk, and G. I. Stegeman, Opt. Lett. 19, 1615 (1994); Opt. Commun. 114, 136 (1995).
[CrossRef] [PubMed]

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); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef] [PubMed]

Trillo, S.

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997); H. He and P. Drummond, Phys. Rev. Lett. 78, 4311 (1997); T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).
[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); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[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); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Opt. Quantum Electron.

For reviews, see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); K. Blow and G. Stegeman, eds., feature on nonlinear guided waves: physics and applications, J. Opt. Soc. Am. B 14, 2950–3260 (1997).
[CrossRef]

Phys. Rev. A

P. D. Drummond and H. He, Phys. Rev. A 56, R1107 (1997); M. J. Werner and P. D. Drummond, Phys. Rev. A 56, 1508 (1997).
[CrossRef]

Phys. Rev. Lett.

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); R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef] [PubMed]

C. Etrich, U. Peschel, and F. Lederer, Phys. Rev. Lett. 79, 2454 (1997).
[CrossRef]

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997); H. He and P. Drummond, Phys. Rev. Lett. 78, 4311 (1997); T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).
[CrossRef]

C. B. Clausen, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

Sov. Phys. JETP

Yu. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

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Figures (4)

Fig. 1
Fig. 1

Variation of the width (FWHM) and the fraction of energy carried by FH and SH beams forming a soliton with a given total energy flow as a function of wave-vector mismatch. Solid curves, I=15; dashed curves, I=30. Only stable solitons are plotted.

Fig. 2
Fig. 2

Evolution of (a) the energy fraction and (b) the beam width of the energy for sample length L=50. A=7, β0=25, and βL=-5. For a nominal QPM period of 20 µm, such values of β correspond to a domain length variation of 1.2 µm over the sample.

Fig. 3
Fig. 3

Same as in Fig.  2 but for L=10. For the experimental conditions discussed in the text, this corresponds to a sample length of 2 cm.

Fig. 4
Fig. 4

Detail of the beam-amplitude profiles for the case L=10. Solid curves, output SH; dashed curves, output FH; dotted curves, input FH. (a) Output of a chirped QPM sample. (b) Output of a sample with constant mismatch β=-5.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

ia1ξ-r22a1+dξa1*a2 exp-iβ0ξ=0,  ia2ξ-α22a2+dξa12 expiβ0ξ=0,
dξ=exp-iν=1Dνξνn=-Cn expinq0ξ,
τξ=τ0β0β0-νDνξν-1.
ia1ξ-r22a1-i2πa1*a2 exp-iβξξ0,  ia2ξ-α22a2+i2πa12 expiβξξ0,

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