Abstract

Starting from Maxwell’s equations and taking the nonlinearity of linear electro-optic effect as a perturbation, we derive general wave coupling equations of quasi-phase-matched (QPM) linear electro-optic effect. And then we use the equations to study the electro-optic effect in PPLN. The numerical results indicate that the QPM condition plays an important role in electro-optic coupling. In addition, the coupling is very sensitive to the temperature and incident light wavelength, but it has a large tolerance to the direction of incident light.

© 2006 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. K. Mizuuchi and K. Yamamoto, "Highly efficient quasi-phase-matched second-harmonic generation using a first-order periodically domain-inverted LiTaO3 waveguide," Appl. Phys. Lett. 60, 1283-1285 (1992).
    [CrossRef]
  3. 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]
  4. D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, "Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains," Appl. Phys. Lett. 37, 607-609 (1980).
    [CrossRef]
  5. 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, 2752-2755 (1997).
    [CrossRef]
  6. G. Z. Luo, S. N. Zhu, J. L. He, Y. Y. Zhu, H. T. Wang, Z. W. Liu, C. Zhang, and N. B. Ming, "Simultaneously efficient blue and red light generations in a periodically poled LiTaO3," Appl. Phys. Lett. 78, 3006-3008 (2001).
    [CrossRef]
  7. K. K. Fradkin, A. Arie, P. Urenski, and G. Rosenman, "Multiple nonlinear optical interactions with arbitrary wave vector differences," Phys. Rev. Lett. 88,023903 (2002).
    [CrossRef]
  8. P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, "Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal," Phys. Rev. Lett. 93,133904 (2004).
    [CrossRef] [PubMed]
  9. A. Chowdhury, H. M. Ng, M. Bhardwaj, and N.G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83,1077-1079 (2003).
    [CrossRef]
  10. Y.Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, "Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications," Appl. Phys. Lett. 77,3719-3721 (2000).
    [CrossRef]
  11. Y. Q. Lu, M. Xiao, and G. J. Salamo, "Wide-bandwidth high frequency electro-optic modulator based on periodically poled LiNbO3," Appl. Phys. Lett. 78,1035-1037 (2001).
    [CrossRef]
  12. K. T. Gahagan, D. A. Scrymgeour, J. L. Casson, V. Gopalan, and J. M. Robinson, "Integrated high-power electro-optic lens and large-angle deflector," Appl. Opt. 40,5638-5642 (2001).
    [CrossRef]
  13. D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, and J. L. Casson, "Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics," Appl. Phys. Lett. 81,3140-3142 (2002).
    [CrossRef]
  14. A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron.QE 9,919-933 (1973).
    [CrossRef]
  15. W. L. She and W. K. Lee, "Wave coupling theory of linear electrooptic effect," Opt. Commun. 195, 303-311 (2001).
    [CrossRef]
  16. D. D. Wu, H. B. Chen, W. L. She, and W. K. Lee, "Wave coupling theory of the linear electro-optic effect in a linear absorbent medium," J. Opt. Soc. Am. B 22, 2366-2371 (2005).
    [CrossRef]
  17. J. F. Nye, Physical properties of crystals (Oxford University Press, Oxford, 1985), Chap. 13.
  18. M. V. Hobden and J. Warner, "The temperature dependence of the refractive indices of pure lithium niobate," Phys. Lett. 22, 243-244 (1966).
    [CrossRef]

2005

2004

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, "Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal," Phys. Rev. Lett. 93,133904 (2004).
[CrossRef] [PubMed]

2003

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N.G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83,1077-1079 (2003).
[CrossRef]

2002

K. K. Fradkin, A. Arie, P. Urenski, and G. Rosenman, "Multiple nonlinear optical interactions with arbitrary wave vector differences," Phys. Rev. Lett. 88,023903 (2002).
[CrossRef]

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, and J. L. Casson, "Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics," Appl. Phys. Lett. 81,3140-3142 (2002).
[CrossRef]

2001

Y. Q. Lu, M. Xiao, and G. J. Salamo, "Wide-bandwidth high frequency electro-optic modulator based on periodically poled LiNbO3," Appl. Phys. Lett. 78,1035-1037 (2001).
[CrossRef]

K. T. Gahagan, D. A. Scrymgeour, J. L. Casson, V. Gopalan, and J. M. Robinson, "Integrated high-power electro-optic lens and large-angle deflector," Appl. Opt. 40,5638-5642 (2001).
[CrossRef]

W. L. She and W. K. Lee, "Wave coupling theory of linear electrooptic effect," Opt. Commun. 195, 303-311 (2001).
[CrossRef]

G. Z. Luo, S. N. Zhu, J. L. He, Y. Y. Zhu, H. T. Wang, Z. W. Liu, C. Zhang, and N. B. Ming, "Simultaneously efficient blue and red light generations in a periodically poled LiTaO3," Appl. Phys. Lett. 78, 3006-3008 (2001).
[CrossRef]

2000

Y.Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, "Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications," Appl. Phys. Lett. 77,3719-3721 (2000).
[CrossRef]

1997

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, 2752-2755 (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]

1992

K. Mizuuchi and K. Yamamoto, "Highly efficient quasi-phase-matched second-harmonic generation using a first-order periodically domain-inverted LiTaO3 waveguide," Appl. Phys. Lett. 60, 1283-1285 (1992).
[CrossRef]

1980

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, "Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains," Appl. Phys. Lett. 37, 607-609 (1980).
[CrossRef]

1973

A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron.QE 9,919-933 (1973).
[CrossRef]

1966

M. V. Hobden and J. Warner, "The temperature dependence of the refractive indices of pure lithium niobate," Phys. Lett. 22, 243-244 (1966).
[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.

K. K. Fradkin, A. Arie, P. Urenski, and G. Rosenman, "Multiple nonlinear optical interactions with arbitrary wave vector differences," Phys. Rev. Lett. 88,023903 (2002).
[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]

Bhardwaj, M.

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N.G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83,1077-1079 (2003).
[CrossRef]

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]

Casson, J. L.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, and J. L. Casson, "Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics," Appl. Phys. Lett. 81,3140-3142 (2002).
[CrossRef]

K. T. Gahagan, D. A. Scrymgeour, J. L. Casson, V. Gopalan, and J. M. Robinson, "Integrated high-power electro-optic lens and large-angle deflector," Appl. Opt. 40,5638-5642 (2001).
[CrossRef]

Chen, H. B.

Chowdhury, A.

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N.G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83,1077-1079 (2003).
[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]

Feng, D.

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, "Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains," Appl. Phys. Lett. 37, 607-609 (1980).
[CrossRef]

Fradkin, K. K.

K. K. Fradkin, A. Arie, P. Urenski, and G. Rosenman, "Multiple nonlinear optical interactions with arbitrary wave vector differences," Phys. Rev. Lett. 88,023903 (2002).
[CrossRef]

Gahagan, K. T.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, and J. L. Casson, "Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics," Appl. Phys. Lett. 81,3140-3142 (2002).
[CrossRef]

K. T. Gahagan, D. A. Scrymgeour, J. L. Casson, V. Gopalan, and J. M. Robinson, "Integrated high-power electro-optic lens and large-angle deflector," Appl. Opt. 40,5638-5642 (2001).
[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, 2752-2755 (1997).
[CrossRef]

Gopalan, V.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, and J. L. Casson, "Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics," Appl. Phys. Lett. 81,3140-3142 (2002).
[CrossRef]

K. T. Gahagan, D. A. Scrymgeour, J. L. Casson, V. Gopalan, and J. M. Robinson, "Integrated high-power electro-optic lens and large-angle deflector," Appl. Opt. 40,5638-5642 (2001).
[CrossRef]

He, J. L.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, "Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal," Phys. Rev. Lett. 93,133904 (2004).
[CrossRef] [PubMed]

G. Z. Luo, S. N. Zhu, J. L. He, Y. Y. Zhu, H. T. Wang, Z. W. Liu, C. Zhang, and N. B. Ming, "Simultaneously efficient blue and red light generations in a periodically poled LiTaO3," Appl. Phys. Lett. 78, 3006-3008 (2001).
[CrossRef]

Hobden, M. V.

M. V. Hobden and J. Warner, "The temperature dependence of the refractive indices of pure lithium niobate," Phys. Lett. 22, 243-244 (1966).
[CrossRef]

Hong, J. F.

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, "Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains," Appl. Phys. Lett. 37, 607-609 (1980).
[CrossRef]

Ji, S. H.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, "Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal," Phys. Rev. Lett. 93,133904 (2004).
[CrossRef] [PubMed]

Lee, W. K.

Liu, Z. W.

G. Z. Luo, S. N. Zhu, J. L. He, Y. Y. Zhu, H. T. Wang, Z. W. Liu, C. Zhang, and N. B. Ming, "Simultaneously efficient blue and red light generations in a periodically poled LiTaO3," Appl. Phys. Lett. 78, 3006-3008 (2001).
[CrossRef]

Lu, Y. Q.

Y. Q. Lu, M. Xiao, and G. J. Salamo, "Wide-bandwidth high frequency electro-optic modulator based on periodically poled LiNbO3," Appl. Phys. Lett. 78,1035-1037 (2001).
[CrossRef]

Lu, Y.Q.

Y.Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, "Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications," Appl. Phys. Lett. 77,3719-3721 (2000).
[CrossRef]

Luo, G. Z.

G. Z. Luo, S. N. Zhu, J. L. He, Y. Y. Zhu, H. T. Wang, Z. W. Liu, C. Zhang, and N. B. Ming, "Simultaneously efficient blue and red light generations in a periodically poled LiTaO3," Appl. Phys. Lett. 78, 3006-3008 (2001).
[CrossRef]

Ming, N. B.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, "Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal," Phys. Rev. Lett. 93,133904 (2004).
[CrossRef] [PubMed]

G. Z. Luo, S. N. Zhu, J. L. He, Y. Y. Zhu, H. T. Wang, Z. W. Liu, C. Zhang, and N. B. Ming, "Simultaneously efficient blue and red light generations in a periodically poled LiTaO3," Appl. Phys. Lett. 78, 3006-3008 (2001).
[CrossRef]

Y.Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, "Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications," Appl. Phys. Lett. 77,3719-3721 (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, 2752-2755 (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]

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, "Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains," Appl. Phys. Lett. 37, 607-609 (1980).
[CrossRef]

Mizuuchi, K.

K. Mizuuchi and K. Yamamoto, "Highly efficient quasi-phase-matched second-harmonic generation using a first-order periodically domain-inverted LiTaO3 waveguide," Appl. Phys. Lett. 60, 1283-1285 (1992).
[CrossRef]

Ng, H. M.

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N.G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83,1077-1079 (2003).
[CrossRef]

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]

Qin, Y. Q.

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, 2752-2755 (1997).
[CrossRef]

Robinson, J. M.

Rosenman, G.

K. K. Fradkin, A. Arie, P. Urenski, and G. Rosenman, "Multiple nonlinear optical interactions with arbitrary wave vector differences," Phys. Rev. Lett. 88,023903 (2002).
[CrossRef]

Salamo, G. J.

Y. Q. Lu, M. Xiao, and G. J. Salamo, "Wide-bandwidth high frequency electro-optic modulator based on periodically poled LiNbO3," Appl. Phys. Lett. 78,1035-1037 (2001).
[CrossRef]

Scrymgeour, D. A.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, and J. L. Casson, "Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics," Appl. Phys. Lett. 81,3140-3142 (2002).
[CrossRef]

K. T. Gahagan, D. A. Scrymgeour, J. L. Casson, V. Gopalan, and J. M. Robinson, "Integrated high-power electro-optic lens and large-angle deflector," Appl. Opt. 40,5638-5642 (2001).
[CrossRef]

Sharan, A.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, and J. L. Casson, "Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics," Appl. Phys. Lett. 81,3140-3142 (2002).
[CrossRef]

She, W. L.

Sun, J.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, "Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal," Phys. Rev. Lett. 93,133904 (2004).
[CrossRef] [PubMed]

Urenski, P.

K. K. Fradkin, A. Arie, P. Urenski, and G. Rosenman, "Multiple nonlinear optical interactions with arbitrary wave vector differences," Phys. Rev. Lett. 88,023903 (2002).
[CrossRef]

Wan, Z. L.

Y.Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, "Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications," Appl. Phys. Lett. 77,3719-3721 (2000).
[CrossRef]

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, 2752-2755 (1997).
[CrossRef]

Wang, H. T.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, "Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal," Phys. Rev. Lett. 93,133904 (2004).
[CrossRef] [PubMed]

G. Z. Luo, S. N. Zhu, J. L. He, Y. Y. Zhu, H. T. Wang, Z. W. Liu, C. Zhang, and N. B. Ming, "Simultaneously efficient blue and red light generations in a periodically poled LiTaO3," Appl. Phys. Lett. 78, 3006-3008 (2001).
[CrossRef]

Wang, Q.

Y.Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, "Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications," Appl. Phys. Lett. 77,3719-3721 (2000).
[CrossRef]

Wang, Y. N.

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, "Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains," Appl. Phys. Lett. 37, 607-609 (1980).
[CrossRef]

Warner, J.

M. V. Hobden and J. Warner, "The temperature dependence of the refractive indices of pure lithium niobate," Phys. Lett. 22, 243-244 (1966).
[CrossRef]

Weimann, N.G.

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N.G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83,1077-1079 (2003).
[CrossRef]

Wu, D. D.

Xi, Y. X.

Y.Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, "Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications," Appl. Phys. Lett. 77,3719-3721 (2000).
[CrossRef]

Xiao, M.

Y. Q. Lu, M. Xiao, and G. J. Salamo, "Wide-bandwidth high frequency electro-optic modulator based on periodically poled LiNbO3," Appl. Phys. Lett. 78,1035-1037 (2001).
[CrossRef]

Xu, P.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, "Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal," Phys. Rev. Lett. 93,133904 (2004).
[CrossRef] [PubMed]

Yamamoto, K.

K. Mizuuchi and K. Yamamoto, "Highly efficient quasi-phase-matched second-harmonic generation using a first-order periodically domain-inverted LiTaO3 waveguide," Appl. Phys. Lett. 60, 1283-1285 (1992).
[CrossRef]

Yang, Y. S.

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, "Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains," Appl. Phys. Lett. 37, 607-609 (1980).
[CrossRef]

Yang, Z.

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, "Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains," Appl. Phys. Lett. 37, 607-609 (1980).
[CrossRef]

Yariv, A.

A. Yariv, "Coupled-mode theory for guided-wave optics," IEEE J. Quantum Electron.QE 9,919-933 (1973).
[CrossRef]

Yu, X. Q.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, "Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal," Phys. Rev. Lett. 93,133904 (2004).
[CrossRef] [PubMed]

Zhang, C.

G. Z. Luo, S. N. Zhu, J. L. He, Y. Y. Zhu, H. T. Wang, Z. W. Liu, C. Zhang, and N. B. Ming, "Simultaneously efficient blue and red light generations in a periodically poled LiTaO3," Appl. Phys. Lett. 78, 3006-3008 (2001).
[CrossRef]

Zhu, J. S.

D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, "Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains," Appl. Phys. Lett. 37, 607-609 (1980).
[CrossRef]

Zhu, S. N.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, "Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal," Phys. Rev. Lett. 93,133904 (2004).
[CrossRef] [PubMed]

G. Z. Luo, S. N. Zhu, J. L. He, Y. Y. Zhu, H. T. Wang, Z. W. Liu, C. Zhang, and N. B. Ming, "Simultaneously efficient blue and red light generations in a periodically poled LiTaO3," Appl. Phys. Lett. 78, 3006-3008 (2001).
[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, 2752-2755 (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]

Zhu, Y. Y.

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, "Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal," Phys. Rev. Lett. 93,133904 (2004).
[CrossRef] [PubMed]

G. Z. Luo, S. N. Zhu, J. L. He, Y. Y. Zhu, H. T. Wang, Z. W. Liu, C. Zhang, and N. B. Ming, "Simultaneously efficient blue and red light generations in a periodically poled LiTaO3," Appl. Phys. Lett. 78, 3006-3008 (2001).
[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, 2752-2755 (1997).
[CrossRef]

Appl. Opt.

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D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, and J. L. Casson, "Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics," Appl. Phys. Lett. 81,3140-3142 (2002).
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K. Mizuuchi and K. Yamamoto, "Highly efficient quasi-phase-matched second-harmonic generation using a first-order periodically domain-inverted LiTaO3 waveguide," Appl. Phys. Lett. 60, 1283-1285 (1992).
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D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, "Enhancement of second-harmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains," Appl. Phys. Lett. 37, 607-609 (1980).
[CrossRef]

G. Z. Luo, S. N. Zhu, J. L. He, Y. Y. Zhu, H. T. Wang, Z. W. Liu, C. Zhang, and N. B. Ming, "Simultaneously efficient blue and red light generations in a periodically poled LiTaO3," Appl. Phys. Lett. 78, 3006-3008 (2001).
[CrossRef]

A. Chowdhury, H. M. Ng, M. Bhardwaj, and N.G. Weimann, "Second-harmonic generation in periodically poled GaN," Appl. Phys. Lett. 83,1077-1079 (2003).
[CrossRef]

Y.Q. Lu, Z. L. Wan, Q. Wang, Y. X. Xi, and N. B. Ming, "Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications," Appl. Phys. Lett. 77,3719-3721 (2000).
[CrossRef]

Y. Q. Lu, M. Xiao, and G. J. Salamo, "Wide-bandwidth high frequency electro-optic modulator based on periodically poled LiNbO3," Appl. Phys. Lett. 78,1035-1037 (2001).
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W. L. She and W. K. Lee, "Wave coupling theory of linear electrooptic effect," Opt. Commun. 195, 303-311 (2001).
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K. K. Fradkin, A. Arie, P. Urenski, and G. Rosenman, "Multiple nonlinear optical interactions with arbitrary wave vector differences," Phys. Rev. Lett. 88,023903 (2002).
[CrossRef]

P. Xu, S. H. Ji, S. N. Zhu, X. Q. Yu, J. Sun, H. T. Wang, J. L. He, Y. Y. Zhu, and N. B. Ming, "Conical second harmonic generation in a two-dimensional χ(2) photonic crystal: a hexagonally poled LiTaO3 crystal," Phys. Rev. Lett. 93,133904 (2004).
[CrossRef] [PubMed]

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, 2752-2755 (1997).
[CrossRef]

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[CrossRef]

Science

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]

Other

J. F. Nye, Physical properties of crystals (Oxford University Press, Oxford, 1985), Chap. 13.

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Figures (4)

Fig. 1.
Fig. 1.

Plots of intensity and phase change of the extraordinary (solid curves) and ordinary waves (dashed curves) when (a, b) the QPM condition is satisfied or not (c, d).

Fig. 2.
Fig. 2.

The effect of the angles (θ and φ) on the output intensity of ordinary wave.

Fig. 3.
Fig. 3.

The effect of (a) the temperature T and (b) the wavelength λ on the output intensities of the extraordinary (solid curves) and ordinary waves (dashed curves).

Fig. 4.
Fig. 4.

Plots of intensity and phase change of the extraordinary (solid curves) and ordinary waves (dashed curves) when (a, b) v1q and v2q are considered; and (c, d) v1q and v2q are neglected.

Equations (22)

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E ( t ) = E ( 0 ) + [ E ω exp ( i ω t ) 2 + c . c . ] ,
E ω = E 1 ω + E 2 ω = E 1 ( r ) exp ( ik 1 r ) + E 2 ( r ) exp ( ik 2 r )
E 1 ( r ) = ω n 1 A 1 ( r ) a , E 2 ( r ) = ω n 2 A 2 ( r ) b , E ( 0 ) = E 0 c ,
dA 1 ( r ) dr = i κ · g ( r ) A 2 ( r ) exp ( i Δ k r ) iv 1 · g ( r ) A 1 ( r )
dA 2 ( r ) dr = i κ · g ( r ) A 1 ( r ) exp ( i Δ k r ) iv 2 · g ( r ) A 2 ( r ) .
κ = k 0 2 n 1 n 2 r eff 1 E 0 , v 1 = k 0 2 n 1 r eff 2 E 0 , v 2 = k 0 2 n 2 r eff 3 E 0 ,
g ( r ) = m = + G m exp ( i α m r ) ,
dA 1 ( r ) dr i κ q A 2 ( r ) exp ( i Δ k r ) iv 1 q A 1 ( r )
dA 2 ( r ) dr i κ q * A 1 ( r ) exp ( i Δ k r ) iv 2 q A 2 ( r ) ,
κ q = κ G m , κ q * = κ G m , v 1 q = v 1 G 0 , v 2 q = v 2 G 0 .
A 1 ( r ) = ρ 1 ( r ) exp [ i β r + i ϕ 1 ( r ) ] ,
A 2 ( r ) = ρ 2 ( r ) exp [ i ( β Δ k ) r + i ϕ 2 ( r ) ] ,
ρ 1 ( r ) = { A 1 2 ( 0 ) cos 2 ( μ r ) + [ γ A 1 ( 0 ) κ q A 2 ( 0 ) μ ] 2 sin 2 ( μ r ) } 1 2 ,
ϕ 1 ( r ) = arg [ A 1 ( 0 ) cos ( μ r ) + i γ A 1 ( 0 ) κ q A 2 ( 0 ) μ sin ( μ r ) ] ,
ρ 2 ( r ) = { A 2 2 ( 0 ) cos 2 ( μ r ) + [ γ A 2 ( 0 ) + κ q * A 1 ( 0 ) μ ] 2 sin 2 ( μ r ) } 1 2 ,
ϕ 2 ( r ) = arg [ A 2 ( 0 ) cos ( μ r ) + i γ A 2 ( 0 ) κ q * A 1 ( 0 ) μ sin ( μ r ) ] ,
μ = 1 2 ( Δ k + v 1 q v 2 q ) 2 + 4 κ q · κ q * ,
γ = 1 2 ( v 2 q v 1 q Δ k ) , β = 1 2 ( Δ k v 1 q v 2 q ) .
g ( r ) = { + 1 if r is in the positive domains 1 if r is in the negative domains ,
G m = { 1 i π m [ 1 cos ( 2 π mD ) + i sin ( 2 π mD ) ] ( m 0 ) 2 D 1 ( m = 0 ) ,
n o 2 = 4.9130 + 1.173 × 10 5 + 1.65 × 10 2 T 2 λ 2 ( 2.12 × 10 2 + 2.7 × 10 5 T 2 ) 2 2.78 × 10 8 λ 2 ,
n e 2 = 4.5567 + 2.605 × 10 7 T 2 + 0.970 × 10 5 + 2.70 × 10 2 T 2 λ 2 ( 2.01 × 10 2 + 5.4 × 10 5 T 2 ) 2 2.24 × 10 8 λ 2 ,

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