Abstract

We experimentally study the behavior of orbital angular momentum (OAM) of light in a noncollinear second- harmonic generation process. The experiment is performed by using a Type I BBO crystal under phase-matching conditions with femtosecond pumping fields at 830nm. Two specular off-axis vortex beams carrying fractional OAM at the fundamental frequency are used. We analyze the behavior of the OAM of the second-harmonic (SH) signal when the optical vortex of each input field at the FF is displaced from the beam’s axis. We obtain different spatial configurations of the SH field, always carrying the same zero angular momentum.

© 2011 Optical Society of America

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  1. M. Soskin and M. Vasnetsov, “Singular optics,” in Progress in Optics, E.Wolf, ed. (Elsevier, 2001), Vol.  42, pp. 219–276.
    [CrossRef]
  2. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
    [CrossRef]
  3. I. V. Basistiy, M. Soskin, and M. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612(1995).
    [CrossRef]
  4. A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science Publishing, 2008)
  5. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  6. V. Y. Bazhenov, M. Soskin, and M. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
    [CrossRef]
  7. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
    [CrossRef]
  8. S. S. R. Oemrawsingh, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S288–S290 (2004).
    [CrossRef]
  9. F. A. Bovino, Quantum Optics Lab, Selex S.I., Via Puccini 2, 16154 Genova, Italy (personal communication, 2010).
  10. V. Basistiy, V. Bazhenov, M. Soskin, and M. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
    [CrossRef]
  11. K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
    [CrossRef] [PubMed]
  12. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes,” Phys. Rev. A 56, 4193–4196 (1997).
    [CrossRef]
  13. A. P. Sukhorukov, A. Kalinovich, G. Molina-Terriza, and L. Torner, “Superposition of noncoaxial vortices in parametric wave mixing,” Phys. Rev. E 66, 036608 (2002).
    [CrossRef]
  14. A. Dreischuh, D. Neshev, V. Kolev, S. Saltiel, M. Samoc, W. Krolikowski, and Y. Kivshar, “Nonlinear dynamics of two color optical vortices in lithium niobate crystals,” Opt. Express 16, 5406–5420 (2008).
    [CrossRef] [PubMed]
  15. A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Conversion of topological charge of optical vortices in a parametric frequency converter,” Opt. Commun. 140, 273–276 (1997).
    [CrossRef]
  16. A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Sum frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150, 372–380 (1998).
    [CrossRef]
  17. Y. Toda, S. Honda, and R. Morita, “Dynamics of a paired optical vortex generated by second-harmonic generation,” Opt. Express 18, 17796–17804 (2010).
    [CrossRef] [PubMed]
  18. R. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2003).
  19. A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
    [CrossRef] [PubMed]
  20. S. S. R. Oemrawsingh, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “Intrinsic orbital angular momentum of paraxial beams with off-axis imprinted vortices,” J. Opt. Soc. Am. A 21, 2089–2096 (2004).
    [CrossRef]
  21. L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol.  39, pp. 291–372.
    [CrossRef]
  22. S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Production and characterization of a spiral phase plate for optical wavelengths,” Appl. Opt. 43, 688–696(2004).
    [CrossRef] [PubMed]

2010 (1)

2008 (1)

2004 (3)

2002 (2)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

A. P. Sukhorukov, A. Kalinovich, G. Molina-Terriza, and L. Torner, “Superposition of noncoaxial vortices in parametric wave mixing,” Phys. Rev. E 66, 036608 (2002).
[CrossRef]

1998 (1)

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Sum frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150, 372–380 (1998).
[CrossRef]

1997 (2)

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Conversion of topological charge of optical vortices in a parametric frequency converter,” Opt. Commun. 140, 273–276 (1997).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes,” Phys. Rev. A 56, 4193–4196 (1997).
[CrossRef]

1996 (1)

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
[CrossRef] [PubMed]

1995 (1)

I. V. Basistiy, M. Soskin, and M. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612(1995).
[CrossRef]

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

1993 (1)

V. Basistiy, V. Bazhenov, M. Soskin, and M. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

1992 (2)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

V. Y. Bazhenov, M. Soskin, and M. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[CrossRef]

’t Hooft, G. W.

S. S. R. Oemrawsingh, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S288–S290 (2004).
[CrossRef]

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Production and characterization of a spiral phase plate for optical wavelengths,” Appl. Opt. 43, 688–696(2004).
[CrossRef] [PubMed]

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes,” Phys. Rev. A 56, 4193–4196 (1997).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol.  39, pp. 291–372.
[CrossRef]

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol.  39, pp. 291–372.
[CrossRef]

Basistiy, I. V.

I. V. Basistiy, M. Soskin, and M. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612(1995).
[CrossRef]

Basistiy, V.

V. Basistiy, V. Bazhenov, M. Soskin, and M. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

Bazhenov, V.

V. Basistiy, V. Bazhenov, M. Soskin, and M. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

Bazhenov, V. Y.

V. Y. Bazhenov, M. Soskin, and M. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Bekshaev, A.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science Publishing, 2008)

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[CrossRef]

Berzanskis, A.

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Sum frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150, 372–380 (1998).
[CrossRef]

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Conversion of topological charge of optical vortices in a parametric frequency converter,” Opt. Commun. 140, 273–276 (1997).
[CrossRef]

Bovino, F. A.

F. A. Bovino, Quantum Optics Lab, Selex S.I., Via Puccini 2, 16154 Genova, Italy (personal communication, 2010).

Boyd, R.

R. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2003).

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Courtial, J.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes,” Phys. Rev. A 56, 4193–4196 (1997).
[CrossRef]

Dholakia, K.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes,” Phys. Rev. A 56, 4193–4196 (1997).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
[CrossRef] [PubMed]

Dreischuh, A.

Eliel, E. R.

Honda, S.

Kalinovich, A.

A. P. Sukhorukov, A. Kalinovich, G. Molina-Terriza, and L. Torner, “Superposition of noncoaxial vortices in parametric wave mixing,” Phys. Rev. E 66, 036608 (2002).
[CrossRef]

Kivshar, Y.

Kloosterboer, J. G.

S. S. R. Oemrawsingh, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S288–S290 (2004).
[CrossRef]

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Production and characterization of a spiral phase plate for optical wavelengths,” Appl. Opt. 43, 688–696(2004).
[CrossRef] [PubMed]

Kolev, V.

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Krolikowski, W.

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Matijosius, A.

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Sum frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150, 372–380 (1998).
[CrossRef]

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Conversion of topological charge of optical vortices in a parametric frequency converter,” Opt. Commun. 140, 273–276 (1997).
[CrossRef]

Molina-Terriza, G.

A. P. Sukhorukov, A. Kalinovich, G. Molina-Terriza, and L. Torner, “Superposition of noncoaxial vortices in parametric wave mixing,” Phys. Rev. E 66, 036608 (2002).
[CrossRef]

Morita, R.

Neshev, D.

Nienhuis, G.

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
[CrossRef]

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Oemrawsingh, S. S. R.

Padgett, M. J.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes,” Phys. Rev. A 56, 4193–4196 (1997).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
[CrossRef] [PubMed]

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol.  39, pp. 291–372.
[CrossRef]

Piskarkas, A.

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Sum frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150, 372–380 (1998).
[CrossRef]

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Conversion of topological charge of optical vortices in a parametric frequency converter,” Opt. Commun. 140, 273–276 (1997).
[CrossRef]

Saltiel, S.

Samoc, M.

Simpson, N. B.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
[CrossRef] [PubMed]

Smilgevicius, V.

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Sum frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150, 372–380 (1998).
[CrossRef]

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Conversion of topological charge of optical vortices in a parametric frequency converter,” Opt. Commun. 140, 273–276 (1997).
[CrossRef]

Soskin, M.

I. V. Basistiy, M. Soskin, and M. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612(1995).
[CrossRef]

V. Basistiy, V. Bazhenov, M. Soskin, and M. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

V. Y. Bazhenov, M. Soskin, and M. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science Publishing, 2008)

M. Soskin and M. Vasnetsov, “Singular optics,” in Progress in Optics, E.Wolf, ed. (Elsevier, 2001), Vol.  42, pp. 219–276.
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Stabinis, A.

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Sum frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150, 372–380 (1998).
[CrossRef]

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Conversion of topological charge of optical vortices in a parametric frequency converter,” Opt. Commun. 140, 273–276 (1997).
[CrossRef]

Sukhorukov, A. P.

A. P. Sukhorukov, A. Kalinovich, G. Molina-Terriza, and L. Torner, “Superposition of noncoaxial vortices in parametric wave mixing,” Phys. Rev. E 66, 036608 (2002).
[CrossRef]

Toda, Y.

Torner, L.

A. P. Sukhorukov, A. Kalinovich, G. Molina-Terriza, and L. Torner, “Superposition of noncoaxial vortices in parametric wave mixing,” Phys. Rev. E 66, 036608 (2002).
[CrossRef]

van Houwelingen, J. A. W.

Vasnetsov, M.

I. V. Basistiy, M. Soskin, and M. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612(1995).
[CrossRef]

V. Basistiy, V. Bazhenov, M. Soskin, and M. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

V. Y. Bazhenov, M. Soskin, and M. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science Publishing, 2008)

M. Soskin and M. Vasnetsov, “Singular optics,” in Progress in Optics, E.Wolf, ed. (Elsevier, 2001), Vol.  42, pp. 219–276.
[CrossRef]

Verstegen, E. J. K.

S. S. R. Oemrawsingh, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S288–S290 (2004).
[CrossRef]

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Production and characterization of a spiral phase plate for optical wavelengths,” Appl. Opt. 43, 688–696(2004).
[CrossRef] [PubMed]

Woerdman, J. P.

S. S. R. Oemrawsingh, J. A. W. van Houwelingen, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Production and characterization of a spiral phase plate for optical wavelengths,” Appl. Opt. 43, 688–696(2004).
[CrossRef] [PubMed]

S. S. R. Oemrawsingh, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S288–S290 (2004).
[CrossRef]

S. S. R. Oemrawsingh, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “Intrinsic orbital angular momentum of paraxial beams with off-axis imprinted vortices,” J. Opt. Soc. Am. A 21, 2089–2096 (2004).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Mod. Opt. (1)

V. Y. Bazhenov, M. Soskin, and M. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

J. Opt. A (1)

S. S. R. Oemrawsingh, E. R. Eliel, J. P. Woerdman, E. J. K. Verstegen, J. G. Kloosterboer, and G. W. ’t Hooft, “Half-integral spiral phase plates for optical wavelengths,” J. Opt. A 6, S288–S290 (2004).
[CrossRef]

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

Opt. Commun. (5)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

I. V. Basistiy, M. Soskin, and M. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612(1995).
[CrossRef]

V. Basistiy, V. Bazhenov, M. Soskin, and M. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Conversion of topological charge of optical vortices in a parametric frequency converter,” Opt. Commun. 140, 273–276 (1997).
[CrossRef]

A. Berzanskis, A. Matijosius, A. Piskarkas, V. Smilgevicius, and A. Stabinis, “Sum frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150, 372–380 (1998).
[CrossRef]

Opt. Express (2)

Phys. Rev. A (3)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, R3742–R3745 (1996).
[CrossRef] [PubMed]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre–Gaussian modes,” Phys. Rev. A 56, 4193–4196 (1997).
[CrossRef]

Phys. Rev. E (1)

A. P. Sukhorukov, A. Kalinovich, G. Molina-Terriza, and L. Torner, “Superposition of noncoaxial vortices in parametric wave mixing,” Phys. Rev. E 66, 036608 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Proc. R. Soc. London A (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A 336, 165–190 (1974).
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Other (5)

M. Soskin and M. Vasnetsov, “Singular optics,” in Progress in Optics, E.Wolf, ed. (Elsevier, 2001), Vol.  42, pp. 219–276.
[CrossRef]

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science Publishing, 2008)

F. A. Bovino, Quantum Optics Lab, Selex S.I., Via Puccini 2, 16154 Genova, Italy (personal communication, 2010).

R. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2003).

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1999), Vol.  39, pp. 291–372.
[CrossRef]

Supplementary Material (1)

» Media 1: AVI (857 KB)     

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Figures (7)

Fig. 1
Fig. 1

Experimental setup of noncollinear SHG. The collimated beam impinges on the SPP, and then it is split and focused on the nonlinear crystal with relative angles of ± 3.5 ° (total 7 ° ). Bottom-left corner, scan of the Gaussian beam performed by moving the SPP in the horizontal direction.

Fig. 2
Fig. 2

Noncollinear SHG signal obtained by displacing the SPP along the x axis at y = 0 , for six different x displacement values. (a) Numerically simulated near field; (b) numerically simulated far field; and (c) experimental results.

Fig. 3
Fig. 3

Numerically estimated near-field intensity profiles of the FF beams, (a) and (b), and of the noncollinear SH beam; in FF beams the singularity shifts in opposite directions. The SH beam’s profile carries the singularities of both the FF beams, maintaining their original orientation.

Fig. 4
Fig. 4

Phase plots of the electric field for the FFs, (a) and (b), and for the SH (c), corresponding to the configuration of fields given in Fig. 3. The phase changes from π (dark blue), to 0 (light green), to π (dark red).

Fig. 5
Fig. 5

Frame of the far-field movie of the SHG signal as a function of the SPP’s displacement; the top frame corresponds to zero displacement ( x = 0 ) (Media 1).

Fig. 6
Fig. 6

OAM of pump and SH fields with the SPP’s displacement. As the device is moved from the beam’s axis, both the FF beams [blue (upper) and black (lower) lines] reduce the absolute value of their OAM from the initial values of ± 0.5 . The SH’s OAM [red (middle) line] is always the sum of the other two, that is, zero.

Fig. 7
Fig. 7

Transverse Poynting vector of the SH field generated in the case of on-axis SPP. The absence of rotation of the arrows implies that there is no screw dislocation; therefore, there is no OAM.

Equations (8)

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Q = 1 2 π d f ,
u ( ρ , θ ) = l = p = 0 C l p ψ l p ( ρ , θ ) ,
E ( r , θ , z ) = u ( r , θ , z ) e i k z i ω t ,
P = i ε 0 ω ( u u * u * u ) + 2 k ε 0 ω | u | 2 z .
= i u * ( r , θ ) u ( r , θ ) θ r d r d θ | u ( r , θ ) | 2 r d r d θ .
= l = p = 0 l | C l p | 2 .
I 2 ω | E 1 ω ( r , ϑ , z 0 ) E 2 ω ( r , ϑ , z 0 ) | 2 ,
I 2 ω ( x , y , z ) | d r E 1 ω ( x , y , z 0 ) E 2 ω ( x , y , z 0 ) exp [ i k z ( x x + y y ) ] | 2 ,

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