Abstract

We develop a technique for two-dimensional arbitrary wavefront shaping in quadratic nonlinear crystals by using binary nonlinear computer generated holograms. The method is based on transverse illumination of a binary modulated nonlinear photonic crystal, where the phase matching is partially satisfied through the nonlinear Raman–Nath process. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into three Hermite–Gaussian and three Laguerre–Gaussian beams in the second harmonic. Two-dimensional binary nonlinear computer generated holograms open wide possibilities in the field of nonlinear beam shaping and mode conversion.

© 2012 Optical Society of America

Full Article  |  PDF Article

Corrections

Asia Shapira, Roy Shiloh, Irit Juwiler, and Ady Arie, "Two-dimensional nonlinear beam shaping: erratum," Opt. Lett. 37, 4795-4795 (2012)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-37-22-4795

References

  • View by:
  • |
  • |
  • |

  1. T. Ellenbogen, N. Voloch-Bloch, A. Gannay-Padowicz, and A. Arie, Nature Photon. 3, 395 (2009).
    [CrossRef]
  2. I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581 (2010).
    [CrossRef]
  3. I. Dolev and A. Arie, Appl. Phys. Lett. 97, 171102 (2010).
    [CrossRef]
  4. G. Imeshev, M. Proctor, and M. M. Fejer, Opt. Lett. 23, 673 (1998).
    [CrossRef]
  5. J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. Fejer, IEEE. J. Sel. Top. Quantum Electron. 8, 660 (2002).
    [CrossRef]
  6. Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
    [CrossRef]
  7. T. Ellenbogen, I Dolev, and A. Arie, Opt. Lett. 33, 1207 (2008).
    [CrossRef]
  8. A. Shapira, I. Juwiler, and A. Arie, Opt. Lett. 36, 3015 (2011).
    [CrossRef]
  9. M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993).
    [CrossRef]
  10. B. R. Brown and A. W. Lohmann, Appl. Opt. 5, 967 (1996).
    [CrossRef]
  11. J. J. Burch, IEEE Proc. 55, 599 (1967).
    [CrossRef]
  12. W. H. Lee, Appl. Opt. 18, 3661 (1979).
    [CrossRef]
  13. V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
    [CrossRef]
  14. S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, Opt. Lett. 34, 848 (2009).
    [CrossRef]
  15. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991), Chap. 3.
  16. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  17. A. Bahabad and A. Arie, Opt. Express 15, 17619 (2007).
    [CrossRef]
  18. N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting of light by nonlinear photonic crystals,” Phys. Rev. Lett. (to be published).
  19. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  20. M. A. Bandres, Opt. Lett. 33, 1678 (2008).
    [CrossRef]
  21. S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE. J. Quantum Electron. 45, 1465 (2009).
    [CrossRef]
  22. C. Canalias and V. Pasiskevicius, Nat. Photon. 1, 459 (2007).
    [CrossRef]

2011 (1)

2010 (2)

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581 (2010).
[CrossRef]

I. Dolev and A. Arie, Appl. Phys. Lett. 97, 171102 (2010).
[CrossRef]

2009 (3)

T. Ellenbogen, N. Voloch-Bloch, A. Gannay-Padowicz, and A. Arie, Nature Photon. 3, 395 (2009).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE. J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef]

2008 (3)

2007 (3)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

A. Bahabad and A. Arie, Opt. Express 15, 17619 (2007).
[CrossRef]

C. Canalias and V. Pasiskevicius, Nat. Photon. 1, 459 (2007).
[CrossRef]

2002 (1)

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. Fejer, IEEE. J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

1998 (2)

1996 (1)

1993 (1)

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993).
[CrossRef]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

1979 (1)

1967 (1)

J. J. Burch, IEEE Proc. 55, 599 (1967).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Arie, A.

A. Shapira, I. Juwiler, and A. Arie, Opt. Lett. 36, 3015 (2011).
[CrossRef]

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581 (2010).
[CrossRef]

I. Dolev and A. Arie, Appl. Phys. Lett. 97, 171102 (2010).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE. J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Gannay-Padowicz, and A. Arie, Nature Photon. 3, 395 (2009).
[CrossRef]

T. Ellenbogen, I Dolev, and A. Arie, Opt. Lett. 33, 1207 (2008).
[CrossRef]

A. Bahabad and A. Arie, Opt. Express 15, 17619 (2007).
[CrossRef]

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting of light by nonlinear photonic crystals,” Phys. Rev. Lett. (to be published).

Bahabad, A.

Bandres, M. A.

Bang, O.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Berger, V.

V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
[CrossRef]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Brown, B. R.

Burch, J. J.

J. J. Burch, IEEE Proc. 55, 599 (1967).
[CrossRef]

Canalias, C.

C. Canalias and V. Pasiskevicius, Nat. Photon. 1, 459 (2007).
[CrossRef]

Christodoulides, D. N.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dolev, I

Dolev, I.

I. Dolev and A. Arie, Appl. Phys. Lett. 97, 171102 (2010).
[CrossRef]

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581 (2010).
[CrossRef]

Ellenbogen, T.

Fejer, M.

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. Fejer, IEEE. J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

Fejer, M. M.

Gannay-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Gannay-Padowicz, and A. Arie, Nature Photon. 3, 395 (2009).
[CrossRef]

Hu, X.

Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef]

Hum, D. S.

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. Fejer, IEEE. J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

Imeshev, G.

Juwiler, I.

A. Shapira, I. Juwiler, and A. Arie, Opt. Lett. 36, 3015 (2011).
[CrossRef]

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting of light by nonlinear photonic crystals,” Phys. Rev. Lett. (to be published).

Kivshar, Y. S.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE. J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

Koynov, K.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE. J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

Krolikowski, W.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE. J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

Kurz, J. R.

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. Fejer, IEEE. J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

Lee, W. H.

Lohmann, A. W.

Nada, N.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993).
[CrossRef]

Neshev, D. N.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE. J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef]

Pasiskevicius, V.

C. Canalias and V. Pasiskevicius, Nat. Photon. 1, 459 (2007).
[CrossRef]

Proctor, M.

Qin, Y.

Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef]

Saitoh, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991), Chap. 3.

Saltiel, S. M.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE. J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, Opt. Lett. 34, 848 (2009).
[CrossRef]

Saltzman, A. J.

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. Fejer, IEEE. J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

Schober, A. M.

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. Fejer, IEEE. J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

Shapira, A.

A. Shapira, I. Juwiler, and A. Arie, Opt. Lett. 36, 3015 (2011).
[CrossRef]

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting of light by nonlinear photonic crystals,” Phys. Rev. Lett. (to be published).

Shemer, K.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting of light by nonlinear photonic crystals,” Phys. Rev. Lett. (to be published).

Sheng, Y.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE. J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

Shiloh, R.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting of light by nonlinear photonic crystals,” Phys. Rev. Lett. (to be published).

Siviloglou, G. A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991), Chap. 3.

Voloch-Bloch, N.

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE. J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Gannay-Padowicz, and A. Arie, Nature Photon. 3, 395 (2009).
[CrossRef]

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting of light by nonlinear photonic crystals,” Phys. Rev. Lett. (to be published).

Watanabe, K.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993).
[CrossRef]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Yamada, M.

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993).
[CrossRef]

Zhang, C.

Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef]

Zhao, G.

Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef]

Zhu, Y.

Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993).
[CrossRef]

I. Dolev and A. Arie, Appl. Phys. Lett. 97, 171102 (2010).
[CrossRef]

IEEE Proc. (1)

J. J. Burch, IEEE Proc. 55, 599 (1967).
[CrossRef]

IEEE. J. Quantum Electron. (1)

S. M. Saltiel, Y. Sheng, N. Voloch-Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE. J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

IEEE. J. Sel. Top. Quantum Electron. (1)

J. R. Kurz, A. M. Schober, D. S. Hum, A. J. Saltzman, and M. Fejer, IEEE. J. Sel. Top. Quantum Electron. 8, 660 (2002).
[CrossRef]

Nat. Photon. (1)

C. Canalias and V. Pasiskevicius, Nat. Photon. 1, 459 (2007).
[CrossRef]

Nature Photon. (1)

T. Ellenbogen, N. Voloch-Bloch, A. Gannay-Padowicz, and A. Arie, Nature Photon. 3, 395 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Phys. Rev. Lett. (4)

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, “Twisting of light by nonlinear photonic crystals,” Phys. Rev. Lett. (to be published).

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Y. Qin, C. Zhang, Y. Zhu, X. Hu, and G. Zhao, Phys. Rev. Lett. 100, 063902 (2008).
[CrossRef]

V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
[CrossRef]

Other (1)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991), Chap. 3.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

A Raman–Nath process in a periodically poled crystal (a) and the 2D binary nonlinear CGH setup and far-field results for HG11 (b) and LG11 (c).

Fig. 2.
Fig. 2.

A comparison between calculated (a) and fabricated (b) poling patterns in the HG11, HG12 and LG11 structures.

Fig. 3.
Fig. 3.

A comparison between theoretical (a), and measured (b) HG beam profiles at the first diffraction order.

Fig. 4.
Fig. 4.

A comparison between theoretical (a), and measured (b) LG beam profiles at the first diffraction order.

Tables (1)

Tables Icon

Table 1. Beam Profile Correlation and a Comparison between Predicted and Measured Percentage of SH in the First Diffraction Order

Equations (4)

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

t(x,y)={1cos[2πfcarrierxφ(x,y)]cos[πq(x,y)]0,0otherwise,
dNLO(x,y)=dijsign{cos[2πfcarrierxφ(x,y)]cos[πq(x,y)]},
Ul,m(x,y,0)=Al,mGl[2xW0]Gm[2yW0]
Ul,p(r,ϕ,0)=Cl,pW0(2rW0)|l|exp(r2W02)Lp|l|[2r2W02]exp[ilϕ],

Metrics