Abstract

We present in this paper a wave coupling theory of linear electro-optic (EO) effect for quasi-phase matched (QPM) of focused Gaussian beam in an optical superlattice (OSL). The numerical results indicate that, due to the EO effect of an appropriate applied electric field, the output beam will form spatially inhomogeneous polarization, changing continuously in transverse section of beam; the confocal parameter has a significant impact on the output polarization of Gaussian beam and determines the half-wave voltage.

© 2010 OSA

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    [CrossRef]
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    [CrossRef]
  38. Y. Kong, X. Chen, and Y. Xia, “Competition of frequency conversion and polarization coupling in periodically poled lithium niobate,” Appl. Phys. B 91(3-4), 479–482 (2008).
    [CrossRef]
  39. H. Tang, L. Chen, G. Zheng, D. Huang, and W. She, “Electrically controlled second harmonic generation of circular polarization in a single LiNbO3 optical superlattice,” Appl. Phys. B 94(4), 661–666 (2009).
    [CrossRef]
  40. Z. Y. Yu, F. Xu, F. Leng, X. S. Qian, X. F. Chen, and Y. Q. Lu, “Acousto-optic tunable second harmonic generation in periodically poled LiNbO3,” Opt. Express 17(14), 11965–11971 (2009).
    [CrossRef] [PubMed]

2010 (6)

2009 (3)

2008 (6)

M. Fridman, G. Machavariani, N. Davidson, and A. A. Friesem, “Fiber lasers generating radially and azimuthally polarized light,” Appl. Phys. Lett. 93(19), 191104 (2008).
[CrossRef]

G. MacHavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially and azimuthally-polarized beams,” Opt. Commun. 281(4), 732–738 (2008).
[CrossRef]

L. X. Chen and W. L. She, “Electro-optically forbidden or enhanced spin-to-orbital angular momentum conversion in a focused light beam,” Opt. Lett. 33(7), 696–698 (2008).
[CrossRef] [PubMed]

C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Perfect quasi-phase matching for the third-harmonic generation using focused Gaussian beams,” Opt. Lett. 33(7), 720–722 (2008).
[CrossRef] [PubMed]

H. Kawauchi, Y. Kozawa, and S. Sato, “Generation of radially polarized Ti:sapphire laser beam using a c-cut crystal,” Opt. Lett. 33(17), 1984–1986 (2008).
[CrossRef] [PubMed]

Y. Kong, X. Chen, and Y. Xia, “Competition of frequency conversion and polarization coupling in periodically poled lithium niobate,” Appl. Phys. B 91(3-4), 479–482 (2008).
[CrossRef]

2007 (2)

2006 (2)

2005 (2)

Y. Kozawa and S. Sato, “Generation of a radially polarized laser beam by use of a conical Brewster prism,” Opt. Lett. 30(22), 3063–3065 (2005).
[CrossRef] [PubMed]

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Cascaded frequency doubling and electro-optic coupling in a single optical superlattice,” Appl. Phys. B 80(6), 741–744 (2005).
[CrossRef]

2003 (3)

2002 (5)

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27(5), 285–287 (2002).
[CrossRef]

A. Ciattoni, G. Cincotti, and C. Palma, “Nonparaxial description of reflection and transmission at the interface between an isotropic medium and a uniaxial crystal,” J. Opt. Soc. Am. A 19(7), 1422–1431 (2002).
[CrossRef]

M. A. A. Neil, F. Massoumian, R. Juskaitis, and T. Wilson, “Method for the generation of arbitrary complex vector wave fronts,” Opt. Lett. 27(21), 1929–1931 (2002).
[CrossRef]

Q. Zhan and J. R. Leger, “Interferometric measurement of Berry’s phase in space-variant polarization manipulations,” Opt. Commun. 213(4-6), 241–245 (2002).
[CrossRef]

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, and F. Kiamilev, “Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,” Appl. Phys. Lett. 81(17), 3140–3142 (2002).
[CrossRef]

2001 (3)

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(8), 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(31), 5638–5642 (2001).
[CrossRef]

W. She and W. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. 195(1-4), 303–311 (2001).
[CrossRef]

2000 (3)

A. Ciattoni, B. Crosignani, and P. Porto, “Optimum beams for efficient frequency mixing in crystals with second order nonlinearity,” Opt. Commun. 177, 9–13 (2000).
[CrossRef]

V. Magni, “Optimum beams for efficient frequency mixing in crystals with second order nonlinearity,” Opt. Commun. 184(1-4), 245–255 (2000).
[CrossRef]

Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[CrossRef]

1997 (1)

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

1992 (1)

M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

1966 (1)

M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22(3), 243–244 (1966).
[CrossRef]

1962 (1)

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Ahmed, M. A.

Armstrong, J.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Aytür, O.

Bahabad, A.

A. Bahabad, M. Murnane, and H. Kapteyn, “Quasi-phase-matching of momentum and energy in nonlinear optical processes,” Nat. Photonics 4(8), 571–575 (2010).
[CrossRef]

Biener, G.

Bloembergen, N.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Bomzon, Z.

Brown, T.

Byer, R.

M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Casson, J. L.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, and F. Kiamilev, “Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,” Appl. Phys. Lett. 81(17), 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(31), 5638–5642 (2001).
[CrossRef]

Chandramani, P.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, and F. Kiamilev, “Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,” Appl. Phys. Lett. 81(17), 3140–3142 (2002).
[CrossRef]

Chen, J.

Chen, L.

H. Tang, L. Chen, G. Zheng, D. Huang, and W. She, “Electrically controlled second harmonic generation of circular polarization in a single LiNbO3 optical superlattice,” Appl. Phys. B 94(4), 661–666 (2009).
[CrossRef]

Chen, L. X.

Chen, X.

Y. Kong, X. Chen, and Y. Xia, “Competition of frequency conversion and polarization coupling in periodically poled lithium niobate,” Appl. Phys. B 91(3-4), 479–482 (2008).
[CrossRef]

X. Chen, J. Shi, Y. Chen, Y. Zhu, Y. Xia, and Y. Chen, “Electro-optic Solc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28(21), 2115–2117 (2003).
[CrossRef] [PubMed]

Chen, X. F.

Chen, Y.

Ciattoni, A.

A. Ciattoni, G. Cincotti, and C. Palma, “Nonparaxial description of reflection and transmission at the interface between an isotropic medium and a uniaxial crystal,” J. Opt. Soc. Am. A 19(7), 1422–1431 (2002).
[CrossRef]

A. Ciattoni, B. Crosignani, and P. Porto, “Optimum beams for efficient frequency mixing in crystals with second order nonlinearity,” Opt. Commun. 177, 9–13 (2000).
[CrossRef]

Cincotti, G.

Crosignani, B.

A. Ciattoni, B. Crosignani, and P. Porto, “Optimum beams for efficient frequency mixing in crystals with second order nonlinearity,” Opt. Commun. 177, 9–13 (2000).
[CrossRef]

Davidson, N.

M. Fridman, M. Nixon, E. Grinvald, N. Davidson, and A. A. Friesem, “Real-time measurement of unique space-variant polarizations,” Opt. Express 18(10), 10805–10812 (2010).
[CrossRef] [PubMed]

M. Fridman, G. Machavariani, N. Davidson, and A. A. Friesem, “Fiber lasers generating radially and azimuthally polarized light,” Appl. Phys. Lett. 93(19), 191104 (2008).
[CrossRef]

Ding, J.

Ducuing, J.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Fan, L.

J. W. Zhao, C. P. Huang, Z. Q. Shen, Y. H. Liu, L. Fan, and Y. Y. Zhu, “Simultaneous harmonic generation and polarization control in an optical superlattice,” Appl. Phys. B 99(4), 673–677 (2010).
[CrossRef]

Fejer, M.

M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Figen, Z. G.

Fridman, M.

M. Fridman, M. Nixon, E. Grinvald, N. Davidson, and A. A. Friesem, “Real-time measurement of unique space-variant polarizations,” Opt. Express 18(10), 10805–10812 (2010).
[CrossRef] [PubMed]

M. Fridman, G. Machavariani, N. Davidson, and A. A. Friesem, “Fiber lasers generating radially and azimuthally polarized light,” Appl. Phys. Lett. 93(19), 191104 (2008).
[CrossRef]

Friesem, A. A.

M. Fridman, M. Nixon, E. Grinvald, N. Davidson, and A. A. Friesem, “Real-time measurement of unique space-variant polarizations,” Opt. Express 18(10), 10805–10812 (2010).
[CrossRef] [PubMed]

M. Fridman, G. Machavariani, N. Davidson, and A. A. Friesem, “Fiber lasers generating radially and azimuthally polarized light,” Appl. Phys. Lett. 93(19), 191104 (2008).
[CrossRef]

Gahagan, K. T.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, and F. Kiamilev, “Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,” Appl. Phys. Lett. 81(17), 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(31), 5638–5642 (2001).
[CrossRef]

Gopalan, V.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, and F. Kiamilev, “Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,” Appl. Phys. Lett. 81(17), 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(31), 5638–5642 (2001).
[CrossRef]

Graf, T.

Grinvald, E.

Guo, C. S.

Hasman, E.

Hobden, M. V.

M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22(3), 243–244 (1966).
[CrossRef]

Huang, C. P.

J. W. Zhao, C. P. Huang, Z. Q. Shen, Y. H. Liu, L. Fan, and Y. Y. Zhu, “Simultaneous harmonic generation and polarization control in an optical superlattice,” Appl. Phys. B 99(4), 673–677 (2010).
[CrossRef]

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Cascaded frequency doubling and electro-optic coupling in a single optical superlattice,” Appl. Phys. B 80(6), 741–744 (2005).
[CrossRef]

Huang, D.

H. Tang, L. Chen, G. Zheng, D. Huang, and W. She, “Electrically controlled second harmonic generation of circular polarization in a single LiNbO3 optical superlattice,” Appl. Phys. B 94(4), 661–666 (2009).
[CrossRef]

Jackel, S.

G. MacHavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially and azimuthally-polarized beams,” Opt. Commun. 281(4), 732–738 (2008).
[CrossRef]

Jundt, D.

M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Juskaitis, R.

Kapteyn, H.

A. Bahabad, M. Murnane, and H. Kapteyn, “Quasi-phase-matching of momentum and energy in nonlinear optical processes,” Nat. Photonics 4(8), 571–575 (2010).
[CrossRef]

Kartaloglu, T.

Kawauchi, H.

Kiamilev, F.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, and F. Kiamilev, “Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,” Appl. Phys. Lett. 81(17), 3140–3142 (2002).
[CrossRef]

Kleiner, V.

Kong, Y.

Y. Kong, X. Chen, and Y. Xia, “Competition of frequency conversion and polarization coupling in periodically poled lithium niobate,” Appl. Phys. B 91(3-4), 479–482 (2008).
[CrossRef]

Kozawa, Y.

Lee, W.

W. She and W. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. 195(1-4), 303–311 (2001).
[CrossRef]

Leger, J. R.

Q. Zhan and J. R. Leger, “Interferometric measurement of Berry’s phase in space-variant polarization manipulations,” Opt. Commun. 213(4-6), 241–245 (2002).
[CrossRef]

Leng, F.

Li, Y.

Liu, Y. H.

J. W. Zhao, C. P. Huang, Z. Q. Shen, Y. H. Liu, L. Fan, and Y. Y. Zhu, “Simultaneous harmonic generation and polarization control in an optical superlattice,” Appl. Phys. B 99(4), 673–677 (2010).
[CrossRef]

Lu, Y.

Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[CrossRef]

Lu, Y. Q.

Z. Y. Yu, F. Xu, F. Leng, X. S. Qian, X. F. Chen, and Y. Q. Lu, “Acousto-optic tunable second harmonic generation in periodically poled LiNbO3,” Opt. Express 17(14), 11965–11971 (2009).
[CrossRef] [PubMed]

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(8), 1035–1037 (2001).
[CrossRef]

Lumer, Y.

G. MacHavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially and azimuthally-polarized beams,” Opt. Commun. 281(4), 732–738 (2008).
[CrossRef]

MacHavariani, G.

G. MacHavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially and azimuthally-polarized beams,” Opt. Commun. 281(4), 732–738 (2008).
[CrossRef]

M. Fridman, G. Machavariani, N. Davidson, and A. A. Friesem, “Fiber lasers generating radially and azimuthally polarized light,” Appl. Phys. Lett. 93(19), 191104 (2008).
[CrossRef]

Magel, G.

M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

Magni, V.

V. Magni, “Optimum beams for efficient frequency mixing in crystals with second order nonlinearity,” Opt. Commun. 184(1-4), 245–255 (2000).
[CrossRef]

Massoumian, F.

Meir, A.

G. MacHavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially and azimuthally-polarized beams,” Opt. Commun. 281(4), 732–738 (2008).
[CrossRef]

Ming, N.

G. Xu, T. Ren, Y. Wang, Y. Zhu, S. Zhu, and N. Ming, “Third-harmonic generation by use of focused Gaussian beams in an optical superlattice,” J. Opt. Soc. Am. B 20(2), 360–365 (2003).
[CrossRef]

Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[CrossRef]

Ming, N. B.

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Moshe, I.

G. MacHavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially and azimuthally-polarized beams,” Opt. Commun. 281(4), 732–738 (2008).
[CrossRef]

Muhammad, F.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, and F. Kiamilev, “Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,” Appl. Phys. Lett. 81(17), 3140–3142 (2002).
[CrossRef]

Murnane, M.

A. Bahabad, M. Murnane, and H. Kapteyn, “Quasi-phase-matching of momentum and energy in nonlinear optical processes,” Nat. Photonics 4(8), 571–575 (2010).
[CrossRef]

Neil, M. A. A.

Ni, W. J.

Nixon, M.

Palma, C.

Pershan, P.

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Porto, P.

A. Ciattoni, B. Crosignani, and P. Porto, “Optimum beams for efficient frequency mixing in crystals with second order nonlinearity,” Opt. Commun. 177, 9–13 (2000).
[CrossRef]

Qian, X. S.

Qin, Y. Q.

Ren, T.

Robinson, J. M.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, and F. Kiamilev, “Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,” Appl. Phys. Lett. 81(17), 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(31), 5638–5642 (2001).
[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(8), 1035–1037 (2001).
[CrossRef]

Sander, R.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, and F. Kiamilev, “Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,” Appl. Phys. Lett. 81(17), 3140–3142 (2002).
[CrossRef]

Sato, S.

Schouten, H. F.

Scrymgeour, D. A.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, and F. Kiamilev, “Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,” Appl. Phys. Lett. 81(17), 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(31), 5638–5642 (2001).
[CrossRef]

Sharan, A.

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, and F. Kiamilev, “Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,” Appl. Phys. Lett. 81(17), 3140–3142 (2002).
[CrossRef]

She, W.

H. Tang, L. Chen, G. Zheng, D. Huang, and W. She, “Electrically controlled second harmonic generation of circular polarization in a single LiNbO3 optical superlattice,” Appl. Phys. B 94(4), 661–666 (2009).
[CrossRef]

W. She and W. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. 195(1-4), 303–311 (2001).
[CrossRef]

She, W. L.

Shen, Z. Q.

J. W. Zhao, C. P. Huang, Z. Q. Shen, Y. H. Liu, L. Fan, and Y. Y. Zhu, “Simultaneous harmonic generation and polarization control in an optical superlattice,” Appl. Phys. B 99(4), 673–677 (2010).
[CrossRef]

Shi, J.

Tang, H.

H. Tang, L. Chen, G. Zheng, D. Huang, and W. She, “Electrically controlled second harmonic generation of circular polarization in a single LiNbO3 optical superlattice,” Appl. Phys. B 94(4), 661–666 (2009).
[CrossRef]

Ubachs, W.

van Dijk, T.

Visser, T. D.

Vogel, M. M.

Voss, A.

Wan, Z.

Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[CrossRef]

Wang, H. C.

Wang, H. T.

Wang, Q.

Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[CrossRef]

Wang, Q. J.

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Cascaded frequency doubling and electro-optic coupling in a single optical superlattice,” Appl. Phys. B 80(6), 741–744 (2005).
[CrossRef]

Wang, X. L.

Wang, Y.

Warner, J.

M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22(3), 243–244 (1966).
[CrossRef]

Wilson, T.

Xi, Y.

Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[CrossRef]

Xia, Y.

Y. Kong, X. Chen, and Y. Xia, “Competition of frequency conversion and polarization coupling in periodically poled lithium niobate,” Appl. Phys. B 91(3-4), 479–482 (2008).
[CrossRef]

X. Chen, J. Shi, Y. Chen, Y. Zhu, Y. Xia, and Y. Chen, “Electro-optic Solc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28(21), 2115–2117 (2003).
[CrossRef] [PubMed]

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(8), 1035–1037 (2001).
[CrossRef]

Xu, F.

Xu, G.

Yonezawa, K.

Yu, Z. Y.

Zhan, Q.

Q. Zhan and J. R. Leger, “Interferometric measurement of Berry’s phase in space-variant polarization manipulations,” Opt. Commun. 213(4-6), 241–245 (2002).
[CrossRef]

Zhan, Q. W.

Zhang, C.

Zhao, J. W.

J. W. Zhao, C. P. Huang, Z. Q. Shen, Y. H. Liu, L. Fan, and Y. Y. Zhu, “Simultaneous harmonic generation and polarization control in an optical superlattice,” Appl. Phys. B 99(4), 673–677 (2010).
[CrossRef]

Zheng, G.

H. Tang, L. Chen, G. Zheng, D. Huang, and W. She, “Electrically controlled second harmonic generation of circular polarization in a single LiNbO3 optical superlattice,” Appl. Phys. B 94(4), 661–666 (2009).
[CrossRef]

Zheng, G. L.

Zhu, S.

Zhu, S. N.

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Zhu, Y.

Zhu, Y. Y.

J. W. Zhao, C. P. Huang, Z. Q. Shen, Y. H. Liu, L. Fan, and Y. Y. Zhu, “Simultaneous harmonic generation and polarization control in an optical superlattice,” Appl. Phys. B 99(4), 673–677 (2010).
[CrossRef]

C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Perfect quasi-phase matching for the third-harmonic generation using focused Gaussian beams,” Opt. Lett. 33(7), 720–722 (2008).
[CrossRef] [PubMed]

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Cascaded frequency doubling and electro-optic coupling in a single optical superlattice,” Appl. Phys. B 80(6), 741–744 (2005).
[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(5339), 843–846 (1997).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. B (4)

J. W. Zhao, C. P. Huang, Z. Q. Shen, Y. H. Liu, L. Fan, and Y. Y. Zhu, “Simultaneous harmonic generation and polarization control in an optical superlattice,” Appl. Phys. B 99(4), 673–677 (2010).
[CrossRef]

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Cascaded frequency doubling and electro-optic coupling in a single optical superlattice,” Appl. Phys. B 80(6), 741–744 (2005).
[CrossRef]

Y. Kong, X. Chen, and Y. Xia, “Competition of frequency conversion and polarization coupling in periodically poled lithium niobate,” Appl. Phys. B 91(3-4), 479–482 (2008).
[CrossRef]

H. Tang, L. Chen, G. Zheng, D. Huang, and W. She, “Electrically controlled second harmonic generation of circular polarization in a single LiNbO3 optical superlattice,” Appl. Phys. B 94(4), 661–666 (2009).
[CrossRef]

Appl. Phys. Lett. (4)

Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77(23), 3719–3721 (2000).
[CrossRef]

D. A. Scrymgeour, A. Sharan, V. Gopalan, K. T. Gahagan, J. L. Casson, R. Sander, J. M. Robinson, F. Muhammad, P. Chandramani, and F. Kiamilev, “Cascaded electro-optic scanning of laser light over large angles using domain microengineered ferroelectrics,” Appl. Phys. Lett. 81(17), 3140–3142 (2002).
[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(8), 1035–1037 (2001).
[CrossRef]

M. Fridman, G. Machavariani, N. Davidson, and A. A. Friesem, “Fiber lasers generating radially and azimuthally polarized light,” Appl. Phys. Lett. 93(19), 191104 (2008).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Nat. Photonics (1)

A. Bahabad, M. Murnane, and H. Kapteyn, “Quasi-phase-matching of momentum and energy in nonlinear optical processes,” Nat. Photonics 4(8), 571–575 (2010).
[CrossRef]

Opt. Commun. (5)

G. MacHavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially and azimuthally-polarized beams,” Opt. Commun. 281(4), 732–738 (2008).
[CrossRef]

W. She and W. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. 195(1-4), 303–311 (2001).
[CrossRef]

A. Ciattoni, B. Crosignani, and P. Porto, “Optimum beams for efficient frequency mixing in crystals with second order nonlinearity,” Opt. Commun. 177, 9–13 (2000).
[CrossRef]

V. Magni, “Optimum beams for efficient frequency mixing in crystals with second order nonlinearity,” Opt. Commun. 184(1-4), 245–255 (2000).
[CrossRef]

Q. Zhan and J. R. Leger, “Interferometric measurement of Berry’s phase in space-variant polarization manipulations,” Opt. Commun. 213(4-6), 241–245 (2002).
[CrossRef]

Opt. Express (6)

Opt. Lett. (10)

M. A. A. Neil, F. Massoumian, R. Juskaitis, and T. Wilson, “Method for the generation of arbitrary complex vector wave fronts,” Opt. Lett. 27(21), 1929–1931 (2002).
[CrossRef]

K. Yonezawa, Y. Kozawa, and S. Sato, “Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO4 crystal,” Opt. Lett. 31(14), 2151–2153 (2006).
[CrossRef] [PubMed]

M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, “Multilayer polarizing grating mirror used for the generation of radial polarization in Yb:YAG thin-disk lasers,” Opt. Lett. 32(22), 3272–3274 (2007).
[CrossRef] [PubMed]

X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007).
[CrossRef] [PubMed]

L. X. Chen and W. L. She, “Electro-optically forbidden or enhanced spin-to-orbital angular momentum conversion in a focused light beam,” Opt. Lett. 33(7), 696–698 (2008).
[CrossRef] [PubMed]

C. Zhang, Y. Q. Qin, and Y. Y. Zhu, “Perfect quasi-phase matching for the third-harmonic generation using focused Gaussian beams,” Opt. Lett. 33(7), 720–722 (2008).
[CrossRef] [PubMed]

H. Kawauchi, Y. Kozawa, and S. Sato, “Generation of radially polarized Ti:sapphire laser beam using a c-cut crystal,” Opt. Lett. 33(17), 1984–1986 (2008).
[CrossRef] [PubMed]

X. Chen, J. Shi, Y. Chen, Y. Zhu, Y. Xia, and Y. Chen, “Electro-optic Solc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28(21), 2115–2117 (2003).
[CrossRef] [PubMed]

Y. Kozawa and S. Sato, “Generation of a radially polarized laser beam by use of a conical Brewster prism,” Opt. Lett. 30(22), 3063–3065 (2005).
[CrossRef] [PubMed]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27(5), 285–287 (2002).
[CrossRef]

Phys. Lett. (1)

M. V. Hobden and J. Warner, “The temperature dependence of the refractive indices of pure lithium niobate,” Phys. Lett. 22(3), 243–244 (1966).
[CrossRef]

Phys. Rev. (1)

J. Armstrong, N. Bloembergen, J. Ducuing, and P. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[CrossRef]

Science (1)

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-Phase-Matched Third-Harmonic Generation in a Quasi-Periodic Optical Superlattice,” Science 278(5339), 843–846 (1997).
[CrossRef]

Other (1)

R. Azzam, and N. Bashara, Ellipsometry and Polarized Light (Amsterdam: North-Holland, 1977).

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Figures (7)

Fig. 1
Fig. 1

The experimental schematic diagram of EO effect for QPM of focused Gaussian beam in an OSL. The arrows indicate the directions of the polarizations of crystal domains. x, y and z stand for three principal axes of the crystal. The applied electric field E 0 is along the y -axis of the OSL. a, b, c are three unite vectors of two independent electromagnetic wave components and applied electric field, respectively.

Fig. 2
Fig. 2

The spatial distribution of polarization of output beam for different E 0 and with λ = 632.8 nm, T = 298 K, L = 2.5 cm, W 0 = 15 µm fixed. (a) E 0 = 0; (b) E 0 = 15 V/mm; (c) E 0 = 30 V/mm; (d) E 0 = 45 V/mm; (e) E 0 = 64 V/mm.

Fig. 3
Fig. 3

Dependence of ψ and e on r for different E 0. (a) ψ on r; (b) e on r. Solid, long dashed, short dashed lines correspond respectively to E 0 = 15, 30, and 45 V/mm for λ = 632.8 nm, T = 298 K, L = 2.5 cm, and W 0 = 15 µm fixed.

Fig. 4
Fig. 4

The spatial distribution of polarization of output beam for different b 1 and with λ = 632.8 nm, T = 298 K, L = 2.5 cm, E 0 = 30 V/mm fixed. (a) b 1 = 5.11 mm; (b) b 1 = 4 × 5.11 mm; (c) b 1 = 16 × 5.11 mm; (d) b 1 = 64 × 5.11 mm.

Fig. 5
Fig. 5

Dependence of ψ and e on r for different b 1. (a) ψ on r; (b) e on r. Thick solid, thin solid, long dashed, short dashed lines correspond respectively to b 1 = 5.11, 4 × 5.11, 16 × 5.11, and 64 × 5.11 mm for λ = 632.8 nm, T = 298 K, and L = 2.5 cm fixed.

Fig. 6
Fig. 6

Dependence of the applied electric field E 0' on the confocal parameter b 1 when the output intensity of o-ray obtains its maximum value for λ = 632.8 nm, T = 298 K, L = 2.5 cm.

Fig. 7
Fig. 7

The output intensity of o-ray |A 1(L)|2 as a function of the confocal parameter b 1 and the applied electric field E 0, for λ = 632.8 nm, T = 298 K, L = 2.5 cm.

Equations (9)

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

E ( r , x , t ) = E ( 0 ) + [ E ( r , x ) exp ( i ω t ) / 2 + c . c . ] ,
E ( r , x ) = E 1 ( r , x ) exp ( i k 1 x ) + E 2 ( r , x ) exp ( i k 2 x ) ,
u j ( r , x ) = 2 π 1 W 0 [ 1 i ( 2 x / b j )] exp { r 2 W 0 2 [ 1 i ( 2 x / b j ) ] } ,
d A 1 ( x ) d x = i d 1 f ( x ) A 2 ( x ) exp ( i Δ k x ) 1 1 + i ( x / b 1 ) ( 1 n 1 / n 2 ) i d 2 f ( x ) A 1 ( x ) ,
d A 2 ( x ) d x = i d 3 f ( x ) A 1 ( x ) exp ( i Δ k x ) 1 1 i ( x / b 1 ) ( 1 n 1 / n 2 ) i d 4 f ( x ) A 2 ( x ) ,
d A 1 ( x ) dx = i d 1 A 2 ( x ) f 1 1 1 + ( x / b 1 ) 2 ( 1 n 1 / n 2 ) 2 i d 2 f ( x ) A 1 ( x ) ,
d A 2 ( x ) dx = i d 3 A 1 ( x ) f 1 1 1 + ( x / b 1 ) 2 ( 1 n 1 / n 2 ) 2 i d 4 f ( x ) A 2 ( x ) ,
tan (2 ψ ) = 2Re (X) 1- | X | 2 ,
sin (2arctan   e ) = 2Im (X) 1 + | X | 2 ,

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