Abstract

Edge diffraction of a circular Laguerre–Gaussian beam represents an example of the optical vortex symmetry breakdown in which the hidden “vortex” energy circulation is partially transformed into the visible “asymmetry” form. The diffracted beam evolution is studied in terms of the irradiance moments and the moment-based parameters. In spite of the limited applicability of the moment-based formalism, we show that the “vortex” and “asymmetry” parts of the orbital angular momentum can still be reasonably defined for the hard-edge diffracted beams and retain their physical role of quantifying the corresponding forms of the transverse energy circulation.

© 2014 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Allen, M. J. Padgett, and M. Babiker, “Orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
    [CrossRef]
  2. M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
    [CrossRef]
  3. A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).
  4. M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
    [CrossRef]
  5. A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).
    [CrossRef]
  6. M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
    [CrossRef]
  7. 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]
  8. V. Garcés-Chavéz, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
    [CrossRef]
  9. M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, 021875 (2008).
    [CrossRef]
  10. R. W. Bowman and M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys. 76, 026401 (2013).
    [CrossRef]
  11. M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” J. Exp. Theor. Phys. Lett. 71, 130–133 (2000).
    [CrossRef]
  12. J. Masajada, “Gaussian beams with optical vortex of charge 2- and 3-diffraction by a half-plane and slit,” Opt. Appl. 30, 248–256 (2000).
  13. J. Masajada, “Half-plane diffraction in the case of Gaussian beams containing an optical vortex,” Opt. Commun. 175, 289–294 (2000).
    [CrossRef]
  14. P. Liu and B. Lü, “Propagation of Gaussian background vortex beams diffracted at a half-plane screen,” Opt. Laser Technol. 40, 227–234 (2008).
    [CrossRef]
  15. Y. Luo, Z. Gao, B. Tang, and B. Lü, “Electric and magnetic polarization singularities of first-order Laguerre-Gaussian Beams diffracted at a half-plane screen,” J. Opt. Soc. Am. A 30, 1646–1653 (2013).
    [CrossRef]
  16. J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).
  17. H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14, 055707 (2012).
    [CrossRef]
  18. D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Single-slit diffraction of an optical beam with phase singularity,” Opt. Lasers Eng. 47, 123–126 (2009).
    [CrossRef]
  19. H. V. Bogatyryova, Ch. V. Felde, and P. V. Polyanskii, “Referenceless testing of vortex optical beams,” Opt. Appl. 33, 695–708 (2003).
  20. Ch. V. Felde, “Diffraction diagnostics of phase singularities in optical fields,” Proc. SPIE 5477, 67–76 (2004).
    [CrossRef]
  21. J. Masajada, M. Leniec, S. Drobczyński, H. Thienpont, and B. Kress, “Micro-step localization using double charge optical vortex interferometer,” Opt. Express 17, 16144–16159 (2009).
    [CrossRef]
  22. J. Masajada, M. Leniec, E. Jankowska, H. Thienpont, H. Ottevaere, and V. Gomez, “Deep microstructure topography characterization with optical vortex interferometer,” Opt. Express 16, 19179–19191 (2008).
    [CrossRef]
  23. A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams,” J. Opt. Soc. Am. A 20, 1635–1643 (2003).
    [CrossRef]
  24. A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241, 237–247 (2004).
    [CrossRef]
  25. T. Alieva and M. J. Bastiaans, “Evolution of the vortex and the asymmetrical parts of orbital angular momentum in separable first-order optical systems,” Opt. Lett. 29, 1587–1589 (2004).
    [CrossRef]
  26. M. J. Bastiaans, “Second-order moments of the Wigner distribution function in first-order optical systems,” Optik 88, 163–168 (1991).
  27. D. Dragoman, “The Wigner distribution function in optics and optoelectronics,” Prog. Opt. 37, 1–56 (1997).
    [CrossRef]
  28. R. Simon and N. J. Mukunda, “Optical phase space, Wigner representation, and invariant quality parameters,” J. Opt. Soc. Am. A 17, 2440–2463 (2000).
    [CrossRef]
  29. Yu. A. Anan’ev and A. Ya. Bekshaev, “Theory of intensity moments for arbitrary light beams,” Opt. Spectrosc. 76, 558–568 (1994).
  30. P. M. Mejias, R. Martinez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65–130 (2002).
    [CrossRef]
  31. R. Martinez-Herrero and P. M. Mejias, “Second-order spatial characterization of hard-edge diffracted beams,” Opt. Lett. 18, 1669–1671 (1993).
    [CrossRef]
  32. R. Martinez-Herrero, P. M. Mejias, and M. Arias, “Parametric characterization of coherent, lowest-order Gaussian beams propagating through hard-edged apertures,” Opt. Lett. 20, 124–126 (1995).
    [CrossRef]
  33. Yu. A. Anan’ev, Laser Resonators and the Beam Divergence Problem (Adam Hilger, 1992).
  34. M. Abramovitz and I. Stegun, eds., Handbook of Mathematical Functions, Vol. 55 of Applied Mathematics Series (National Bureau of Standards, 1964).
  35. A. Bekshaev and M. Soskin, “Rotational transformations and transverse energy flow in paraxial light beams: linear azimuthons,” Opt. Lett. 31, 2199–2201 (2006).
    [CrossRef]
  36. A. Ya. Bekshaev and S. V. Sviridova, “Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity,” Opt. Commun. 283, 4866–4876 (2010).
    [CrossRef]
  37. Z. Mei and D. Zhao, “Generalized beam propagation factor of hard-edged diffracted controllable dark-hollow beams,” Opt. Commun. 263, 261–266 (2006).
    [CrossRef]
  38. Z. Lu, H. Jiang, X. Du, and D. Zhao, “Generalized M2 factor of truncated partially coherent controllable dark-hollow beams,” J. Mod. Opt. 55, 2381–2390 (2008).
    [CrossRef]
  39. Z. Mei and D. Zhao, “Approximate method for the generalized M2 factor of rotationally symmetric hard-edged diffracted flattened Gaussian beams,” Appl. Opt. 44, 1381–1386 (2005).
    [CrossRef]
  40. G. Zhou, “Generalized M2 factors of truncated partially coherent Lorentz and Lorentz–Gauss beams,” J. Opt. 12, 015701 (2010).
    [CrossRef]
  41. A. Bekshaev and K. A. Mohammed, “Transverse energy redistribution upon edge diffraction of a paraxial laser beam with optical vortex,” Proc. SPIE 9066, 906602 (2013).
    [CrossRef]

2013 (3)

R. W. Bowman and M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys. 76, 026401 (2013).
[CrossRef]

A. Bekshaev and K. A. Mohammed, “Transverse energy redistribution upon edge diffraction of a paraxial laser beam with optical vortex,” Proc. SPIE 9066, 906602 (2013).
[CrossRef]

Y. Luo, Z. Gao, B. Tang, and B. Lü, “Electric and magnetic polarization singularities of first-order Laguerre-Gaussian Beams diffracted at a half-plane screen,” J. Opt. Soc. Am. A 30, 1646–1653 (2013).
[CrossRef]

2012 (1)

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14, 055707 (2012).
[CrossRef]

2011 (1)

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).
[CrossRef]

2010 (2)

G. Zhou, “Generalized M2 factors of truncated partially coherent Lorentz and Lorentz–Gauss beams,” J. Opt. 12, 015701 (2010).
[CrossRef]

A. Ya. Bekshaev and S. V. Sviridova, “Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity,” Opt. Commun. 283, 4866–4876 (2010).
[CrossRef]

2009 (3)

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Single-slit diffraction of an optical beam with phase singularity,” Opt. Lasers Eng. 47, 123–126 (2009).
[CrossRef]

J. Masajada, M. Leniec, S. Drobczyński, H. Thienpont, and B. Kress, “Micro-step localization using double charge optical vortex interferometer,” Opt. Express 17, 16144–16159 (2009).
[CrossRef]

2008 (4)

J. Masajada, M. Leniec, E. Jankowska, H. Thienpont, H. Ottevaere, and V. Gomez, “Deep microstructure topography characterization with optical vortex interferometer,” Opt. Express 16, 19179–19191 (2008).
[CrossRef]

P. Liu and B. Lü, “Propagation of Gaussian background vortex beams diffracted at a half-plane screen,” Opt. Laser Technol. 40, 227–234 (2008).
[CrossRef]

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, 021875 (2008).
[CrossRef]

Z. Lu, H. Jiang, X. Du, and D. Zhao, “Generalized M2 factor of truncated partially coherent controllable dark-hollow beams,” J. Mod. Opt. 55, 2381–2390 (2008).
[CrossRef]

2006 (2)

Z. Mei and D. Zhao, “Generalized beam propagation factor of hard-edged diffracted controllable dark-hollow beams,” Opt. Commun. 263, 261–266 (2006).
[CrossRef]

A. Bekshaev and M. Soskin, “Rotational transformations and transverse energy flow in paraxial light beams: linear azimuthons,” Opt. Lett. 31, 2199–2201 (2006).
[CrossRef]

2005 (1)

2004 (3)

T. Alieva and M. J. Bastiaans, “Evolution of the vortex and the asymmetrical parts of orbital angular momentum in separable first-order optical systems,” Opt. Lett. 29, 1587–1589 (2004).
[CrossRef]

Ch. V. Felde, “Diffraction diagnostics of phase singularities in optical fields,” Proc. SPIE 5477, 67–76 (2004).
[CrossRef]

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241, 237–247 (2004).
[CrossRef]

2003 (4)

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams,” J. Opt. Soc. Am. A 20, 1635–1643 (2003).
[CrossRef]

V. Garcés-Chavéz, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).

H. V. Bogatyryova, Ch. V. Felde, and P. V. Polyanskii, “Referenceless testing of vortex optical beams,” Opt. Appl. 33, 695–708 (2003).

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]

P. M. Mejias, R. Martinez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65–130 (2002).
[CrossRef]

2001 (1)

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

2000 (4)

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” J. Exp. Theor. Phys. Lett. 71, 130–133 (2000).
[CrossRef]

J. Masajada, “Gaussian beams with optical vortex of charge 2- and 3-diffraction by a half-plane and slit,” Opt. Appl. 30, 248–256 (2000).

J. Masajada, “Half-plane diffraction in the case of Gaussian beams containing an optical vortex,” Opt. Commun. 175, 289–294 (2000).
[CrossRef]

R. Simon and N. J. Mukunda, “Optical phase space, Wigner representation, and invariant quality parameters,” J. Opt. Soc. Am. A 17, 2440–2463 (2000).
[CrossRef]

1999 (1)

L. Allen, M. J. Padgett, and M. Babiker, “Orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

1998 (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[CrossRef]

1997 (1)

D. Dragoman, “The Wigner distribution function in optics and optoelectronics,” Prog. Opt. 37, 1–56 (1997).
[CrossRef]

1995 (1)

1994 (1)

Yu. A. Anan’ev and A. Ya. Bekshaev, “Theory of intensity moments for arbitrary light beams,” Opt. Spectrosc. 76, 558–568 (1994).

1993 (1)

1991 (1)

M. J. Bastiaans, “Second-order moments of the Wigner distribution function in first-order optical systems,” Optik 88, 163–168 (1991).

Alieva, T.

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]

L. Allen, M. J. Padgett, and M. Babiker, “Orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

Anan’ev, Yu. A.

Yu. A. Anan’ev and A. Ya. Bekshaev, “Theory of intensity moments for arbitrary light beams,” Opt. Spectrosc. 76, 558–568 (1994).

Yu. A. Anan’ev, Laser Resonators and the Beam Divergence Problem (Adam Hilger, 1992).

Arias, M.

Arlt, J.

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, “Orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

Bastiaans, M. J.

T. Alieva and M. J. Bastiaans, “Evolution of the vortex and the asymmetrical parts of orbital angular momentum in separable first-order optical systems,” Opt. Lett. 29, 1587–1589 (2004).
[CrossRef]

M. J. Bastiaans, “Second-order moments of the Wigner distribution function in first-order optical systems,” Optik 88, 163–168 (1991).

Bekshaev, A.

A. Bekshaev and K. A. Mohammed, “Transverse energy redistribution upon edge diffraction of a paraxial laser beam with optical vortex,” Proc. SPIE 9066, 906602 (2013).
[CrossRef]

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).
[CrossRef]

A. Bekshaev and M. Soskin, “Rotational transformations and transverse energy flow in paraxial light beams: linear azimuthons,” Opt. Lett. 31, 2199–2201 (2006).
[CrossRef]

Bekshaev, A. Ya.

A. Ya. Bekshaev and S. V. Sviridova, “Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity,” Opt. Commun. 283, 4866–4876 (2010).
[CrossRef]

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241, 237–247 (2004).
[CrossRef]

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams,” J. Opt. Soc. Am. A 20, 1635–1643 (2003).
[CrossRef]

Yu. A. Anan’ev and A. Ya. Bekshaev, “Theory of intensity moments for arbitrary light beams,” Opt. Spectrosc. 76, 558–568 (1994).

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

Bliokh, K.

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).
[CrossRef]

Bogatyryova, H. V.

H. V. Bogatyryova, Ch. V. Felde, and P. V. Polyanskii, “Referenceless testing of vortex optical beams,” Opt. Appl. 33, 695–708 (2003).

Bowman, R. W.

R. W. Bowman and M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys. 76, 026401 (2013).
[CrossRef]

Chen, J.

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14, 055707 (2012).
[CrossRef]

Cui, H. X.

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14, 055707 (2012).
[CrossRef]

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

Dholakia, K.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, 021875 (2008).
[CrossRef]

V. Garcés-Chavéz, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Dienerowitz, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, 021875 (2008).
[CrossRef]

Dragoman, D.

D. Dragoman, “The Wigner distribution function in optics and optoelectronics,” Prog. Opt. 37, 1–56 (1997).
[CrossRef]

Drobczynski, S.

Du, X.

Z. Lu, H. Jiang, X. Du, and D. Zhao, “Generalized M2 factor of truncated partially coherent controllable dark-hollow beams,” J. Mod. Opt. 55, 2381–2390 (2008).
[CrossRef]

Dultz, W.

V. Garcés-Chavéz, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Felde, Ch. V.

Ch. V. Felde, “Diffraction diagnostics of phase singularities in optical fields,” Proc. SPIE 5477, 67–76 (2004).
[CrossRef]

H. V. Bogatyryova, Ch. V. Felde, and P. V. Polyanskii, “Referenceless testing of vortex optical beams,” Opt. Appl. 33, 695–708 (2003).

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[CrossRef]

Gao, Z.

Garcés-Chavéz, V.

V. Garcés-Chavéz, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Ghai, D. P.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Single-slit diffraction of an optical beam with phase singularity,” Opt. Lasers Eng. 47, 123–126 (2009).
[CrossRef]

Gomez, V.

Gu, B.

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14, 055707 (2012).
[CrossRef]

Heckenberg, N. R.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[CrossRef]

Jankowska, E.

Jiang, H.

Z. Lu, H. Jiang, X. Du, and D. Zhao, “Generalized M2 factor of truncated partially coherent controllable dark-hollow beams,” J. Mod. Opt. 55, 2381–2390 (2008).
[CrossRef]

Kress, B.

Leniec, M.

Li, Y. N.

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14, 055707 (2012).
[CrossRef]

Liu, P.

P. Liu and B. Lü, “Propagation of Gaussian background vortex beams diffracted at a half-plane screen,” Opt. Laser Technol. 40, 227–234 (2008).
[CrossRef]

Lu, Z.

Z. Lu, H. Jiang, X. Du, and D. Zhao, “Generalized M2 factor of truncated partially coherent controllable dark-hollow beams,” J. Mod. Opt. 55, 2381–2390 (2008).
[CrossRef]

Lü, B.

Luo, Y.

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]

Marienko, I. G.

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” J. Exp. Theor. Phys. Lett. 71, 130–133 (2000).
[CrossRef]

Martinez-Herrero, R.

Masajada, J.

Mazilu, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, 021875 (2008).
[CrossRef]

McGloin, D.

V. Garcés-Chavéz, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Mei, Z.

Z. Mei and D. Zhao, “Generalized beam propagation factor of hard-edged diffracted controllable dark-hollow beams,” Opt. Commun. 263, 261–266 (2006).
[CrossRef]

Z. Mei and D. Zhao, “Approximate method for the generalized M2 factor of rotationally symmetric hard-edged diffracted flattened Gaussian beams,” Appl. Opt. 44, 1381–1386 (2005).
[CrossRef]

Mejias, P. M.

Mohammed, K. A.

A. Bekshaev and K. A. Mohammed, “Transverse energy redistribution upon edge diffraction of a paraxial laser beam with optical vortex,” Proc. SPIE 9066, 906602 (2013).
[CrossRef]

Movilla, J. M.

P. M. Mejias, R. Martinez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65–130 (2002).
[CrossRef]

Mukunda, N. J.

Nieminen, T. A.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[CrossRef]

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[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]

Ottevaere, H.

Padgett, M. J.

R. W. Bowman and M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys. 76, 026401 (2013).
[CrossRef]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

V. Garcés-Chavéz, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

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]

L. Allen, M. J. Padgett, and M. Babiker, “Orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

Piquero, G.

P. M. Mejias, R. Martinez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65–130 (2002).
[CrossRef]

Polyanskii, P. V.

H. V. Bogatyryova, Ch. V. Felde, and P. V. Polyanskii, “Referenceless testing of vortex optical beams,” Opt. Appl. 33, 695–708 (2003).

Rubinsztein-Dunlop, H.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[CrossRef]

Schmitzer, H.

V. Garcés-Chavéz, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Senthilkumaran, P.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Single-slit diffraction of an optical beam with phase singularity,” Opt. Lasers Eng. 47, 123–126 (2009).
[CrossRef]

Simon, R.

Sirohi, R. S.

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Single-slit diffraction of an optical beam with phase singularity,” Opt. Lasers Eng. 47, 123–126 (2009).
[CrossRef]

Soskin, M.

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).
[CrossRef]

A. Bekshaev and M. Soskin, “Rotational transformations and transverse energy flow in paraxial light beams: linear azimuthons,” Opt. Lett. 31, 2199–2201 (2006).
[CrossRef]

Soskin, M. S.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241, 237–247 (2004).
[CrossRef]

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams,” J. Opt. Soc. Am. A 20, 1635–1643 (2003).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” J. Exp. Theor. Phys. Lett. 71, 130–133 (2000).
[CrossRef]

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

Sviridova, S. V.

A. Ya. Bekshaev and S. V. Sviridova, “Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity,” Opt. Commun. 283, 4866–4876 (2010).
[CrossRef]

Tang, B.

Thienpont, H.

Vasnetsov, M. V.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241, 237–247 (2004).
[CrossRef]

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams,” J. Opt. Soc. Am. A 20, 1635–1643 (2003).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” J. Exp. Theor. Phys. Lett. 71, 130–133 (2000).
[CrossRef]

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

Wang, H. T.

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14, 055707 (2012).
[CrossRef]

Wang, X. L.

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14, 055707 (2012).
[CrossRef]

Zhao, D.

Z. Lu, H. Jiang, X. Du, and D. Zhao, “Generalized M2 factor of truncated partially coherent controllable dark-hollow beams,” J. Mod. Opt. 55, 2381–2390 (2008).
[CrossRef]

Z. Mei and D. Zhao, “Generalized beam propagation factor of hard-edged diffracted controllable dark-hollow beams,” Opt. Commun. 263, 261–266 (2006).
[CrossRef]

Z. Mei and D. Zhao, “Approximate method for the generalized M2 factor of rotationally symmetric hard-edged diffracted flattened Gaussian beams,” Appl. Opt. 44, 1381–1386 (2005).
[CrossRef]

Zhou, G.

G. Zhou, “Generalized M2 factors of truncated partially coherent Lorentz and Lorentz–Gauss beams,” J. Opt. 12, 015701 (2010).
[CrossRef]

Appl. Opt. (1)

J. Exp. Theor. Phys. Lett. (1)

M. V. Vasnetsov, I. G. Marienko, and M. S. Soskin, “Self-reconstruction of an optical vortex,” J. Exp. Theor. Phys. Lett. 71, 130–133 (2000).
[CrossRef]

J. Mod. Opt. (2)

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).

Z. Lu, H. Jiang, X. Du, and D. Zhao, “Generalized M2 factor of truncated partially coherent controllable dark-hollow beams,” J. Mod. Opt. 55, 2381–2390 (2008).
[CrossRef]

J. Nanophotonics (1)

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophotonics 2, 021875 (2008).
[CrossRef]

J. Opt. (3)

A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).
[CrossRef]

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14, 055707 (2012).
[CrossRef]

G. Zhou, “Generalized M2 factors of truncated partially coherent Lorentz and Lorentz–Gauss beams,” J. Opt. 12, 015701 (2010).
[CrossRef]

J. Opt. Soc. Am. A (3)

Nature (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[CrossRef]

Opt. Appl. (2)

H. V. Bogatyryova, Ch. V. Felde, and P. V. Polyanskii, “Referenceless testing of vortex optical beams,” Opt. Appl. 33, 695–708 (2003).

J. Masajada, “Gaussian beams with optical vortex of charge 2- and 3-diffraction by a half-plane and slit,” Opt. Appl. 30, 248–256 (2000).

Opt. Commun. (4)

J. Masajada, “Half-plane diffraction in the case of Gaussian beams containing an optical vortex,” Opt. Commun. 175, 289–294 (2000).
[CrossRef]

A. Ya. Bekshaev and S. V. Sviridova, “Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity,” Opt. Commun. 283, 4866–4876 (2010).
[CrossRef]

Z. Mei and D. Zhao, “Generalized beam propagation factor of hard-edged diffracted controllable dark-hollow beams,” Opt. Commun. 263, 261–266 (2006).
[CrossRef]

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “Transformation of higher-order optical vortices upon focusing by an astigmatic lens,” Opt. Commun. 241, 237–247 (2004).
[CrossRef]

Opt. Express (2)

Opt. Laser Technol. (1)

P. Liu and B. Lü, “Propagation of Gaussian background vortex beams diffracted at a half-plane screen,” Opt. Laser Technol. 40, 227–234 (2008).
[CrossRef]

Opt. Lasers Eng. (1)

D. P. Ghai, P. Senthilkumaran, and R. S. Sirohi, “Single-slit diffraction of an optical beam with phase singularity,” Opt. Lasers Eng. 47, 123–126 (2009).
[CrossRef]

Opt. Lett. (4)

Opt. Spectrosc. (1)

Yu. A. Anan’ev and A. Ya. Bekshaev, “Theory of intensity moments for arbitrary light beams,” Opt. Spectrosc. 76, 558–568 (1994).

Optik (1)

M. J. Bastiaans, “Second-order moments of the Wigner distribution function in first-order optical systems,” Optik 88, 163–168 (1991).

Phys. Rev. Lett. (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]

V. Garcés-Chavéz, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Proc. SPIE (2)

Ch. V. Felde, “Diffraction diagnostics of phase singularities in optical fields,” Proc. SPIE 5477, 67–76 (2004).
[CrossRef]

A. Bekshaev and K. A. Mohammed, “Transverse energy redistribution upon edge diffraction of a paraxial laser beam with optical vortex,” Proc. SPIE 9066, 906602 (2013).
[CrossRef]

Prog. Opt. (4)

D. Dragoman, “The Wigner distribution function in optics and optoelectronics,” Prog. Opt. 37, 1–56 (1997).
[CrossRef]

L. Allen, M. J. Padgett, and M. Babiker, “Orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

Prog. Quantum Electron. (1)

P. M. Mejias, R. Martinez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65–130 (2002).
[CrossRef]

Rep. Prog. Phys. (1)

R. W. Bowman and M. J. Padgett, “Optical trapping and binding,” Rep. Prog. Phys. 76, 026401 (2013).
[CrossRef]

Other (3)

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

Yu. A. Anan’ev, Laser Resonators and the Beam Divergence Problem (Adam Hilger, 1992).

M. Abramovitz and I. Stegun, eds., Handbook of Mathematical Functions, Vol. 55 of Applied Mathematics Series (National Bureau of Standards, 1964).

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.


Metrics