Abstract

We propose a method to realize perfect quasi-phase matching (QPM) for nonlinear optical interactions involving Gaussian beams. Using this method, both the wave-vector mismatching and the Gouy phase shift can be compensated. Numerical simulations for the third-harmonic generation show that conversion efficiency near to 100% can be realized even if the fundamental wave is tightly focused, which is difficult or even impossible with the conventional QPM method.

© 2008 Optical Society of America

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References

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  1. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 1992).
  2. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  3. M. M. Fejer, G. A. Mager, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
    [CrossRef]
  4. S. N. Zhu, Y. Y. Zhu, and N. B. Ming, Science 278, 843 (1997).
    [CrossRef]
  5. C. Zhang, Y. Y. Zhu, S. X. Yang, Y. Q. Qin, S. N. Zhu, Y. B. Chen, H. Liu, and N. B. Ming, Opt. Lett. 25, 436 (2000).
    [CrossRef]
  6. G. D. Xu, T. W. Ren, Y. H. Wang, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, J. Opt. Soc. Am. B 20, 360 (2003).
    [CrossRef]
  7. G. D. Xu, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, Opt. Commun. 223, 211 (2003).
    [CrossRef]
  8. R. Ivanov and S. Saltiel, J. Opt. Soc. Am. B 22, 1691 (2005).
    [CrossRef]
  9. M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, and H. Suzuki, Opt. Lett. 28, 558 (2003).
    [CrossRef] [PubMed]
  10. M. Asobe, Y. Nishida, O. Tadanaga, H. Miyazawa, and H. Suzuki, IEEE J. Quantum Electron. 41, 1540 (2005).
    [CrossRef]
  11. T. Kartaloglu, Z. G. Figen, and O. Aytür, J. Opt. Soc. Am. B 20, 343 (2003).
    [CrossRef]

2005 (2)

R. Ivanov and S. Saltiel, J. Opt. Soc. Am. B 22, 1691 (2005).
[CrossRef]

M. Asobe, Y. Nishida, O. Tadanaga, H. Miyazawa, and H. Suzuki, IEEE J. Quantum Electron. 41, 1540 (2005).
[CrossRef]

2003 (4)

2000 (1)

1997 (1)

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, Science 278, 843 (1997).
[CrossRef]

1992 (2)

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

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 1992).

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Asobe, M.

M. Asobe, Y. Nishida, O. Tadanaga, H. Miyazawa, and H. Suzuki, IEEE J. Quantum Electron. 41, 1540 (2005).
[CrossRef]

M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, and H. Suzuki, Opt. Lett. 28, 558 (2003).
[CrossRef] [PubMed]

Aytür, O.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 1992).

Byer, R. L.

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

Chen, Y. B.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Fejer, M. M.

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

Figen, Z. G.

Ivanov, R.

Jundt, D. H.

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

Kartaloglu, T.

Liu, H.

Mager, G. A.

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

Ming, N. B.

Miyazawa, H.

M. Asobe, Y. Nishida, O. Tadanaga, H. Miyazawa, and H. Suzuki, IEEE J. Quantum Electron. 41, 1540 (2005).
[CrossRef]

M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, and H. Suzuki, Opt. Lett. 28, 558 (2003).
[CrossRef] [PubMed]

Nishida, Y.

M. Asobe, Y. Nishida, O. Tadanaga, H. Miyazawa, and H. Suzuki, IEEE J. Quantum Electron. 41, 1540 (2005).
[CrossRef]

M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, and H. Suzuki, Opt. Lett. 28, 558 (2003).
[CrossRef] [PubMed]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Qin, Y. Q.

Ren, T. W.

Saltiel, S.

Suzuki, H.

M. Asobe, Y. Nishida, O. Tadanaga, H. Miyazawa, and H. Suzuki, IEEE J. Quantum Electron. 41, 1540 (2005).
[CrossRef]

M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, and H. Suzuki, Opt. Lett. 28, 558 (2003).
[CrossRef] [PubMed]

Tadanaga, O.

M. Asobe, Y. Nishida, O. Tadanaga, H. Miyazawa, and H. Suzuki, IEEE J. Quantum Electron. 41, 1540 (2005).
[CrossRef]

M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, and H. Suzuki, Opt. Lett. 28, 558 (2003).
[CrossRef] [PubMed]

Wang, Y. H.

Xu, G. D.

Yang, S. X.

Zhang, C.

Zhu, S. N.

Zhu, Y. Y.

IEEE J. Quantum Electron. (2)

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

M. Asobe, Y. Nishida, O. Tadanaga, H. Miyazawa, and H. Suzuki, IEEE J. Quantum Electron. 41, 1540 (2005).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

G. D. Xu, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, Opt. Commun. 223, 211 (2003).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Science (1)

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, Science 278, 843 (1997).
[CrossRef]

Other (1)

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 1992).

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Figures (3)

Fig. 1
Fig. 1

Schematic structure of the perfect QPM structure for interaction of Gaussian beams. The arrows indicate the directions of the spontaneous polarization.

Fig. 2
Fig. 2

Dependence of the conversion efficiency of the THG on the intensity of the fundamental. The solid curve is the result calculated from the 1D coupled equations of Eqs. (2), and the open circles are the results calculated from the 3D nonlinear paraxial equations of Eqs. (1).

Fig. 3
Fig. 3

Field distribution of the harmonic waves in the optical superlattice under the optimum QPM condition. (a) Third-harmonic, (b) second-harmonic, (c) fundamental wave.

Equations (20)

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E 1 x = i 2 k 1 ( 2 E 1 r 2 + 1 r E 1 r ) i ω 1 2 d 33 f ( x ) k 1 c 2 [ E 2 E 1 * exp ( i Δ k 1 x ) + E 3 E 2 * exp ( i Δ k 2 x ) ] ,
E 2 x = i 2 k 2 ( 2 E 2 r 2 + 1 r E 2 r ) i ω 2 2 d 33 f ( x ) k 2 c 2 [ 1 2 E 1 2 exp ( i Δ k 1 x ) + E 3 E 1 * exp ( i Δ k 2 x ) ] ,
E 3 x = i 2 k 3 ( 2 E 3 r 2 + 1 r E 3 r ) i ω 3 2 d 33 f ( x ) k 3 c 2 E 1 E 2 exp ( i Δ k 2 x ) ,
d A 1 d x = i b ( 1 + 2 i b 1 x ) [ K 1 f ( x ) A 2 A 1 * exp ( i Δ k 1 x ) + K 2 f ( x ) A 3 A 2 * exp ( i Δ k 2 x ) ] ,
d A 2 d x = i 2 b ( 1 2 i b 1 x ) K 1 f ( x ) A 1 2 exp ( i Δ k 1 x ) i b ( 1 + 2 i b 1 x ) A 3 A 1 * K 2 f ( x ) exp ( i Δ k 2 x ) ,
d A 3 d x = i b ( 1 2 i b 1 x ) K 2 f ( x ) A 1 A 2 exp ( i Δ k 2 x ) .
E j ( x , r ) = A j ( x ) 2 ω j π n j j W 10 ( 1 2 i b 1 x ) exp ( j 1 2 i b 1 x r 2 W 10 2 ) , j = 1 , 2 , 3 ,
b = k j W 0 j 2 , j = 1 , 2 , 3 ,
K 1 = d 33 ω 1 3 ω 2 π c 3 n 1 n 2 ,
K 2 = 2 d 33 ω 1 2 ω 2 ω 3 3 π c 3 n 2 n 3 ,
f ( x ) = sgn [ Re ( 1 1 2 i b 1 x exp ( i Δ k 1 x ) ) ] ,
sgn ( x ) = { 1 , x 0 1 , x < 0 } .
f ( x ) = sgn [ C 1 Re ( 1 1 2 i b 1 x exp ( i Δ k 1 x ) ) + C 2 Re ( 1 1 2 i b 1 x exp ( i Δ k 2 x ) ) ] ,
d A 1 d x = i b + 4 b 1 x 2 ( K 1 A 2 A 1 * + K 2 A 3 A 2 * ) ,
d A 2 d x = i b + 4 b 1 x 2 ( 1 2 K 1 A 1 2 + K 2 A 3 A 1 * ) ,
d A 3 d x = i b + 4 b 1 x 2 K 2 A 1 A 2 ,
K 1 = K 1 γ ( G 1 ) ,
K 2 = K 2 γ ( G 2 ) ,
γ ( G ) = 1 L 0 L f ( x ) exp [ i G x + θ ( x ) ] d x ,
θ ( x ) = arg ( 1 1 2 i b 1 x ) .

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