Abstract

We proposed a new scheme of controlling second-harmonic generation by enhanced Kerr electro-optic nonlinearity. We designed a structure that can implement the cascaded Pockels effect and second-harmonic generation simultaneously. The energy coupling between the fundamental lights of different polarizations led to a large nonlinear phase shift and, thus, an effective electro-optic nonlinear refractive index. The effective nonlinearity can be either positive or negative, causing the second-harmonic spectra to move toward the coupling center, which, in turn, offered us a way to measure the effective electro-optic nonlinear refractive index. The corresponding enhanced Kerr electro-optic nonlinearity is more than three orders of magnitude higher than the intrinsic value. These results open a door to manipulate the nonlinear phase by applying an external electric field instead of light intensity in noncentrosymmetric crystals.

© 2015 Chinese Laser Press

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References

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  1. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), Vol. 8.
  2. R. W. Boyd, Nonlinear Optics (Academic, 2003).
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    [Crossref]
  4. E. C. Stevenson and J. W. Beams, “The electro-optical kerr effect in gases,” Phys. Rev. 38, 133–140 (1931).
    [Crossref]
  5. M. Melnichuk and L. T. Wood, “Direct Kerr electro-optic effect in noncentrosymmetric materials,” Phys. Rev. A 82, 013821 (2010).
    [Crossref]
  6. C. Kolleck, “Cascaded second-order contribution to the third-order nonlinear susceptibility,” Phys. Rev. A 69, 053812 (2004).
    [Crossref]
  7. D. Wang, Y. Zhang, and M. Xiao, “Quantum limits for cascaded optical parametric amplifiers,” Phys. Rev. A 87, 023834 (2013).
    [Crossref]
  8. G. I. Stegeman, D. J. Hagan, and L. Torner, “χ (2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
  9. C. Bosshard, R. Spreiter, M. Zgonik, and P. Günter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74, 2816–2819 (1995).
    [Crossref]
  10. T. Z. Shen, S. H. Hong, and J. K. Song, “Electro-optical switching of graphene oxide liquid crystals with an extremely large kerr coefficient,” Nat. Mater. 13, 394–399 (2014).
  11. R. L. Jin, Y. H. Yu, H. Yang, F. Zhu, Q. D. Chen, M. B. Yi, and H. B. Sun, “Electro-optical detection based on large kerr effect in polymer-stabilized liquid crystals,” Opt. Lett. 37, 842–844 (2012).
    [Crossref]
  12. Y. Hisakado, H. Kikuchi, T. Nagamura, and T. Kajiyama, “Large electro-optic kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17, 96–98 (2005).
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    [Crossref]
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    [Crossref]
  15. 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]
  16. K. Liu, W. J. Lu, Y. P. Chen, and X. F. Chen, “Active control of group velocity by use of folded dielectric axes structures,” Appl. Phys. Lett. 97, 071104 (2010).
    [Crossref]
  17. Y. Shen, T. Watanabe, D. A. Arena, C. C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr, “Nonlinear cross-phase modulation with intense single-cycle terahertz pulses,” Phys. Rev. Lett. 99, 043901 (2007).
    [Crossref]
  18. X. F. Chen, J. H. Shi, Y. P. Chen, Y. M. Zhu, Y. X. Xia, and Y. L. Chen, “Electro-optic solc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28, 2115–2117 (2003).
    [Crossref]
  19. R. DeSalvo, H. Vanherzeele, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, “Self-focusing and self-defocusing by cascaded second-order effects in ktp,” Opt. Lett. 17, 28–30 (1992).
    [Crossref]
  20. M. Luennemann, U. Hartwig, G. Panotopoulos, and K. Buse, “Electrooptic properties of lithium niobate crystals for extremely high external electric fields,” Appl. Phys. B 76, 403–406 (2003).
    [Crossref]
  21. J. Xie, Y. Chen, W. Lu, and X. Chen, “Bidirectionally tunable all-optical switch based on multiple nano-structured resonators using backward quasi-phase-matching,” Chin. Opt. Lett. 9, 041902 (2011).
    [Crossref]
  22. X. P. Hu, P. Xu, and S. N. Zhu, “Engineered quasi-phase-matching for laser techniques invited,” Photon. Res. 1, 171–185 (2013).
  23. Y. P. Chen, R. Wu, X. L. Zeng, Y. X. Xia, and X. F. Chen, “Type i quasi-phase-matched blue second harmonic generation with different polarizations in periodically poled linbo3,” Opt. Laser Technol. 38, 19–22 (2006).
  24. J. F. Zhang, Y. P. Chen, F. Lu, and X. F. Chen, “Flexible wavelength conversion via cascaded second order nonlinearity using broadband shg in mgo-doped ppln,” Opt. Express 16, 6957–6962 (2008).
    [Crossref]
  25. O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for mgo-doped congruent and stoichiometric linbo3,” Appl. Phys. B 91, 343–348 (2008).
    [Crossref]

2014 (1)

T. Z. Shen, S. H. Hong, and J. K. Song, “Electro-optical switching of graphene oxide liquid crystals with an extremely large kerr coefficient,” Nat. Mater. 13, 394–399 (2014).

2013 (2)

D. Wang, Y. Zhang, and M. Xiao, “Quantum limits for cascaded optical parametric amplifiers,” Phys. Rev. A 87, 023834 (2013).
[Crossref]

X. P. Hu, P. Xu, and S. N. Zhu, “Engineered quasi-phase-matching for laser techniques invited,” Photon. Res. 1, 171–185 (2013).

2012 (2)

2011 (1)

2010 (2)

M. Melnichuk and L. T. Wood, “Direct Kerr electro-optic effect in noncentrosymmetric materials,” Phys. Rev. A 82, 013821 (2010).
[Crossref]

K. Liu, W. J. Lu, Y. P. Chen, and X. F. Chen, “Active control of group velocity by use of folded dielectric axes structures,” Appl. Phys. Lett. 97, 071104 (2010).
[Crossref]

2008 (2)

J. F. Zhang, Y. P. Chen, F. Lu, and X. F. Chen, “Flexible wavelength conversion via cascaded second order nonlinearity using broadband shg in mgo-doped ppln,” Opt. Express 16, 6957–6962 (2008).
[Crossref]

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for mgo-doped congruent and stoichiometric linbo3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

2007 (1)

Y. Shen, T. Watanabe, D. A. Arena, C. C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr, “Nonlinear cross-phase modulation with intense single-cycle terahertz pulses,” Phys. Rev. Lett. 99, 043901 (2007).
[Crossref]

2006 (1)

Y. P. Chen, R. Wu, X. L. Zeng, Y. X. Xia, and X. F. Chen, “Type i quasi-phase-matched blue second harmonic generation with different polarizations in periodically poled linbo3,” Opt. Laser Technol. 38, 19–22 (2006).

2005 (1)

Y. Hisakado, H. Kikuchi, T. Nagamura, and T. Kajiyama, “Large electro-optic kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17, 96–98 (2005).

2004 (1)

C. Kolleck, “Cascaded second-order contribution to the third-order nonlinear susceptibility,” Phys. Rev. A 69, 053812 (2004).
[Crossref]

2003 (2)

X. F. Chen, J. H. Shi, Y. P. Chen, Y. M. Zhu, Y. X. Xia, and Y. L. Chen, “Electro-optic solc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28, 2115–2117 (2003).
[Crossref]

M. Luennemann, U. Hartwig, G. Panotopoulos, and K. Buse, “Electrooptic properties of lithium niobate crystals for extremely high external electric fields,” Appl. Phys. B 76, 403–406 (2003).
[Crossref]

2000 (1)

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]

1996 (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ (2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).

1995 (1)

C. Bosshard, R. Spreiter, M. Zgonik, and P. Günter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74, 2816–2819 (1995).
[Crossref]

1992 (1)

1990 (1)

1986 (1)

1931 (1)

E. C. Stevenson and J. W. Beams, “The electro-optical kerr effect in gases,” Phys. Rev. 38, 133–140 (1931).
[Crossref]

Arena, D. A.

Y. Shen, T. Watanabe, D. A. Arena, C. C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr, “Nonlinear cross-phase modulation with intense single-cycle terahertz pulses,” Phys. Rev. Lett. 99, 043901 (2007).
[Crossref]

Arie, A.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for mgo-doped congruent and stoichiometric linbo3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

Beams, J. W.

E. C. Stevenson and J. W. Beams, “The electro-optical kerr effect in gases,” Phys. Rev. 38, 133–140 (1931).
[Crossref]

Bosshard, C.

C. Bosshard, R. Spreiter, M. Zgonik, and P. Günter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74, 2816–2819 (1995).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2003).

Buse, K.

M. Luennemann, U. Hartwig, G. Panotopoulos, and K. Buse, “Electrooptic properties of lithium niobate crystals for extremely high external electric fields,” Appl. Phys. B 76, 403–406 (2003).
[Crossref]

Carr, G. L.

Y. Shen, T. Watanabe, D. A. Arena, C. C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr, “Nonlinear cross-phase modulation with intense single-cycle terahertz pulses,” Phys. Rev. Lett. 99, 043901 (2007).
[Crossref]

Chen, Q. D.

Chen, X.

Chen, X. F.

J. Huo and X. F. Chen, “Large phase shift via polarization-coupling cascading,” Opt. Express 20, 13419–13424 (2012).
[Crossref]

K. Liu, W. J. Lu, Y. P. Chen, and X. F. Chen, “Active control of group velocity by use of folded dielectric axes structures,” Appl. Phys. Lett. 97, 071104 (2010).
[Crossref]

J. F. Zhang, Y. P. Chen, F. Lu, and X. F. Chen, “Flexible wavelength conversion via cascaded second order nonlinearity using broadband shg in mgo-doped ppln,” Opt. Express 16, 6957–6962 (2008).
[Crossref]

Y. P. Chen, R. Wu, X. L. Zeng, Y. X. Xia, and X. F. Chen, “Type i quasi-phase-matched blue second harmonic generation with different polarizations in periodically poled linbo3,” Opt. Laser Technol. 38, 19–22 (2006).

X. F. Chen, J. H. Shi, Y. P. Chen, Y. M. Zhu, Y. X. Xia, and Y. L. Chen, “Electro-optic solc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28, 2115–2117 (2003).
[Crossref]

Chen, Y.

Chen, Y. L.

Chen, Y. P.

K. Liu, W. J. Lu, Y. P. Chen, and X. F. Chen, “Active control of group velocity by use of folded dielectric axes structures,” Appl. Phys. Lett. 97, 071104 (2010).
[Crossref]

J. F. Zhang, Y. P. Chen, F. Lu, and X. F. Chen, “Flexible wavelength conversion via cascaded second order nonlinearity using broadband shg in mgo-doped ppln,” Opt. Express 16, 6957–6962 (2008).
[Crossref]

Y. P. Chen, R. Wu, X. L. Zeng, Y. X. Xia, and X. F. Chen, “Type i quasi-phase-matched blue second harmonic generation with different polarizations in periodically poled linbo3,” Opt. Laser Technol. 38, 19–22 (2006).

X. F. Chen, J. H. Shi, Y. P. Chen, Y. M. Zhu, Y. X. Xia, and Y. L. Chen, “Electro-optic solc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28, 2115–2117 (2003).
[Crossref]

Daino, B.

DeSalvo, R.

Dirk, C. W.

Galun, E.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for mgo-doped congruent and stoichiometric linbo3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

Gayer, O.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for mgo-doped congruent and stoichiometric linbo3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

Gregori, G.

Günter, P.

C. Bosshard, R. Spreiter, M. Zgonik, and P. Günter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74, 2816–2819 (1995).
[Crossref]

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ (2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).

R. DeSalvo, H. Vanherzeele, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, and E. W. Van Stryland, “Self-focusing and self-defocusing by cascaded second-order effects in ktp,” Opt. Lett. 17, 28–30 (1992).
[Crossref]

Hartwig, U.

M. Luennemann, U. Hartwig, G. Panotopoulos, and K. Buse, “Electrooptic properties of lithium niobate crystals for extremely high external electric fields,” Appl. Phys. B 76, 403–406 (2003).
[Crossref]

Hisakado, Y.

Y. Hisakado, H. Kikuchi, T. Nagamura, and T. Kajiyama, “Large electro-optic kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17, 96–98 (2005).

Hong, S. H.

T. Z. Shen, S. H. Hong, and J. K. Song, “Electro-optical switching of graphene oxide liquid crystals with an extremely large kerr coefficient,” Nat. Mater. 13, 394–399 (2014).

Hu, X. P.

Huo, J.

Jin, R. L.

Kajiyama, T.

Y. Hisakado, H. Kikuchi, T. Nagamura, and T. Kajiyama, “Large electro-optic kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17, 96–98 (2005).

Kao, C. C.

Y. Shen, T. Watanabe, D. A. Arena, C. C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr, “Nonlinear cross-phase modulation with intense single-cycle terahertz pulses,” Phys. Rev. Lett. 99, 043901 (2007).
[Crossref]

Kikuchi, H.

Y. Hisakado, H. Kikuchi, T. Nagamura, and T. Kajiyama, “Large electro-optic kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17, 96–98 (2005).

Kolleck, C.

C. Kolleck, “Cascaded second-order contribution to the third-order nonlinear susceptibility,” Phys. Rev. A 69, 053812 (2004).
[Crossref]

Kuzyk, M. G.

Liu, K.

K. Liu, W. J. Lu, Y. P. Chen, and X. F. Chen, “Active control of group velocity by use of folded dielectric axes structures,” Appl. Phys. Lett. 97, 071104 (2010).
[Crossref]

Lu, F.

Lu, W.

Lu, W. J.

K. Liu, W. J. Lu, Y. P. Chen, and X. F. Chen, “Active control of group velocity by use of folded dielectric axes structures,” Appl. Phys. Lett. 97, 071104 (2010).
[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]

Luennemann, M.

M. Luennemann, U. Hartwig, G. Panotopoulos, and K. Buse, “Electrooptic properties of lithium niobate crystals for extremely high external electric fields,” Appl. Phys. B 76, 403–406 (2003).
[Crossref]

Melnichuk, M.

M. Melnichuk and L. T. Wood, “Direct Kerr electro-optic effect in noncentrosymmetric materials,” Phys. Rev. A 82, 013821 (2010).
[Crossref]

Ming, N. B.

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]

Murphy, J. B.

Y. Shen, T. Watanabe, D. A. Arena, C. C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr, “Nonlinear cross-phase modulation with intense single-cycle terahertz pulses,” Phys. Rev. Lett. 99, 043901 (2007).
[Crossref]

Nagamura, T.

Y. Hisakado, H. Kikuchi, T. Nagamura, and T. Kajiyama, “Large electro-optic kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17, 96–98 (2005).

Panotopoulos, G.

M. Luennemann, U. Hartwig, G. Panotopoulos, and K. Buse, “Electrooptic properties of lithium niobate crystals for extremely high external electric fields,” Appl. Phys. B 76, 403–406 (2003).
[Crossref]

Sacks, Z.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for mgo-doped congruent and stoichiometric linbo3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

Sheik-Bahae, M.

Shen, T. Z.

T. Z. Shen, S. H. Hong, and J. K. Song, “Electro-optical switching of graphene oxide liquid crystals with an extremely large kerr coefficient,” Nat. Mater. 13, 394–399 (2014).

Shen, Y.

Y. Shen, T. Watanabe, D. A. Arena, C. C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr, “Nonlinear cross-phase modulation with intense single-cycle terahertz pulses,” Phys. Rev. Lett. 99, 043901 (2007).
[Crossref]

Shi, J. H.

Sohn, J. E.

Song, J. K.

T. Z. Shen, S. H. Hong, and J. K. Song, “Electro-optical switching of graphene oxide liquid crystals with an extremely large kerr coefficient,” Nat. Mater. 13, 394–399 (2014).

Spreiter, R.

C. Bosshard, R. Spreiter, M. Zgonik, and P. Günter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74, 2816–2819 (1995).
[Crossref]

Stegeman, G.

Stegeman, G. I.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ (2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).

Stevenson, E. C.

E. C. Stevenson and J. W. Beams, “The electro-optical kerr effect in gases,” Phys. Rev. 38, 133–140 (1931).
[Crossref]

Sun, H. B.

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ (2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).

Tsang, T. Y.

Y. Shen, T. Watanabe, D. A. Arena, C. C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr, “Nonlinear cross-phase modulation with intense single-cycle terahertz pulses,” Phys. Rev. Lett. 99, 043901 (2007).
[Crossref]

Van Stryland, E. W.

Vanherzeele, H.

Wabnitz, S.

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, D.

D. Wang, Y. Zhang, and M. Xiao, “Quantum limits for cascaded optical parametric amplifiers,” Phys. Rev. A 87, 023834 (2013).
[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, X. J.

Y. Shen, T. Watanabe, D. A. Arena, C. C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr, “Nonlinear cross-phase modulation with intense single-cycle terahertz pulses,” Phys. Rev. Lett. 99, 043901 (2007).
[Crossref]

Watanabe, T.

Y. Shen, T. Watanabe, D. A. Arena, C. C. Kao, J. B. Murphy, T. Y. Tsang, X. J. Wang, and G. L. Carr, “Nonlinear cross-phase modulation with intense single-cycle terahertz pulses,” Phys. Rev. Lett. 99, 043901 (2007).
[Crossref]

Wood, L. T.

M. Melnichuk and L. T. Wood, “Direct Kerr electro-optic effect in noncentrosymmetric materials,” Phys. Rev. A 82, 013821 (2010).
[Crossref]

Wu, R.

Y. P. Chen, R. Wu, X. L. Zeng, Y. X. Xia, and X. F. Chen, “Type i quasi-phase-matched blue second harmonic generation with different polarizations in periodically poled linbo3,” Opt. Laser Technol. 38, 19–22 (2006).

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]

Xia, Y. X.

Y. P. Chen, R. Wu, X. L. Zeng, Y. X. Xia, and X. F. Chen, “Type i quasi-phase-matched blue second harmonic generation with different polarizations in periodically poled linbo3,” Opt. Laser Technol. 38, 19–22 (2006).

X. F. Chen, J. H. Shi, Y. P. Chen, Y. M. Zhu, Y. X. Xia, and Y. L. Chen, “Electro-optic solc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28, 2115–2117 (2003).
[Crossref]

Xiao, M.

D. Wang, Y. Zhang, and M. Xiao, “Quantum limits for cascaded optical parametric amplifiers,” Phys. Rev. A 87, 023834 (2013).
[Crossref]

Xie, J.

Xu, P.

Yang, H.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), Vol. 8.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), Vol. 8.

Yi, M. B.

Yu, Y. H.

Zeng, X. L.

Y. P. Chen, R. Wu, X. L. Zeng, Y. X. Xia, and X. F. Chen, “Type i quasi-phase-matched blue second harmonic generation with different polarizations in periodically poled linbo3,” Opt. Laser Technol. 38, 19–22 (2006).

Zgonik, M.

C. Bosshard, R. Spreiter, M. Zgonik, and P. Günter, “Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect,” Phys. Rev. Lett. 74, 2816–2819 (1995).
[Crossref]

Zhang, J. F.

Zhang, Y.

D. Wang, Y. Zhang, and M. Xiao, “Quantum limits for cascaded optical parametric amplifiers,” Phys. Rev. A 87, 023834 (2013).
[Crossref]

Zhu, F.

Zhu, S. N.

Zhu, Y. M.

Adv. Mater. (1)

Y. Hisakado, H. Kikuchi, T. Nagamura, and T. Kajiyama, “Large electro-optic kerr effect in polymer-stabilized liquid-crystalline blue phases,” Adv. Mater. 17, 96–98 (2005).

Appl. Phys. B (2)

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for mgo-doped congruent and stoichiometric linbo3,” Appl. Phys. B 91, 343–348 (2008).
[Crossref]

M. Luennemann, U. Hartwig, G. Panotopoulos, and K. Buse, “Electrooptic properties of lithium niobate crystals for extremely high external electric fields,” Appl. Phys. B 76, 403–406 (2003).
[Crossref]

Appl. Phys. Lett. (2)

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]

K. Liu, W. J. Lu, Y. P. Chen, and X. F. Chen, “Active control of group velocity by use of folded dielectric axes structures,” Appl. Phys. Lett. 97, 071104 (2010).
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Figures (6)

Fig. 1.
Fig. 1. (a) Rotation of the optical axes under applied y-direction external electric field. (b) Schematic of achieving cascaded linear EO effects and SHG simultaneously in a single PPLN. The periodically inverted optical axes of PPLN lead to the periodic alteration of the sign of electro-optic coefficients (±γij). (c) Illustration of cascaded linear EO effects. (d) Changes of refractive indices caused by linear, Kerr, and cascaded linear EO effects, respectively. (e) Part of etched poling surface of the sample, with domain inversion period of 20.3 μm.
Fig. 2.
Fig. 2. Calculated transmission spectrum and the effective EO nonlinear refractive index as a function of ΔβL. Δβ=0 corresponds to the central wavelength λc of the transmission spectrum.
Fig. 3.
Fig. 3. (a) Measured transmission and SHG spectra fully overlapped at T=26.3°C. SHG spectra with varied external electric fields at (b) 26.3°C; (c) 24.1°C; (d) 27.6°C. The intensity of SHG was modulated by the enhanced Kerr EO nonlinearity.
Fig. 4.
Fig. 4. (a) Index variations caused by the linear and intrinsic Kerr EO effects as a function of the external electric field. (b) Nonlinear refractive index caused by cascaded linear EO effects versus the external electric field for the specific case of λ=1581.9nm (Δn2eff<0) in Fig. 3(c) and λ=1582.6nm (Δn2eff>0) in Fig. 3(d). Points A, B, and C mark the index changes at 0.1 V/μm.
Fig. 5.
Fig. 5. Measured normalized transmission (a) and SHG intensity (b) at two selected wavelengths [1581.8 and 1582.3 nm in Fig. 3(c)] as a function of the external electric fields. At Ey=0.32V/μm, the two wavelengths have the same transmittances but quite different SHG intensities.
Fig. 6.
Fig. 6. Calculated inversion domain periods for achieving SHG (solid) and the cascading effects (dashed) as a function of fundamental wavelengths at different temperatures. Points a, b, and c correspond to the three inversion domain periods we performed in our experiment. Inset figure shows the relationship among the three parameters to realize the cascading process and SHG simultaneously.

Equations (4)

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

nz=neω12s13(neω)3Ey2+12(γ51Eys41Ey2)(neω)3tanθ,
ΔΦeNL=ΔβL2arctan[Δβ2stan(sL)],
Δn2eff2(noωneω)3γ512πλΔβEy2.
Δk=[ne2ω(neω+Δn2eff)]4πλ2πΛ.

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