Abstract

We describe a method for shaping the wavefront of the second-harmonic light generated in nonlinear materials with a disordered structure using a spatial light modulator on the fundamental beam. We show that, for the case of a transparent strontium-barium niobate crystal with a random distribution of antiparallel domains, the speckle generation can be concentrated into a single spot.

© 2012 Optical Society of America

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  1. S. K. Kurtz and T. T. Perry, J. Appl. Phys. 39, 3798 (1968).
    [CrossRef]
  2. S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
    [CrossRef]
  3. A. R. Tunyagi, M. Ulex, and K. Betzler, Phys. Rev. Lett. 90, 243901 (2003).
    [CrossRef]
  4. R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
    [CrossRef]
  5. J. Bravo-Abad, X. Vidal, J. L. Domínguez-Juárez, and J. Martorell, Opt. Express 18, 14202 (2010).
    [CrossRef]
  6. W. Wang, K. Kalinowski, V. Roppo, Y. Sheng, K. Koynov, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, and W. Krolikowski, J. Phys. B At. Mol. Opt. Phys. 43, 215404 (2010).
    [CrossRef]
  7. F. J. Rodríguez, C. Yao, J. L. Domínguez-Juarez, J. Bravo-Abad, and J. Martorell, Opt. Lett. 36, 1347 (2011).
    [CrossRef]
  8. M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
    [CrossRef]
  9. X. Vidal and J. Martorell, Phys. Rev. Lett. 97, 013902(2006).
    [CrossRef]
  10. I. M. Vellekoop and A. P. Mosk, Opt. Lett. 32, 2309(2007).
    [CrossRef]
  11. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
    [CrossRef]
  12. J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
    [CrossRef]
  13. D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
    [CrossRef]
  14. O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
    [CrossRef]
  15. I. M. Vellekoop and A. P. Mosk, Opt. Commun. 281, 3071 (2008).
    [CrossRef]
  16. J. J. Romero, D. Jaque, J. García Solé, and A. A. Kaminskii, Appl. Phys. Lett. 81, 4106 (2002).
    [CrossRef]

2011

F. J. Rodríguez, C. Yao, J. L. Domínguez-Juarez, J. Bravo-Abad, and J. Martorell, Opt. Lett. 36, 1347 (2011).
[CrossRef]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
[CrossRef]

2010

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

J. Bravo-Abad, X. Vidal, J. L. Domínguez-Juárez, and J. Martorell, Opt. Express 18, 14202 (2010).
[CrossRef]

W. Wang, K. Kalinowski, V. Roppo, Y. Sheng, K. Koynov, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, and W. Krolikowski, J. Phys. B At. Mol. Opt. Phys. 43, 215404 (2010).
[CrossRef]

2008

I. M. Vellekoop and A. P. Mosk, Opt. Commun. 281, 3071 (2008).
[CrossRef]

2007

2006

X. Vidal and J. Martorell, Phys. Rev. Lett. 97, 013902(2006).
[CrossRef]

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

2004

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[CrossRef]

2003

A. R. Tunyagi, M. Ulex, and K. Betzler, Phys. Rev. Lett. 90, 243901 (2003).
[CrossRef]

2002

J. J. Romero, D. Jaque, J. García Solé, and A. A. Kaminskii, Appl. Phys. Lett. 81, 4106 (2002).
[CrossRef]

1998

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[CrossRef]

1968

S. K. Kurtz and T. T. Perry, J. Appl. Phys. 39, 3798 (1968).
[CrossRef]

Aulbach, J.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Austin, D. R.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Baudrier-Raybaut, M.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[CrossRef]

Betzler, K.

A. R. Tunyagi, M. Ulex, and K. Betzler, Phys. Rev. Lett. 90, 243901 (2003).
[CrossRef]

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Bondareff, P.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Bravo-Abad, J.

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
[CrossRef]

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Chatel, B.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Cojocaru, C.

W. Wang, K. Kalinowski, V. Roppo, Y. Sheng, K. Koynov, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, and W. Krolikowski, J. Phys. B At. Mol. Opt. Phys. 43, 215404 (2010).
[CrossRef]

DeMattei, R. C.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[CrossRef]

Domínguez-Juarez, J. L.

Domínguez-Juárez, J. L.

Feigelson, R. S.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[CrossRef]

Fink, M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Fischer, R.

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

García Solé, J.

J. J. Romero, D. Jaque, J. García Solé, and A. A. Kaminskii, Appl. Phys. Lett. 81, 4106 (2002).
[CrossRef]

Gigan, S.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Gjonaj, B.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Haidar, R.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[CrossRef]

Jaque, D.

J. J. Romero, D. Jaque, J. García Solé, and A. A. Kaminskii, Appl. Phys. Lett. 81, 4106 (2002).
[CrossRef]

Johnson, P. M.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Kalinowski, K.

W. Wang, K. Kalinowski, V. Roppo, Y. Sheng, K. Koynov, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, and W. Krolikowski, J. Phys. B At. Mol. Opt. Phys. 43, 215404 (2010).
[CrossRef]

Kaminskii, A. A.

J. J. Romero, D. Jaque, J. García Solé, and A. A. Kaminskii, Appl. Phys. Lett. 81, 4106 (2002).
[CrossRef]

Katz, O.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
[CrossRef]

Kawai, S.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[CrossRef]

Kivshar, Yu. S.

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Kong, Y.

W. Wang, K. Kalinowski, V. Roppo, Y. Sheng, K. Koynov, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, and W. Krolikowski, J. Phys. B At. Mol. Opt. Phys. 43, 215404 (2010).
[CrossRef]

Koynov, K.

W. Wang, K. Kalinowski, V. Roppo, Y. Sheng, K. Koynov, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, and W. Krolikowski, J. Phys. B At. Mol. Opt. Phys. 43, 215404 (2010).
[CrossRef]

Krolikowski, W.

W. Wang, K. Kalinowski, V. Roppo, Y. Sheng, K. Koynov, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, and W. Krolikowski, J. Phys. B At. Mol. Opt. Phys. 43, 215404 (2010).
[CrossRef]

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Kupecek, Ph.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[CrossRef]

Kurtz, S. K.

S. K. Kurtz and T. T. Perry, J. Appl. Phys. 39, 3798 (1968).
[CrossRef]

Lagendijk, A.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

Lee, H. S.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[CrossRef]

Lemasson, Ph.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[CrossRef]

Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Martorell, J.

McCabe, D. J.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Mosk, A. P.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, Opt. Commun. 281, 3071 (2008).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, Opt. Lett. 32, 2309(2007).
[CrossRef]

Neshev, D. N.

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Ogawa, T.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[CrossRef]

Perry, T. T.

S. K. Kurtz and T. T. Perry, J. Appl. Phys. 39, 3798 (1968).
[CrossRef]

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

Rodríguez, F. J.

Romero, J. J.

J. J. Romero, D. Jaque, J. García Solé, and A. A. Kaminskii, Appl. Phys. Lett. 81, 4106 (2002).
[CrossRef]

Roppo, V.

W. Wang, K. Kalinowski, V. Roppo, Y. Sheng, K. Koynov, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, and W. Krolikowski, J. Phys. B At. Mol. Opt. Phys. 43, 215404 (2010).
[CrossRef]

Rosencher, E.

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[CrossRef]

Saltiel, S. M.

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

Sheng, Y.

W. Wang, K. Kalinowski, V. Roppo, Y. Sheng, K. Koynov, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, and W. Krolikowski, J. Phys. B At. Mol. Opt. Phys. 43, 215404 (2010).
[CrossRef]

Silberberg, Y.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
[CrossRef]

Small, E.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
[CrossRef]

Tajalli, A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Trull, J.

W. Wang, K. Kalinowski, V. Roppo, Y. Sheng, K. Koynov, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, and W. Krolikowski, J. Phys. B At. Mol. Opt. Phys. 43, 215404 (2010).
[CrossRef]

Tunyagi, A. R.

A. R. Tunyagi, M. Ulex, and K. Betzler, Phys. Rev. Lett. 90, 243901 (2003).
[CrossRef]

Ulex, M.

A. R. Tunyagi, M. Ulex, and K. Betzler, Phys. Rev. Lett. 90, 243901 (2003).
[CrossRef]

Vellekoop, I. M.

I. M. Vellekoop and A. P. Mosk, Opt. Commun. 281, 3071 (2008).
[CrossRef]

I. M. Vellekoop and A. P. Mosk, Opt. Lett. 32, 2309(2007).
[CrossRef]

Vidal, X.

Vilaseca, R.

W. Wang, K. Kalinowski, V. Roppo, Y. Sheng, K. Koynov, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, and W. Krolikowski, J. Phys. B At. Mol. Opt. Phys. 43, 215404 (2010).
[CrossRef]

Walmsley, I. A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Wang, W.

W. Wang, K. Kalinowski, V. Roppo, Y. Sheng, K. Koynov, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, and W. Krolikowski, J. Phys. B At. Mol. Opt. Phys. 43, 215404 (2010).
[CrossRef]

Yao, C.

Appl. Phys. Lett.

S. Kawai, T. Ogawa, H. S. Lee, R. C. DeMattei, and R. S. Feigelson, Appl. Phys. Lett. 73, 768 (1998).
[CrossRef]

R. Fischer, S. M. Saltiel, D. N. Neshev, W. Krolikowski, and Yu. S. Kivshar, Appl. Phys. Lett. 89, 191105 (2006).
[CrossRef]

J. J. Romero, D. Jaque, J. García Solé, and A. A. Kaminskii, Appl. Phys. Lett. 81, 4106 (2002).
[CrossRef]

J. Appl. Phys.

S. K. Kurtz and T. T. Perry, J. Appl. Phys. 39, 3798 (1968).
[CrossRef]

J. Phys. B At. Mol. Opt. Phys.

W. Wang, K. Kalinowski, V. Roppo, Y. Sheng, K. Koynov, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, and W. Krolikowski, J. Phys. B At. Mol. Opt. Phys. 43, 215404 (2010).
[CrossRef]

Nat. Commun.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, and B. Chatel, Nat. Commun. 2, 447 (2011).
[CrossRef]

Nat. Photon.

O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, Nat. Photon. 5, 372 (2011).
[CrossRef]

Nature

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, Nature 432, 374 (2004).
[CrossRef]

Opt. Commun.

I. M. Vellekoop and A. P. Mosk, Opt. Commun. 281, 3071 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[CrossRef]

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, Phys. Rev. Lett. 106, 103901 (2011).
[CrossRef]

X. Vidal and J. Martorell, Phys. Rev. Lett. 97, 013902(2006).
[CrossRef]

A. R. Tunyagi, M. Ulex, and K. Betzler, Phys. Rev. Lett. 90, 243901 (2003).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Scheme of the experimental setup. A laser beam is expanded and modulated by a phase only SLM. The image of the SLM is then reduced and projected on the nonlinear crystal by a 4f lens system formed by lenses L1 and L2. The SHG is imaged at the far field using a CCD sensor on the focal plane of lens L3. Upper left inset: example of intensity measurement during the phase modulation.

Fig. 2.
Fig. 2.

(a) Fundamental beam intensity distribution at the crystal obtained by focusing the image of the crystal on the CCD without the short-pass filter. (b) SHG pattern at the far field when the SLM is configured with a constant phase, obtained by placing the CCD at the focal plane of L3.

Fig. 3.
Fig. 3.

Results of the optimization process. (a) Initial CCD image of the SHG pattern at the far field. The picture brightness is increased ten times for clarity. The image is also magnified compared with Fig. 2(b). (b) CCD image after the optimization process. (c) Intensity growth at the chosen point during the process normalized to the initial average. (d) Intensity profile normalized to the background average.

Equations (4)

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

Eo=itoiEi.
Eo=iAjBtoijEiAEjB.
Eo=ao11ei(ϕo11+2φ)+ao22eiϕo22+ao12ei(ϕo12+φ),
I=ao112+ao222+ao122+2ao11ao22cos(2φ+ϕ1-ϕ2)+2ao11ao12cos(φ+ϕ1)+2ao22ao12cos(φϕ2),

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