Abstract

Based on nonlinear Talbot effect, we propose an acousto-optic tunable second-harmonic (SH) array in a one-dimensional periodically poled LiNbO3 (PPLN) crystal. The SH array is the self-imaging of χ(2) in the PPLN crystal. By applying an acoustic wave, we can tune the period, the distribution, and even the dimension of the array. Such a phenomenon has potential applications in tunable high-resolution Talbot illuminators, beam shapers, and image processing.

© 2012 Optical Society of America

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References

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  1. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).
    [CrossRef]
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    [CrossRef]
  4. P. Xi, C. Zhou, E. Dai, and L. Liu, “Generation of near-field hexagonal array illumination with a phase grating,” Opt. Lett. 27, 228–230 (2002).
    [CrossRef]
  5. C. Canalias and V. Pasiskevicius, “Mirrorless optical parametric oscillator,” Nat. Photonics 1, 459–462 (2007).
    [CrossRef]
  6. H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
    [CrossRef]
  7. Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, “Čerenkov-type second-harmonic generation with fundamental beams of different polarizations,” Opt. Lett. 35, 1317–1319 (2010).
    [CrossRef]
  8. L. H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, “Wavelength tenability of second-harmonic generation from two-dimensional x(2) nonlinear photonic crystals with a tetragonal lattice structure,” Appl. Phys. Lett. 84, 3250–3252 (2004).
    [CrossRef]
  9. M. Paturzo, P. De Natale, S. De Nicola, P. Ferraro, S. Mailis, R. Eason, G. Coppola, M. Iodice, and M. Gioffre, “Tunable two-dimensional hexagonal phase array in domain-engineered Z-cut lithium niobate crystal,” Opt. Lett. 31, 3164–3166(2006).
    [CrossRef]
  10. C. Canalias, V. Pasiskevicius, R. Clemens, and F. Laurell, “Submicron periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 82, 4233–4235 (2003).
    [CrossRef]
  11. Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104, 183901 (2010).
    [CrossRef]
  12. J. Wen, Y. Zhang, S. N. Zhu, and M. Xiao, “Theory of nonlinear Talbot effect,” J. Opt. Soc. Am. B 28, 275–280 (2011).
    [CrossRef]
  13. Z. Chen, D. Liu, Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Fractional second-harmonic Talbot effect,” Opt. Lett. 37, 689–691 (2012).
    [CrossRef]
  14. T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct observation of pinning and bowing of a single ferroelectric domain wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
    [CrossRef]
  15. Y. Y. Zhu, S. N. Zhu, Y. Q. Qin, and N. B. Min, “Further studies on ultrasonic excitation in an acoustic superlattice,” J. Appl. Phys. 79, 2221–2224 (1996).
    [CrossRef]
  16. Y. Y. Zhu and N. B. Min, “Ultrasonic excitation and propagation in an acoustic superlattice,” J. Appl. Phys. 72, 904–914(1992).
    [CrossRef]
  17. Y. Y. Zhu, N. B. Min, W. Jiang, and Y. Shui, “Acoustic superlattice of LiNbO3 crystals and its supplications to bulk-wave transducers for ultrasonic generation and detection up to 800 MHz,” Appl. Phys. Lett. 53, 1381–1383 (1988).
    [CrossRef]
  18. J. H. Cantrell and W. T. Yost, “Ultrasonic velocity,” in Handbook of Acoustics, M. J. Crocker, ed. (Wiley, 1998), pp. 483–494.
  19. A. P. Goutzoulis and V. V. Kludzin, “Principles of acousto-optics’,” in Design and Fabrication of Acousto-Optic Devices, A. P. Goutzoulis and D. R. Pape, eds. (Taylor & Francis, 1994), pp. 1–68.
  20. P. Szwakykowski and K. Patorski, “Properties of the Fresnel field of a double-diffraction system,” J. Opt. 16, 95–103 (1985).
    [CrossRef]

2012 (1)

2011 (2)

J. Wen, Y. Zhang, S. N. Zhu, and M. Xiao, “Theory of nonlinear Talbot effect,” J. Opt. Soc. Am. B 28, 275–280 (2011).
[CrossRef]

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef]

2010 (2)

2007 (2)

2006 (1)

2004 (1)

L. H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, “Wavelength tenability of second-harmonic generation from two-dimensional x(2) nonlinear photonic crystals with a tetragonal lattice structure,” Appl. Phys. Lett. 84, 3250–3252 (2004).
[CrossRef]

2003 (1)

C. Canalias, V. Pasiskevicius, R. Clemens, and F. Laurell, “Submicron periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 82, 4233–4235 (2003).
[CrossRef]

2002 (1)

1999 (1)

T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct observation of pinning and bowing of a single ferroelectric domain wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
[CrossRef]

1996 (1)

Y. Y. Zhu, S. N. Zhu, Y. Q. Qin, and N. B. Min, “Further studies on ultrasonic excitation in an acoustic superlattice,” J. Appl. Phys. 79, 2221–2224 (1996).
[CrossRef]

1995 (1)

1992 (1)

Y. Y. Zhu and N. B. Min, “Ultrasonic excitation and propagation in an acoustic superlattice,” J. Appl. Phys. 72, 904–914(1992).
[CrossRef]

1988 (1)

Y. Y. Zhu, N. B. Min, W. Jiang, and Y. Shui, “Acoustic superlattice of LiNbO3 crystals and its supplications to bulk-wave transducers for ultrasonic generation and detection up to 800 MHz,” Appl. Phys. Lett. 53, 1381–1383 (1988).
[CrossRef]

1985 (1)

P. Szwakykowski and K. Patorski, “Properties of the Fresnel field of a double-diffraction system,” J. Opt. 16, 95–103 (1985).
[CrossRef]

1836 (1)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).
[CrossRef]

Arie, A.

Arrizon, V.

Canalias, C.

C. Canalias and V. Pasiskevicius, “Mirrorless optical parametric oscillator,” Nat. Photonics 1, 459–462 (2007).
[CrossRef]

C. Canalias, V. Pasiskevicius, R. Clemens, and F. Laurell, “Submicron periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 82, 4233–4235 (2003).
[CrossRef]

Cantrell, J. H.

J. H. Cantrell and W. T. Yost, “Ultrasonic velocity,” in Handbook of Acoustics, M. J. Crocker, ed. (Wiley, 1998), pp. 483–494.

Chen, Z.

Clemens, R.

C. Canalias, V. Pasiskevicius, R. Clemens, and F. Laurell, “Submicron periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 82, 4233–4235 (2003).
[CrossRef]

Coppola, G.

Dai, E.

De Natale, P.

De Nicola, S.

Eason, R.

Ferraro, P.

Gioffre, M.

Gong, Y. X.

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef]

Gopalan, V.

T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct observation of pinning and bowing of a single ferroelectric domain wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
[CrossRef]

Goutzoulis, A. P.

A. P. Goutzoulis and V. V. Kludzin, “Principles of acousto-optics’,” in Design and Fabrication of Acousto-Optic Devices, A. P. Goutzoulis and D. R. Pape, eds. (Taylor & Francis, 1994), pp. 1–68.

Guo, C. S.

Hong, Z. P.

Hsu, C. C.

L. H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, “Wavelength tenability of second-harmonic generation from two-dimensional x(2) nonlinear photonic crystals with a tetragonal lattice structure,” Appl. Phys. Lett. 84, 3250–3252 (2004).
[CrossRef]

Iodice, M.

Jiang, W.

Y. Y. Zhu, N. B. Min, W. Jiang, and Y. Shui, “Acoustic superlattice of LiNbO3 crystals and its supplications to bulk-wave transducers for ultrasonic generation and detection up to 800 MHz,” Appl. Phys. Lett. 53, 1381–1383 (1988).
[CrossRef]

Jin, H.

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef]

Kivshar, Y. S.

Kludzin, V. V.

A. P. Goutzoulis and V. V. Kludzin, “Principles of acousto-optics’,” in Design and Fabrication of Acousto-Optic Devices, A. P. Goutzoulis and D. R. Pape, eds. (Taylor & Francis, 1994), pp. 1–68.

Koynov, K.

Krolikowski, W.

Kung, A. H.

L. H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, “Wavelength tenability of second-harmonic generation from two-dimensional x(2) nonlinear photonic crystals with a tetragonal lattice structure,” Appl. Phys. Lett. 84, 3250–3252 (2004).
[CrossRef]

Laurell, F.

C. Canalias, V. Pasiskevicius, R. Clemens, and F. Laurell, “Submicron periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 82, 4233–4235 (2003).
[CrossRef]

Leng, H. Y.

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef]

Liu, D.

Liu, L.

Mailis, S.

Min, N. B.

Y. Y. Zhu, S. N. Zhu, Y. Q. Qin, and N. B. Min, “Further studies on ultrasonic excitation in an acoustic superlattice,” J. Appl. Phys. 79, 2221–2224 (1996).
[CrossRef]

Y. Y. Zhu and N. B. Min, “Ultrasonic excitation and propagation in an acoustic superlattice,” J. Appl. Phys. 72, 904–914(1992).
[CrossRef]

Y. Y. Zhu, N. B. Min, W. Jiang, and Y. Shui, “Acoustic superlattice of LiNbO3 crystals and its supplications to bulk-wave transducers for ultrasonic generation and detection up to 800 MHz,” Appl. Phys. Lett. 53, 1381–1383 (1988).
[CrossRef]

Mohideen, U.

T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct observation of pinning and bowing of a single ferroelectric domain wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
[CrossRef]

Ng, J.

L. H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, “Wavelength tenability of second-harmonic generation from two-dimensional x(2) nonlinear photonic crystals with a tetragonal lattice structure,” Appl. Phys. Lett. 84, 3250–3252 (2004).
[CrossRef]

Ojeda-Castaneda, J.

Pasiskevicius, V.

C. Canalias and V. Pasiskevicius, “Mirrorless optical parametric oscillator,” Nat. Photonics 1, 459–462 (2007).
[CrossRef]

C. Canalias, V. Pasiskevicius, R. Clemens, and F. Laurell, “Submicron periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 82, 4233–4235 (2003).
[CrossRef]

Patorski, K.

P. Szwakykowski and K. Patorski, “Properties of the Fresnel field of a double-diffraction system,” J. Opt. 16, 95–103 (1985).
[CrossRef]

Paturzo, M.

Peng, L. H.

L. H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, “Wavelength tenability of second-harmonic generation from two-dimensional x(2) nonlinear photonic crystals with a tetragonal lattice structure,” Appl. Phys. Lett. 84, 3250–3252 (2004).
[CrossRef]

Qin, Y. Q.

Y. Y. Zhu, S. N. Zhu, Y. Q. Qin, and N. B. Min, “Further studies on ultrasonic excitation in an acoustic superlattice,” J. Appl. Phys. 79, 2221–2224 (1996).
[CrossRef]

Saltiel, S. M.

Sheng, Y.

Shui, Y.

Y. Y. Zhu, N. B. Min, W. Jiang, and Y. Shui, “Acoustic superlattice of LiNbO3 crystals and its supplications to bulk-wave transducers for ultrasonic generation and detection up to 800 MHz,” Appl. Phys. Lett. 53, 1381–1383 (1988).
[CrossRef]

Swart, P. J.

T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct observation of pinning and bowing of a single ferroelectric domain wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
[CrossRef]

Szwakykowski, P.

P. Szwakykowski and K. Patorski, “Properties of the Fresnel field of a double-diffraction system,” J. Opt. 16, 95–103 (1985).
[CrossRef]

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).
[CrossRef]

Wen, J.

Xi, P.

Xiao, M.

Xie, Z. D.

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef]

Xu, P.

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef]

Yang, T. J.

T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct observation of pinning and bowing of a single ferroelectric domain wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
[CrossRef]

Yin, X.

Yost, W. T.

J. H. Cantrell and W. T. Yost, “Ultrasonic velocity,” in Handbook of Acoustics, M. J. Crocker, ed. (Wiley, 1998), pp. 483–494.

Yu, X. Q.

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef]

Zhang, C.

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef]

Zhang, Y.

Zhou, C.

Zhu, L. W.

Zhu, S. N.

Z. Chen, D. Liu, Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Fractional second-harmonic Talbot effect,” Opt. Lett. 37, 689–691 (2012).
[CrossRef]

J. Wen, Y. Zhang, S. N. Zhu, and M. Xiao, “Theory of nonlinear Talbot effect,” J. Opt. Soc. Am. B 28, 275–280 (2011).
[CrossRef]

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef]

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104, 183901 (2010).
[CrossRef]

Y. Y. Zhu, S. N. Zhu, Y. Q. Qin, and N. B. Min, “Further studies on ultrasonic excitation in an acoustic superlattice,” J. Appl. Phys. 79, 2221–2224 (1996).
[CrossRef]

Zhu, Y. Y.

Y. Y. Zhu, S. N. Zhu, Y. Q. Qin, and N. B. Min, “Further studies on ultrasonic excitation in an acoustic superlattice,” J. Appl. Phys. 79, 2221–2224 (1996).
[CrossRef]

Y. Y. Zhu and N. B. Min, “Ultrasonic excitation and propagation in an acoustic superlattice,” J. Appl. Phys. 72, 904–914(1992).
[CrossRef]

Y. Y. Zhu, N. B. Min, W. Jiang, and Y. Shui, “Acoustic superlattice of LiNbO3 crystals and its supplications to bulk-wave transducers for ultrasonic generation and detection up to 800 MHz,” Appl. Phys. Lett. 53, 1381–1383 (1988).
[CrossRef]

Appl. Phys. Lett. (3)

L. H. Peng, C. C. Hsu, J. Ng, and A. H. Kung, “Wavelength tenability of second-harmonic generation from two-dimensional x(2) nonlinear photonic crystals with a tetragonal lattice structure,” Appl. Phys. Lett. 84, 3250–3252 (2004).
[CrossRef]

C. Canalias, V. Pasiskevicius, R. Clemens, and F. Laurell, “Submicron periodically poled flux-grown KTiOPO4,” Appl. Phys. Lett. 82, 4233–4235 (2003).
[CrossRef]

Y. Y. Zhu, N. B. Min, W. Jiang, and Y. Shui, “Acoustic superlattice of LiNbO3 crystals and its supplications to bulk-wave transducers for ultrasonic generation and detection up to 800 MHz,” Appl. Phys. Lett. 53, 1381–1383 (1988).
[CrossRef]

J. Appl. Phys. (2)

Y. Y. Zhu, S. N. Zhu, Y. Q. Qin, and N. B. Min, “Further studies on ultrasonic excitation in an acoustic superlattice,” J. Appl. Phys. 79, 2221–2224 (1996).
[CrossRef]

Y. Y. Zhu and N. B. Min, “Ultrasonic excitation and propagation in an acoustic superlattice,” J. Appl. Phys. 72, 904–914(1992).
[CrossRef]

J. Opt. (1)

P. Szwakykowski and K. Patorski, “Properties of the Fresnel field of a double-diffraction system,” J. Opt. 16, 95–103 (1985).
[CrossRef]

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

Nat. Commun. (1)

H. Y. Leng, X. Q. Yu, Y. X. Gong, P. Xu, Z. D. Xie, H. Jin, C. Zhang, and S. N. Zhu, “On-chip steering of entangled photons in nonlinear photonic crystals,” Nat. Commun. 2, 429 (2011).
[CrossRef]

Nat. Photonics (1)

C. Canalias and V. Pasiskevicius, “Mirrorless optical parametric oscillator,” Nat. Photonics 1, 459–462 (2007).
[CrossRef]

Opt. Lett. (6)

Philos. Mag. (1)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).
[CrossRef]

Phys. Rev. Lett. (2)

T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct observation of pinning and bowing of a single ferroelectric domain wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
[CrossRef]

Y. Zhang, J. Wen, S. N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104, 183901 (2010).
[CrossRef]

Other (2)

J. H. Cantrell and W. T. Yost, “Ultrasonic velocity,” in Handbook of Acoustics, M. J. Crocker, ed. (Wiley, 1998), pp. 483–494.

A. P. Goutzoulis and V. V. Kludzin, “Principles of acousto-optics’,” in Design and Fabrication of Acousto-Optic Devices, A. P. Goutzoulis and D. R. Pape, eds. (Taylor & Francis, 1994), pp. 1–68.

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the setup. An 800 nm laser (red arrow) travels along the y axis of the PPLN crystal and generates SH waves (blue arrow). A cross-field RF signal drives an acoustic standing wave (black curve), which modulates the phases of the SH waves.

Fig.2.
Fig.2.

“Object” (a) is the SH pattern at the end face of the sample. “Imaging” (b) is the pattern at the first Talbot plane without acoustic fields.

Fig. 3.
Fig. 3.

SH pattern modulated by the acoustic waves generated in the PPLN crystal. The acoustic power is 0.10 (a), 0.54 (b), 0.64 (c), and 1.38 W (d), respectively.

Fig. 4.
Fig. 4.

(a) SH pattern with an external acoustic (0.34 W) field along the x axis. (b) SH pattern with a 1.0 W acoustic field along the z axis.

Equations (6)

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

t 1 ( x ) = n = c n exp ( i 2 π n x d 1 ) ,
{ c 0 = 1 2 α c n = 2 α sinc ( n α ) exp ( i n π α ) ,
Δ φ m = π λ M 2 2 P s L y L z .
t 2 ( x ) = exp [ i Δ φ sin ( 2 π x d 2 ) ] rect ( x L x ) = [ m = J m ( Δ φ ) exp ( i 2 π m x d 2 ) ] rect ( x L x ) ,
U ( x ) = n = m = T 1 ( n d 1 ) T 2 ( m d 2 ) exp [ i π λ ( n d 1 + m d 2 ) 2 Z t ] exp [ i 2 π x ( n d 1 + m d 2 ) ] ,
t 2 ( z ) = exp [ i Δ ϕ sin ( 2 π z d 2 ) ] rect ( z L z ) = [ m = J m ( Δ ϕ ) sin ( 2 π m z d 2 ) ] rect ( z L z ) .

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