Abstract

We experimentally demonstrate that the orbital angular momentum (OAM) of a second harmonic (SH) beam, generated within twisted nonlinear photonic crystals, depends both on the OAM of the input pump beam and on the quasi-angular momentum of the crystal. In addition, when the pump’s radial index is zero, the radial index of the SH beam is equal to that of the nonlinear crystal. Furthermore, by mixing two noncollinear pump beams in this crystal, we generate, in addition to the SH beams, a new “virtual beam” having multiple values of OAM that are determined by the nonlinear process.

© 2013 Optical Society of America

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  2. L. Allen, M. J. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
    [CrossRef]
  3. A. M. Yao and M. J. Padgett, Adv. Opt. Photon. 3, 161 (2011).
    [CrossRef]
  4. G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
    [CrossRef]
  5. S. Franke-Arnold, L. Allen, and M. J. Padgett, Laser Photon. Rev. 2, 299 (2008).
    [CrossRef]
  6. I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
    [CrossRef]
  7. A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
    [CrossRef]
  8. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
    [CrossRef]
  9. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
    [CrossRef]
  10. K. Dholakia and T. Cizmar, Nat. Photonics 5, 335 (2011).
    [CrossRef]
  11. J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
    [CrossRef]
  12. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
    [CrossRef]
  13. R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, Science 338, 640 (2012).
    [CrossRef]
  14. K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996).
    [CrossRef]
  15. N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Phys. Rev. Lett. 108, 233902 (2012).
    [CrossRef]
  16. A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Opt. Lett. 37, 2136 (2012).
    [CrossRef]
  17. S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
    [CrossRef]
  18. S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
    [CrossRef]
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    [CrossRef]
  20. S. M. Saltiel, D. N. Neshev, W. Krolikowski, A. Arie, O. Bang, and Y. S. Kivshar, Opt. Lett. 34, 848 (2009).
    [CrossRef]
  21. I. Dolev, A. Libster, and A. Arie, Appl. Phys. Lett. 101, 101109 (2012).
    [CrossRef]

2012 (5)

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, Science 338, 640 (2012).
[CrossRef]

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Opt. Lett. 37, 2136 (2012).
[CrossRef]

I. Dolev, A. Libster, and A. Arie, Appl. Phys. Lett. 101, 101109 (2012).
[CrossRef]

2011 (3)

2010 (1)

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef]

2009 (1)

2008 (1)

S. Franke-Arnold, L. Allen, and M. J. Padgett, Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

2007 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

2005 (1)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

2002 (1)

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
[CrossRef]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

1999 (1)

L. Allen, M. J. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

1997 (1)

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

1996 (1)

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996).
[CrossRef]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

1993 (1)

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

1992 (1)

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

Ahmed, N.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Allen, L.

S. Franke-Arnold, L. Allen, and M. J. Padgett, Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
[CrossRef]

L. Allen, M. J. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996).
[CrossRef]

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

Arie, A.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Opt. Lett. 37, 2136 (2012).
[CrossRef]

I. Dolev, A. Libster, and A. Arie, Appl. Phys. Lett. 101, 101109 (2012).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef]

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

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

Bang, O.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef]

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

Barnett, S. M.

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
[CrossRef]

Basistiy, I. V.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Bazhenov, V. Yu.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Beijersbergen, M. W.

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

Bovino, F. A.

Braccini, M.

Cizmar, T.

K. Dholakia and T. Cizmar, Nat. Photonics 5, 335 (2011).
[CrossRef]

Courtial, J.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Desyatnikov, A. S.

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

Dholakia, K.

K. Dholakia and T. Cizmar, Nat. Photonics 5, 335 (2011).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996).
[CrossRef]

Dolev, I.

I. Dolev, A. Libster, and A. Arie, Appl. Phys. Lett. 101, 101109 (2012).
[CrossRef]

Dolinar, S.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Fazal, I. M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Fickler, R.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, Science 338, 640 (2012).
[CrossRef]

Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. J. Padgett, Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
[CrossRef]

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

Giardina, M.

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

Huang, H.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Juwiler, I.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Opt. Lett. 37, 2136 (2012).
[CrossRef]

Kivshar, Y. S.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef]

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

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

Krenn, M.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, Science 338, 640 (2012).
[CrossRef]

Krolikowski, W.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef]

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

Lapkiewicz, R.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, Science 338, 640 (2012).
[CrossRef]

Libster, A.

I. Dolev, A. Libster, and A. Arie, Appl. Phys. Lett. 101, 101109 (2012).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Neshev, D. N.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef]

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

Padgett, M. J.

A. M. Yao and M. J. Padgett, Adv. Opt. Photon. 3, 161 (2011).
[CrossRef]

S. Franke-Arnold, L. Allen, and M. J. Padgett, Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
[CrossRef]

L. Allen, M. J. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996).
[CrossRef]

Plick, W. N.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, Science 338, 640 (2012).
[CrossRef]

Ramelow, S.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, Science 338, 640 (2012).
[CrossRef]

Ren, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

Saltiel, S. M.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef]

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

Schaeff, C.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, Science 338, 640 (2012).
[CrossRef]

Shapira, A.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Opt. Lett. 37, 2136 (2012).
[CrossRef]

Shemer, K.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

Shiloh, R.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Opt. Lett. 37, 2136 (2012).
[CrossRef]

Sibilia, C.

Simpson, N. B.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996).
[CrossRef]

Soskin, M. S.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[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]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Tur, M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Vasnetsov, M. V.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Voloch-Bloch, N.

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef]

Wang, J.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Willner, A. E.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Woerdman, J. P.

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

Yan, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yang, J. Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Yao, A. M.

Yue, Y.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Zeilinger, A.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, Science 338, 640 (2012).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (1)

I. Dolev, A. Libster, and A. Arie, Appl. Phys. Lett. 101, 101109 (2012).
[CrossRef]

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

Laser Photon. Rev. (1)

S. Franke-Arnold, L. Allen, and M. J. Padgett, Laser Photon. Rev. 2, 299 (2008).
[CrossRef]

Nat. Photonics (2)

K. Dholakia and T. Cizmar, Nat. Photonics 5, 335 (2011).
[CrossRef]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, Nat. Photonics 6, 488 (2012).
[CrossRef]

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, Nat. Phys. 3, 305 (2007).
[CrossRef]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Opt. Commun. (1)

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (4)

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

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

Phys. Rev. Lett. (3)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

N. Voloch-Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Phys. Rev. Lett. 108, 233902 (2012).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef]

Prog. Opt. (2)

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Science (1)

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[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Experiment Setup. (a) Beams carrying OAM are generated by the use of a fork-shaped linear phase mask. The filtered first diffraction order (LG10) transversely illuminates the twisted NPC, yielding various SH vortices. (b) 3D microscope image of the fabricated linear phase mask.

Fig. 2.
Fig. 2.

NPC Structures. Microscope images of the poling patterns of the fabricated NPC structures (left) versus their theoretical designs (right). Top to bottom: LG01, LG02, LG11, and LG20.

Fig. 3.
Fig. 3.

Azimuthal control. Numerical (subscript 1) compared to experimental (subscript 2) profiles of (a) an LG20 fundamental beam entering an LG20 NPC, and an LG10 fundamental beam entering (b) an LG20 NPC and (c) an LG11 NPC. The orders where l2ω=0 are framed by dashed lines. All images are 7 mm wide by 2.2 mm long.

Fig. 4.
Fig. 4.

Radial Control. Numerical (subscript 1) compared to experimental (subscript 2) profiles of an LG10 fundamental beam entering (a) an LG01 NPC and (b) an LG02 NPC. (b3) Numerical profile after considering the linear phase mask on the crystal’s facet. All images are 7 mm wide by 2.2 mm long.

Fig. 5.
Fig. 5.

Vortices’ radius. Numerical (circles) and experimental (crosses) results for the SH vortices’ radii as a function of the topological charge.

Fig. 6.
Fig. 6.

Generation of virtual vortex beams. (a) Experimental setup: two noncollinear beams interfere inside the twisted NPC. The resulting nonlinear diffraction pattern includes the SH of each of the input beams (top and bottom rows), as well as the SFG from both beams (middle row). (b) Experimental profile captured 7.5 cm after an LG20 NPC. The image is 7 mm wide by 3 mm long.

Equations (2)

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Ul,p(r,φ,0)=U0(r2ω0)|l|exp(r2ω02)Lp|l|[2r2ω02]exp(ilφ),
l2ω,m=2·lω+m·lc,

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