Abstract

Weak modulation of a quasi-phase-matching (QPM) grating opens possibilities for engineering both the average quadratic nonlinearity and the incoherent average cubic nonlinearity induced by QPM. The relative strength of the average quadratic and effective (intrinsic plus induced) cubic nonlinearity is studied for LiNbO3. We show how the induced average cubic nonlinearity can be engineered to dominate the intrinsic material cubic nonlinearity and how doing so will allow the intensity at which the quadratic and cubic nonlinearities balance and thus compete to be decreased to a few gigawatts per square centimeter.

© 1999 Optical Society of America

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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), p. 375.
  2. M. A. Arbore, O. Marco, and M. M. Fejer, Opt. Lett. 22, 865 (1997). M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, Opt. Lett. 22, 1341 (1997).
    [CrossRef] [PubMed]
  3. L. Torner, C. Balslev Clausen, and M. M. Fejer, Opt. Lett. 23, 903 (1998).
    [CrossRef]
  4. K. Mizuuchi and K. Yamamoto, Opt. Lett. 23, 1880 (1998).
    [CrossRef]
  5. S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, Phys. Rev. Lett. 78, 2752 (1997).
    [CrossRef]
  6. M. Cha, Opt. Lett. 23, 250 (1998).
    [CrossRef]
  7. G. Imeshev, M. Proctor, and M. M. Fejer, Opt. Lett. 23, 673 (1998).
    [CrossRef]
  8. P. E. Powers, T. J. Kulp, and S. E. Bisson, Opt. Lett. 23, 159 (1998).
    [CrossRef]
  9. C. Balslev Clausen and L. Torner, Phys. Rev. Lett. 81, 790 (1998); Opt. Lett. 24, 7 (1999).
    [CrossRef]
  10. C. Balslev Clausen, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
    [CrossRef]
  11. O. Bang, Y. S. Kivshar, A. V. Buryak, A. De Rossi, and S. Trillo, Phys. Rev. E 58, 5057 (1998).
    [CrossRef]
  12. Y. Zhao, G. Town, and M. Sceats, Opt. Commun. 115, 129 (1995); R. Maleck Rassoul, A. Ivanov, E. Freysz, A. Ducasse, and F. Hache, Opt. Lett. 22, 268 (1998).
    [CrossRef]
  13. A. Kobyakov, F. Lederer, O. Bang, and Y. S. Kivshar, Opt. Lett. 23, 506 (1998).
    [CrossRef]
  14. R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
    [CrossRef]
  15. T. J. Alexander, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 23, 670 (1998).
    [CrossRef]

1998 (9)

1997 (3)

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

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, Phys. Rev. Lett. 78, 2752 (1997).
[CrossRef]

M. A. Arbore, O. Marco, and M. M. Fejer, Opt. Lett. 22, 865 (1997). M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, Opt. Lett. 22, 1341 (1997).
[CrossRef] [PubMed]

1996 (1)

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

1995 (1)

Y. Zhao, G. Town, and M. Sceats, Opt. Commun. 115, 129 (1995); R. Maleck Rassoul, A. Ivanov, E. Freysz, A. Ducasse, and F. Hache, Opt. Lett. 22, 268 (1998).
[CrossRef]

Alexander, T. J.

Arbore, M. A.

Balslev Clausen, C.

C. Balslev Clausen and L. Torner, Phys. Rev. Lett. 81, 790 (1998); Opt. Lett. 24, 7 (1999).
[CrossRef]

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

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

Bang, O.

A. Kobyakov, F. Lederer, O. Bang, and Y. S. Kivshar, Opt. Lett. 23, 506 (1998).
[CrossRef]

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

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

Bisson, S. E.

Buryak, A. V.

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]

Cha, M.

De Rossi, A.

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

DeSalvo, R.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

Fejer, M. M.

Ge, C.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, Phys. Rev. Lett. 78, 2752 (1997).
[CrossRef]

Hagan, D. J.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

Imeshev, G.

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]

A. Kobyakov, F. Lederer, O. Bang, and Y. S. Kivshar, Opt. Lett. 23, 506 (1998).
[CrossRef]

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

Kobyakov, A.

Kulp, T. J.

Lederer, F.

Marco, O.

Ming, N.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, Phys. Rev. Lett. 78, 2752 (1997).
[CrossRef]

Mizuuchi, K.

Powers, P. E.

Proctor, M.

Qin, Y.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, Phys. Rev. Lett. 78, 2752 (1997).
[CrossRef]

Said, A. A.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

Sceats, M.

Y. Zhao, G. Town, and M. Sceats, Opt. Commun. 115, 129 (1995); R. Maleck Rassoul, A. Ivanov, E. Freysz, A. Ducasse, and F. Hache, Opt. Lett. 22, 268 (1998).
[CrossRef]

Sheik-Bahae, M.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

Torner, L.

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

C. Balslev Clausen and L. Torner, Phys. Rev. Lett. 81, 790 (1998); Opt. Lett. 24, 7 (1999).
[CrossRef]

Town, G.

Y. Zhao, G. Town, and M. Sceats, Opt. Commun. 115, 129 (1995); R. Maleck Rassoul, A. Ivanov, E. Freysz, A. Ducasse, and F. Hache, Opt. Lett. 22, 268 (1998).
[CrossRef]

Trillo, S.

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

Van Stryland, E. W.

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

Wang, H.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, Phys. Rev. Lett. 78, 2752 (1997).
[CrossRef]

Yamamoto, K.

Zhao, Y.

Y. Zhao, G. Town, and M. Sceats, Opt. Commun. 115, 129 (1995); R. Maleck Rassoul, A. Ivanov, E. Freysz, A. Ducasse, and F. Hache, Opt. Lett. 22, 268 (1998).
[CrossRef]

Zhu, S.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, Phys. Rev. Lett. 78, 2752 (1997).
[CrossRef]

Zhu, Y.

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, Phys. Rev. Lett. 78, 2752 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, IEEE J. Quantum Electron. 32, 1324 (1996).
[CrossRef]

Opt. Commun. (1)

Y. Zhao, G. Town, and M. Sceats, Opt. Commun. 115, 129 (1995); R. Maleck Rassoul, A. Ivanov, E. Freysz, A. Ducasse, and F. Hache, Opt. Lett. 22, 268 (1998).
[CrossRef]

Opt. Lett. (8)

Phys. Rev. E (1)

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

Phys. Rev. Lett. (3)

C. Balslev Clausen and L. Torner, Phys. Rev. Lett. 81, 790 (1998); Opt. Lett. 24, 7 (1999).
[CrossRef]

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

S. Zhu, Y. Zhu, Y. Qin, H. Wang, C. Ge, and N. Ming, Phys. Rev. Lett. 78, 2752 (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), p. 375.

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Figures (4)

Fig. 1
Fig. 1

Modulated QPM grating function Gz (left y axis, dotted line) with the corresponding local domain length Ldz (right y axis, solid line) for L2=10L0=40 µm and 2=1.2.

Fig. 2
Fig. 2

Left, amplitude spectrum of Gz for 2=1.2 and L2=20L0=100 µm. Right, block structure near κ=κ0, showing order m of effective mismatch βm.

Fig. 3
Fig. 3

(a) Normalized average quadratic nonlinearity η1m/η1 and (b) induced average cubic nonlinearity γ2m/γ2 versus modulation parameter 2 for L2=20L0=100 µm. The right-hand ordinate axis shows the actual strength for bulk LiNbO3.

Fig. 4
Fig. 4

(a) Modulation depth Lm and threshold intensity Ith versus L2 for bulk LiNbO3 with 2=1.2 and L0=10 µm. (b) Effective averaged χ2 coefficient deffqpm and Ith versus L2 for bulk LiNbO3 with Lm=1 µm and L0=10 µm.

Equations (9)

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izE1+Gzχ1E1*E2 exp-iΔkz=0,
izE2+Gzχ2E12 expiΔkz=0,
izw˜+η1D+w˜*v˜ exp-iβ0z+γ2w˜2-γ1v˜2w˜=0,
izv˜+η2D-w˜2 expiβ0z-2γ2w˜2v˜=0,
D±z=n d±n expinκ2z, dn=Jn2,
izw+η1mw*v exp-iβmz+γ2mw2-γ1mv2w=0,
izv+η2mw2 expiβmz-2γ2mw2v=0,
ηjm=χj2Jm2/π,
γjm=χ1χjπ2-8/κ0-4Sm2/κ2/π2,

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