Abstract

Coupled-wave equations that are suitable for focused Gaussian beams in an optical superlattice are derived. Solving the coupled equations, we find the optimum condition for efficient third-harmonic generation (THG), in which a negative phase mismatch is needed because of the Gouy effect. The conversion efficiency can be kept at a high level over a wide range of the ratio of the two coupling coefficients. The result is of practical importance for the design of THG devices.

© 2003 Optical Society of America

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918-1939 (1962).
    [CrossRef]
  2. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillator in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102-2113 (1995).
    [CrossRef]
  3. M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasiphase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435-436 (1993).
    [CrossRef]
  4. Q. Chen and W. P. Risk, “Periodic poling of KTiOPO4 using an applied electric field,” Electron. Lett. 30, 1516-1517 (1994).
    [CrossRef]
  5. G. Rosenman, A. Skliar, D. Eger, M. Oron, and M. Katz, “Low temperature periodic electric poling of flux-grown KTiOPO4 and isomorphic crystals,” Appl. Phys. Lett. 73, 3650-3652 (1998).
    [CrossRef]
  6. S. N. Zhu, Y. Y. Zhu, Z. J. Yang, H. F. Wang, Z. Y. Zhang, J. F. Hong, C. Z. Ge, and N. B. Ming, “Second-harmonic generation of blue light in bulk periodically poled LiTaO3,” Appl. Phys. Lett. 67, 320-322 (1995).
    [CrossRef]
  7. H. Karlsson, F. Laurell, P. Henriksson, and G. Arvidsson, “Frequency doubling in periodically poled RbTiOAsO4,” Electron. Lett. 32, 556-557 (1996).
    [CrossRef]
  8. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 12, pp. 521-531.
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    [CrossRef]
  10. G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22, 1834-1836 (1997).
    [CrossRef]
  11. S. Wang, V. Pasiskevicius, F. Laurell, and H. Karlsson, “Ultraviolet generation by first-order frequency doubling in periodically poled KTiOPO4,” Opt. Lett. 23, 1883-1885 (1998).
    [CrossRef]
  12. I. Yokohama, M. Asobe, A. Yokoo, H. Itoh, and T. Kaino, “Quasi-phase-matched parametric interactions in proton-exchanged lithium niobate waveguides,” J. Opt. Soc. Am. B 14, 3197-3203 (1997).
    [CrossRef]
  13. L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33, 1663-1671 (1997).
    [CrossRef]
  14. D. L. Williams, D. P. West, and T. A. King, “Quasi-phase-matched third harmonic generation,” Opt. Commun. 148, 208-214 (1998).
    [CrossRef]
  15. J. Feng, Y. Y. Zhu, and N. B. Ming, “Harmonic generation in an optical Fibonacci superlattice,” Phys. Rev. B 41, 5578-5582 (1990).
    [CrossRef]
  16. Y. Y. Zhu and N. B. Ming, “Second-harmonic generation in a Fibonacci optical superlattice and the dispersive effect of the refractive index.” Phys. Rev. B 42, 3676-3679 (1990).
    [CrossRef]
  17. S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843-846 (1997).
    [CrossRef]
  18. S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752-2759 (1997).
    [CrossRef]
  19. Y. Y. Zhu, R. F. Xiao, J. S. Fu, and G. K. L. Wong, “Third harmonic generation through coupled second-order nonlinear optical parametric processes in quasiperiodically domain-inverted Sr0.6Ba0.4Nb2O6,” Appl. Phys. Lett. 73, 432-434 (1998).
    [CrossRef]
  20. C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and induced Kerr effects in quasi-phase matched quadratic media,” Phys. Rev. Lett. 78, 4749-4752 (1997).
    [CrossRef]
  21. V. Magni, “Optimum beams for efficient frequency mixing in crystal with second order nonlinearity,” Opt. Commun. 184, 245-255 (2000).
    [CrossRef]
  22. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631-2654 (1992).
    [CrossRef]
  23. C. Zhang, Y. Y. Zhu, S. X. Yang, Y. Q. Qin, S. N. Zhu, Y. B. Chen, H. Liu, and N. B. Ming, “Crucial effects of coupling coefficient on quasi-phase-matched harmonic generation in an optical superlattice,” Opt. Lett. 25, 436–438 (2000).
    [CrossRef]
  24. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Chap. 3, pp. 81–89.

2000

1998

G. Rosenman, A. Skliar, D. Eger, M. Oron, and M. Katz, “Low temperature periodic electric poling of flux-grown KTiOPO4 and isomorphic crystals,” Appl. Phys. Lett. 73, 3650-3652 (1998).
[CrossRef]

S. Wang, V. Pasiskevicius, F. Laurell, and H. Karlsson, “Ultraviolet generation by first-order frequency doubling in periodically poled KTiOPO4,” Opt. Lett. 23, 1883-1885 (1998).
[CrossRef]

D. L. Williams, D. P. West, and T. A. King, “Quasi-phase-matched third harmonic generation,” Opt. Commun. 148, 208-214 (1998).
[CrossRef]

Y. Y. Zhu, R. F. Xiao, J. S. Fu, and G. K. L. Wong, “Third harmonic generation through coupled second-order nonlinear optical parametric processes in quasiperiodically domain-inverted Sr0.6Ba0.4Nb2O6,” Appl. Phys. Lett. 73, 432-434 (1998).
[CrossRef]

1997

C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and induced Kerr effects in quasi-phase matched quadratic media,” Phys. Rev. Lett. 78, 4749-4752 (1997).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843-846 (1997).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752-2759 (1997).
[CrossRef]

I. Yokohama, M. Asobe, A. Yokoo, H. Itoh, and T. Kaino, “Quasi-phase-matched parametric interactions in proton-exchanged lithium niobate waveguides,” J. Opt. Soc. Am. B 14, 3197-3203 (1997).
[CrossRef]

L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33, 1663-1671 (1997).
[CrossRef]

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142, 265-268 (1997).
[CrossRef]

G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22, 1834-1836 (1997).
[CrossRef]

1996

H. Karlsson, F. Laurell, P. Henriksson, and G. Arvidsson, “Frequency doubling in periodically poled RbTiOAsO4,” Electron. Lett. 32, 556-557 (1996).
[CrossRef]

1995

S. N. Zhu, Y. Y. Zhu, Z. J. Yang, H. F. Wang, Z. Y. Zhang, J. F. Hong, C. Z. Ge, and N. B. Ming, “Second-harmonic generation of blue light in bulk periodically poled LiTaO3,” Appl. Phys. Lett. 67, 320-322 (1995).
[CrossRef]

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillator in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102-2113 (1995).
[CrossRef]

1994

Q. Chen and W. P. Risk, “Periodic poling of KTiOPO4 using an applied electric field,” Electron. Lett. 30, 1516-1517 (1994).
[CrossRef]

1993

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasiphase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

1992

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

1990

J. Feng, Y. Y. Zhu, and N. B. Ming, “Harmonic generation in an optical Fibonacci superlattice,” Phys. Rev. B 41, 5578-5582 (1990).
[CrossRef]

Y. Y. Zhu and N. B. Ming, “Second-harmonic generation in a Fibonacci optical superlattice and the dispersive effect of the refractive index.” Phys. Rev. B 42, 3676-3679 (1990).
[CrossRef]

1962

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Arie, A.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142, 265-268 (1997).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Arvidsson, G.

H. Karlsson, F. Laurell, P. Henriksson, and G. Arvidsson, “Frequency doubling in periodically poled RbTiOAsO4,” Electron. Lett. 32, 556-557 (1996).
[CrossRef]

Asobe, M.

Bang, O.

C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and induced Kerr effects in quasi-phase matched quadratic media,” Phys. Rev. Lett. 78, 4749-4752 (1997).
[CrossRef]

Batchko, R. G.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Bosenberg, W. R.

L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33, 1663-1671 (1997).
[CrossRef]

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillator in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102-2113 (1995).
[CrossRef]

Byer, R. L.

Chen, Q.

Q. Chen and W. P. Risk, “Periodic poling of KTiOPO4 using an applied electric field,” Electron. Lett. 30, 1516-1517 (1994).
[CrossRef]

Chen, Y. B.

Clausen, C. B.

C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and induced Kerr effects in quasi-phase matched quadratic media,” Phys. Rev. Lett. 78, 4749-4752 (1997).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Eckardt, R. C.

Eger, D.

G. Rosenman, A. Skliar, D. Eger, M. Oron, and M. Katz, “Low temperature periodic electric poling of flux-grown KTiOPO4 and isomorphic crystals,” Appl. Phys. Lett. 73, 3650-3652 (1998).
[CrossRef]

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142, 265-268 (1997).
[CrossRef]

Fejer, M. M.

Feng, J.

J. Feng, Y. Y. Zhu, and N. B. Ming, “Harmonic generation in an optical Fibonacci superlattice,” Phys. Rev. B 41, 5578-5582 (1990).
[CrossRef]

Fu, J. S.

Y. Y. Zhu, R. F. Xiao, J. S. Fu, and G. K. L. Wong, “Third harmonic generation through coupled second-order nonlinear optical parametric processes in quasiperiodically domain-inverted Sr0.6Ba0.4Nb2O6,” Appl. Phys. Lett. 73, 432-434 (1998).
[CrossRef]

Ge, C. Z.

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752-2759 (1997).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, Z. J. Yang, H. F. Wang, Z. Y. Zhang, J. F. Hong, C. Z. Ge, and N. B. Ming, “Second-harmonic generation of blue light in bulk periodically poled LiTaO3,” Appl. Phys. Lett. 67, 320-322 (1995).
[CrossRef]

Henriksson, P.

H. Karlsson, F. Laurell, P. Henriksson, and G. Arvidsson, “Frequency doubling in periodically poled RbTiOAsO4,” Electron. Lett. 32, 556-557 (1996).
[CrossRef]

Hong, J. F.

S. N. Zhu, Y. Y. Zhu, Z. J. Yang, H. F. Wang, Z. Y. Zhang, J. F. Hong, C. Z. Ge, and N. B. Ming, “Second-harmonic generation of blue light in bulk periodically poled LiTaO3,” Appl. Phys. Lett. 67, 320-322 (1995).
[CrossRef]

Itoh, H.

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Kaino, T.

Karlsson, H.

S. Wang, V. Pasiskevicius, F. Laurell, and H. Karlsson, “Ultraviolet generation by first-order frequency doubling in periodically poled KTiOPO4,” Opt. Lett. 23, 1883-1885 (1998).
[CrossRef]

H. Karlsson, F. Laurell, P. Henriksson, and G. Arvidsson, “Frequency doubling in periodically poled RbTiOAsO4,” Electron. Lett. 32, 556-557 (1996).
[CrossRef]

Katz, M.

G. Rosenman, A. Skliar, D. Eger, M. Oron, and M. Katz, “Low temperature periodic electric poling of flux-grown KTiOPO4 and isomorphic crystals,” Appl. Phys. Lett. 73, 3650-3652 (1998).
[CrossRef]

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142, 265-268 (1997).
[CrossRef]

King, T. A.

D. L. Williams, D. P. West, and T. A. King, “Quasi-phase-matched third harmonic generation,” Opt. Commun. 148, 208-214 (1998).
[CrossRef]

Kivshar, Y. S.

C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and induced Kerr effects in quasi-phase matched quadratic media,” Phys. Rev. Lett. 78, 4749-4752 (1997).
[CrossRef]

Laurell, F.

S. Wang, V. Pasiskevicius, F. Laurell, and H. Karlsson, “Ultraviolet generation by first-order frequency doubling in periodically poled KTiOPO4,” Opt. Lett. 23, 1883-1885 (1998).
[CrossRef]

H. Karlsson, F. Laurell, P. Henriksson, and G. Arvidsson, “Frequency doubling in periodically poled RbTiOAsO4,” Electron. Lett. 32, 556-557 (1996).
[CrossRef]

Liu, H.

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631-2654 (1992).
[CrossRef]

Magni, V.

V. Magni, “Optimum beams for efficient frequency mixing in crystal with second order nonlinearity,” Opt. Commun. 184, 245-255 (2000).
[CrossRef]

Mahal, V.

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142, 265-268 (1997).
[CrossRef]

Miller, G. D.

Ming, N. B.

C. Zhang, Y. Y. Zhu, S. X. Yang, Y. Q. Qin, S. N. Zhu, Y. B. Chen, H. Liu, and N. B. Ming, “Crucial effects of coupling coefficient on quasi-phase-matched harmonic generation in an optical superlattice,” Opt. Lett. 25, 436–438 (2000).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752-2759 (1997).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843-846 (1997).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, Z. J. Yang, H. F. Wang, Z. Y. Zhang, J. F. Hong, C. Z. Ge, and N. B. Ming, “Second-harmonic generation of blue light in bulk periodically poled LiTaO3,” Appl. Phys. Lett. 67, 320-322 (1995).
[CrossRef]

J. Feng, Y. Y. Zhu, and N. B. Ming, “Harmonic generation in an optical Fibonacci superlattice,” Phys. Rev. B 41, 5578-5582 (1990).
[CrossRef]

Y. Y. Zhu and N. B. Ming, “Second-harmonic generation in a Fibonacci optical superlattice and the dispersive effect of the refractive index.” Phys. Rev. B 42, 3676-3679 (1990).
[CrossRef]

Myers, L. E.

L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. 33, 1663-1671 (1997).
[CrossRef]

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillator in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102-2113 (1995).
[CrossRef]

Nada, N.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasiphase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

Oron, M.

G. Rosenman, A. Skliar, D. Eger, M. Oron, and M. Katz, “Low temperature periodic electric poling of flux-grown KTiOPO4 and isomorphic crystals,” Appl. Phys. Lett. 73, 3650-3652 (1998).
[CrossRef]

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142, 265-268 (1997).
[CrossRef]

Pasiskevicius, V.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Pierce, J. W.

Qin, Y. Q.

C. Zhang, Y. Y. Zhu, S. X. Yang, Y. Q. Qin, S. N. Zhu, Y. B. Chen, H. Liu, and N. B. Ming, “Crucial effects of coupling coefficient on quasi-phase-matched harmonic generation in an optical superlattice,” Opt. Lett. 25, 436–438 (2000).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752-2759 (1997).
[CrossRef]

Risk, W. P.

Q. Chen and W. P. Risk, “Periodic poling of KTiOPO4 using an applied electric field,” Electron. Lett. 30, 1516-1517 (1994).
[CrossRef]

Rosenman, G.

G. Rosenman, A. Skliar, D. Eger, M. Oron, and M. Katz, “Low temperature periodic electric poling of flux-grown KTiOPO4 and isomorphic crystals,” Appl. Phys. Lett. 73, 3650-3652 (1998).
[CrossRef]

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142, 265-268 (1997).
[CrossRef]

Saitoh, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasiphase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

Skliar, A.

G. Rosenman, A. Skliar, D. Eger, M. Oron, and M. Katz, “Low temperature periodic electric poling of flux-grown KTiOPO4 and isomorphic crystals,” Appl. Phys. Lett. 73, 3650-3652 (1998).
[CrossRef]

A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase matched second harmonic generation in bulk periodically-poled KTiOPO4,” Opt. Commun. 142, 265-268 (1997).
[CrossRef]

Tulloch, W. M.

Wang, H. F.

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752-2759 (1997).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, Z. J. Yang, H. F. Wang, Z. Y. Zhang, J. F. Hong, C. Z. Ge, and N. B. Ming, “Second-harmonic generation of blue light in bulk periodically poled LiTaO3,” Appl. Phys. Lett. 67, 320-322 (1995).
[CrossRef]

Wang, S.

Watanabe, K.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasiphase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

Weise, D. R.

West, D. P.

D. L. Williams, D. P. West, and T. A. King, “Quasi-phase-matched third harmonic generation,” Opt. Commun. 148, 208-214 (1998).
[CrossRef]

Williams, D. L.

D. L. Williams, D. P. West, and T. A. King, “Quasi-phase-matched third harmonic generation,” Opt. Commun. 148, 208-214 (1998).
[CrossRef]

Wong, G. K. L.

Y. Y. Zhu, R. F. Xiao, J. S. Fu, and G. K. L. Wong, “Third harmonic generation through coupled second-order nonlinear optical parametric processes in quasiperiodically domain-inverted Sr0.6Ba0.4Nb2O6,” Appl. Phys. Lett. 73, 432-434 (1998).
[CrossRef]

Xiao, R. F.

Y. Y. Zhu, R. F. Xiao, J. S. Fu, and G. K. L. Wong, “Third harmonic generation through coupled second-order nonlinear optical parametric processes in quasiperiodically domain-inverted Sr0.6Ba0.4Nb2O6,” Appl. Phys. Lett. 73, 432-434 (1998).
[CrossRef]

Yamada, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, “First-order quasiphase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation,” Appl. Phys. Lett. 62, 435-436 (1993).
[CrossRef]

Yang, S. X.

Yang, Z. J.

S. N. Zhu, Y. Y. Zhu, Z. J. Yang, H. F. Wang, Z. Y. Zhang, J. F. Hong, C. Z. Ge, and N. B. Ming, “Second-harmonic generation of blue light in bulk periodically poled LiTaO3,” Appl. Phys. Lett. 67, 320-322 (1995).
[CrossRef]

Yokohama, I.

Yokoo, A.

Zhang, C.

Zhang, Z. Y.

S. N. Zhu, Y. Y. Zhu, Z. J. Yang, H. F. Wang, Z. Y. Zhang, J. F. Hong, C. Z. Ge, and N. B. Ming, “Second-harmonic generation of blue light in bulk periodically poled LiTaO3,” Appl. Phys. Lett. 67, 320-322 (1995).
[CrossRef]

Zhu, S. N.

C. Zhang, Y. Y. Zhu, S. X. Yang, Y. Q. Qin, S. N. Zhu, Y. B. Chen, H. Liu, and N. B. Ming, “Crucial effects of coupling coefficient on quasi-phase-matched harmonic generation in an optical superlattice,” Opt. Lett. 25, 436–438 (2000).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752-2759 (1997).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843-846 (1997).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, Z. J. Yang, H. F. Wang, Z. Y. Zhang, J. F. Hong, C. Z. Ge, and N. B. Ming, “Second-harmonic generation of blue light in bulk periodically poled LiTaO3,” Appl. Phys. Lett. 67, 320-322 (1995).
[CrossRef]

Zhu, Y. Y.

C. Zhang, Y. Y. Zhu, S. X. Yang, Y. Q. Qin, S. N. Zhu, Y. B. Chen, H. Liu, and N. B. Ming, “Crucial effects of coupling coefficient on quasi-phase-matched harmonic generation in an optical superlattice,” Opt. Lett. 25, 436–438 (2000).
[CrossRef]

Y. Y. Zhu, R. F. Xiao, J. S. Fu, and G. K. L. Wong, “Third harmonic generation through coupled second-order nonlinear optical parametric processes in quasiperiodically domain-inverted Sr0.6Ba0.4Nb2O6,” Appl. Phys. Lett. 73, 432-434 (1998).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843-846 (1997).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752-2759 (1997).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, Z. J. Yang, H. F. Wang, Z. Y. Zhang, J. F. Hong, C. Z. Ge, and N. B. Ming, “Second-harmonic generation of blue light in bulk periodically poled LiTaO3,” Appl. Phys. Lett. 67, 320-322 (1995).
[CrossRef]

Y. Y. Zhu and N. B. Ming, “Second-harmonic generation in a Fibonacci optical superlattice and the dispersive effect of the refractive index.” Phys. Rev. B 42, 3676-3679 (1990).
[CrossRef]

J. Feng, Y. Y. Zhu, and N. B. Ming, “Harmonic generation in an optical Fibonacci superlattice,” Phys. Rev. B 41, 5578-5582 (1990).
[CrossRef]

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S. N. Zhu, Y. Y. Zhu, Z. J. Yang, H. F. Wang, Z. Y. Zhang, J. F. Hong, C. Z. Ge, and N. B. Ming, “Second-harmonic generation of blue light in bulk periodically poled LiTaO3,” Appl. Phys. Lett. 67, 320-322 (1995).
[CrossRef]

Y. Y. Zhu, R. F. Xiao, J. S. Fu, and G. K. L. Wong, “Third harmonic generation through coupled second-order nonlinear optical parametric processes in quasiperiodically domain-inverted Sr0.6Ba0.4Nb2O6,” Appl. Phys. Lett. 73, 432-434 (1998).
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J. Feng, Y. Y. Zhu, and N. B. Ming, “Harmonic generation in an optical Fibonacci superlattice,” Phys. Rev. B 41, 5578-5582 (1990).
[CrossRef]

Y. Y. Zhu and N. B. Ming, “Second-harmonic generation in a Fibonacci optical superlattice and the dispersive effect of the refractive index.” Phys. Rev. B 42, 3676-3679 (1990).
[CrossRef]

Phys. Rev. Lett.

S. N. Zhu, Y. Y. Zhu, Y. Q. Qin, H. F. Wang, C. Z. Ge, and N. B. Ming, “Experimental realization of second harmonic generation in a Fibonacci optical superlattice of LiTaO3,” Phys. Rev. Lett. 78, 2752-2759 (1997).
[CrossRef]

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[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Variation of conversion efficiency inside the crystal relative to the distance over which light travels under optimum conditions.

Fig. 2
Fig. 2

Dependence of conversion efficiency on phase mismatch Δk1L for α/β=2.45 and Δk2L=-3.9.

Fig. 3
Fig. 3

Dependence of conversion efficiency on phase mismatch Δk2L for α/β=2.45 and Δk1L=0.

Fig. 4
Fig. 4

Variation of conversion efficiency with α/β for Δk1L=0 and Δk2L=-3.9.

Fig. 5
Fig. 5

Variation of conversion efficiency with α/β for Δk1L=0 and Δk2L=0.

Equations (37)

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εj(r, x, t)=½ Ej(r, x)exp[i(ωjt-kjx)]+c.c.,j=1, 2, 3,
2εj-μ0ε 2εjt2=μ02PjNLt2,
T2E1-2ik1E1x=-2ω12c2 d(x)[E2E1*exp(-iΔk1x)+E3E2*exp(-iΔk2x)],
T2E2-2ik2E2x=-2ω22c2 d(x)12 E12exp(iΔk1x)+E3E1*exp(-iΔk2x),
T2E3-2ik3E3x=-2ω32c2 d(x)E2E1exp(iΔk2x),
Ej(r, x)=Bj(x)uj(r, x),
uj(r, x)=2π1W0j(1-iξ)exp[-r2/W0j2(1-iξ)],
ξ=2xb,
b=kjW0j2,
W012W023W03=W0.
0uj*(r, x)uj(r, x)2πrdr=1.
T2uj-2ikjujx=0.
dB1dx u1=-i ω1n1c d(x)[B2B1*u2u1*exp(-iΔk1x)+B3B2*u3u2*exp(-iΔk2x)],
dB2dx u2=-i ω2n2c d(x)12 B12u12exp(iΔk1x)+B3B1*u3u1*exp(-iΔk2x),
dB3dx u3=-i ω3n3c d(x)B2B1u2u1exp(iΔk2x),
dB1dx=-i ω1n1cπ3/2W0(1+iξ) d(x)B2B1*exp(-iΔk1x)+233 B3B2*exp(-iΔk2x).
dB2dx=-i ω2n2cπ3/2W0 d(x)12B121-iξexp(iΔk1x)+233B3B1*1+iξexp(-iΔk2x),
dB3dx=-i ω3n3cπ3/2W0 d(x) 233B1B21-iξexp(iΔk2x).
d(x)=deffm fmexp(iGmx),m=1, 2, 3,,
fm=2mπsin(mπD)
Gm=2mπΛ,
Aj(x)=njωj Bj(x),
dA1(x)dx=-ib(1+iξ) [αA2A1*exp(-iΔk1x)+βA3A2*exp(-iΔk2x)],
dA2(x)dx=-ib12 α A121-iξexp(iΔk1x)+β A3A1*1+iξexp(-iΔk2x),
dA3(x)dx=-ib(1-iξ) βA1A2exp(iΔk2x),
Δk1=Δk1-Gm=k2-2k1-Gm,
Δk2=Δk2-Gn=k3-k2-k1-Gn,
α=deff fmω13ω2(πc)3n1n21/2,
β=23 deff fn3ω12ω2ω3(πc)3n2n31/2.
|A1|2+ 2|A2|2+3|A3|3=|A01|2,
Pj=½ε0cnj0 EjEj*2πrdr=½ε0cωjAjAj*.
ηj=PjP01=j AjAj*A01A01*,
Δk1=k2-2k1-2πΛ=0,
Δk2=k3-k2-k1-2nπΛ=-1.3(i.e.,-3.9/3),n=1, 3, 5,,
αβ=n2n3n1=2.45(oranyoneof1.453.45),
3n3-2n2(n+1)+n1(2n-1)=-1.3λ12π,
n2n3n1=2.45(oranyoneof1.453.45).

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