Abstract

Two forms of the transverse energy circulation within plane-polarized paraxial light beams are specified: one inherent in wave-front singularities (optical vortices) and the other peculiar to astigmatism and asymmetry of beams with a smooth wave front. As quantitative measures of these energy flow components, the concepts of vortex and asymmetry parts of a beam’s orbital angular momentum are introduced and their definitions are proposed on the basis of beam intensity moments. The properties and physical meaning of these concepts are analyzed, and their use for the study of transformations of optical vortices is demonstrated.

© 2003 Optical Society of America

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  1. M. V. Vasnetsov, K. Staliunas, eds., Optical Vortices (Nova Science, New York, 1999).
  2. L. Allen, M. J. Padgett, M. Babiker, “Orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
    [CrossRef]
  3. M. S. Soskin, M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
    [CrossRef]
  4. Yu. A. Anan’ev, Laser Resonators and the Beam Divergence Problem (Hilger, London, 1992).
  5. M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. Heckenberg, “Optical angular momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
    [CrossRef] [PubMed]
  6. L. Allen, M. W. Beijersbergen, R. J. C. Spreuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  7. M. J. Padgett, L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
    [CrossRef]
  8. M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
    [CrossRef]
  9. G. Molina-Terriza, E. M. Wright, L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26, 163–165 (2001).
    [CrossRef]
  10. A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of the orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Letters 75, 127–130 (2002).
    [CrossRef]
  11. A. Ya. Bekshaev, “Mechanical properties of the light wave with phase singularity,” in Fourth International Conference on Correlation Optics, O. V. Angelsky, ed., Proc. SPIE3904, 131–139 (1999).
    [CrossRef]
  12. A. Ya. Bekshaev, A. Yu. Popov, “Measurement of the orbital angular momentum of an optical beam with the help of space-angle intensity moments,” in Selected Papers from Fifth International Conference on Correlation Optics, O. V. Angelsky, ed., Proc. SPIE4607, 90–98 (2002).
    [CrossRef]
  13. M. J. Bastiaans, “Wigner distribution function and its application to first-order optics,” J. Opt. Soc. Am. 69, 1710–1716 (1979).
    [CrossRef]
  14. Yu. A. Anan’ev, A. Ya. Bekshaev, “Theory of intensity moments for arbitrary light beams,” Opt. Spectrosc. 76, 558–568 (1994).
  15. E. G. Abramochkin, V. G. Volostnikov, “Light beams with phase singularities: some aspects of analysis and synthesis,” in 2nd International Conference on Singular Optics (Optical Vortices): Fundamentals and Applications, M. S. Soskin, M. V. Vasnetsov, eds., Proc. SPIE4403, 43–48 (2001).
    [CrossRef]
  16. A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (4) ( 2002).
    [CrossRef] [PubMed]
  17. G. Molina-Terriza, J. P. Torres, L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (4) ( 2002).
    [CrossRef] [PubMed]
  18. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (4) ( 2002).
    [CrossRef] [PubMed]
  19. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
    [CrossRef]
  20. A. Ya. Bekshaev, “Intensity moments of the laser beam formed by superposition of Hermit-Gaussian modes,” Fotoelektronika (Odessa) 8, 22–25 (1999); in Russian.
  21. R. Bellman, Introduction to Matrix Analysis (McGraw-Hill, New York, 1960).
  22. A. E. Siegman, “Handbook of laser beam propagation and beam quality formulas using the spatial-frequency and intensity-moment analysis,” (draft version, 7/2/1991). Manuscript available from A. E. Siegman, Stanford University, 550 Junipero Serra Blvd., Stanford, Calif. 94305; e-mail, siegman@stanford.edu.
  23. I. Freund, N. Shvartsman, V. Freilikher, “Optical dislocation network in highly random media,” Opt. Commun. 101, 247–264 (1993).
    [CrossRef]
  24. M. S. Soskin, M. V. Vasnetsov, I. V. Basistiy, “Optical wavefront dislocations,” in International Conference on Holography and Correlation Optics, O. V. Angelsky, ed., Proc. SPIE2647, 57–62 (1995).
    [CrossRef]
  25. A. Ya. Bekshaev, A. Yu. Popov, “Optical system for Laguerre-Gaussian/Hermite-Gaussian mode conversion,” in 2nd International Conference on Singular Optics (Optical Vortices): Fundamentals and Applications, M. S. Soskin, M. V. Vasnetsov, eds., Proc. SPIE4403, 296–301 (2001).
  26. I. V. Basistiy, L. V. Kreminskaya, I. G. Marienko, M. S. Soskin, M. V. Vasnetsov, “Experimental observation of rotation and diffraction of a “singular” light beam,” in International Conference on Singular Optics, M. S. Soskin, ed., Proc. SPIE3487, 34–38 (1998).
    [CrossRef]
  27. I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
    [CrossRef]
  28. G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
    [CrossRef]
  29. N. S. Kazak, N. A. Khilo, A. A. Ryzhevich, “Generation of Bessel light beams under the conditions of internal conical refraction,” Quantum Electron. 29, 1020–1024 (1999).
    [CrossRef]
  30. J. Arlt, T. Hitomi, K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549–554 (2000).
    [CrossRef]

2002 (4)

A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of the orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Letters 75, 127–130 (2002).
[CrossRef]

A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (4) ( 2002).
[CrossRef] [PubMed]

G. Molina-Terriza, J. P. Torres, L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (4) ( 2002).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (4) ( 2002).
[CrossRef] [PubMed]

2001 (2)

2000 (1)

J. Arlt, T. Hitomi, K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549–554 (2000).
[CrossRef]

1999 (3)

N. S. Kazak, N. A. Khilo, A. A. Ryzhevich, “Generation of Bessel light beams under the conditions of internal conical refraction,” Quantum Electron. 29, 1020–1024 (1999).
[CrossRef]

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

A. Ya. Bekshaev, “Intensity moments of the laser beam formed by superposition of Hermit-Gaussian modes,” Fotoelektronika (Odessa) 8, 22–25 (1999); in Russian.

1997 (1)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

1996 (1)

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. Heckenberg, “Optical angular momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

1995 (1)

M. J. Padgett, L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[CrossRef]

1994 (1)

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

1993 (4)

I. Freund, N. Shvartsman, V. Freilikher, “Optical dislocation network in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

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

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

1992 (1)

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

1979 (1)

Abramochkin, E. G.

E. G. Abramochkin, V. G. Volostnikov, “Light beams with phase singularities: some aspects of analysis and synthesis,” in 2nd International Conference on Singular Optics (Optical Vortices): Fundamentals and Applications, M. S. Soskin, M. V. Vasnetsov, eds., Proc. SPIE4403, 43–48 (2001).
[CrossRef]

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (4) ( 2002).
[CrossRef] [PubMed]

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

M. J. Padgett, L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

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

Anan’ev, Yu. A.

Yu. A. Anan’ev, 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 (Hilger, London, 1992).

Arlt, J.

J. Arlt, T. Hitomi, K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549–554 (2000).
[CrossRef]

Babiker, M.

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

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (4) ( 2002).
[CrossRef] [PubMed]

Basistiy, I. V.

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

I. V. Basistiy, L. V. Kreminskaya, I. G. Marienko, M. S. Soskin, M. V. Vasnetsov, “Experimental observation of rotation and diffraction of a “singular” light beam,” in International Conference on Singular Optics, M. S. Soskin, ed., Proc. SPIE3487, 34–38 (1998).
[CrossRef]

M. S. Soskin, M. V. Vasnetsov, I. V. Basistiy, “Optical wavefront dislocations,” in International Conference on Holography and Correlation Optics, O. V. Angelsky, ed., Proc. SPIE2647, 57–62 (1995).
[CrossRef]

Bastiaans, M. J.

Bazhenov, V. Yu.

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

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

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

Bekshaev, A. Ya.

A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of the orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Letters 75, 127–130 (2002).
[CrossRef]

A. Ya. Bekshaev, “Intensity moments of the laser beam formed by superposition of Hermit-Gaussian modes,” Fotoelektronika (Odessa) 8, 22–25 (1999); in Russian.

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

A. Ya. Bekshaev, “Mechanical properties of the light wave with phase singularity,” in Fourth International Conference on Correlation Optics, O. V. Angelsky, ed., Proc. SPIE3904, 131–139 (1999).
[CrossRef]

A. Ya. Bekshaev, A. Yu. Popov, “Measurement of the orbital angular momentum of an optical beam with the help of space-angle intensity moments,” in Selected Papers from Fifth International Conference on Correlation Optics, O. V. Angelsky, ed., Proc. SPIE4607, 90–98 (2002).
[CrossRef]

A. Ya. Bekshaev, A. Yu. Popov, “Optical system for Laguerre-Gaussian/Hermite-Gaussian mode conversion,” in 2nd International Conference on Singular Optics (Optical Vortices): Fundamentals and Applications, M. S. Soskin, M. V. Vasnetsov, eds., Proc. SPIE4403, 296–301 (2001).

Bellman, R.

R. Bellman, Introduction to Matrix Analysis (McGraw-Hill, New York, 1960).

Courtial, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (4) ( 2002).
[CrossRef] [PubMed]

Denisenko, V. G.

A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of the orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Letters 75, 127–130 (2002).
[CrossRef]

Dholakia, K.

J. Arlt, T. Hitomi, K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549–554 (2000).
[CrossRef]

Enger, J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. Heckenberg, “Optical angular momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (4) ( 2002).
[CrossRef] [PubMed]

Freilikher, V.

I. Freund, N. Shvartsman, V. Freilikher, “Optical dislocation network in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

Freund, I.

I. Freund, N. Shvartsman, V. Freilikher, “Optical dislocation network in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

Friese, M. E. J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. Heckenberg, “Optical angular momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

Heckenberg, N.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. Heckenberg, “Optical angular momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

Hitomi, T.

J. Arlt, T. Hitomi, K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549–554 (2000).
[CrossRef]

Indebetouw, G.

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

Kazak, N. S.

N. S. Kazak, N. A. Khilo, A. A. Ryzhevich, “Generation of Bessel light beams under the conditions of internal conical refraction,” Quantum Electron. 29, 1020–1024 (1999).
[CrossRef]

Khilo, N. A.

N. S. Kazak, N. A. Khilo, A. A. Ryzhevich, “Generation of Bessel light beams under the conditions of internal conical refraction,” Quantum Electron. 29, 1020–1024 (1999).
[CrossRef]

Kreminskaya, L. V.

I. V. Basistiy, L. V. Kreminskaya, I. G. Marienko, M. S. Soskin, M. V. Vasnetsov, “Experimental observation of rotation and diffraction of a “singular” light beam,” in International Conference on Singular Optics, M. S. Soskin, ed., Proc. SPIE3487, 34–38 (1998).
[CrossRef]

Leach, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (4) ( 2002).
[CrossRef] [PubMed]

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (4) ( 2002).
[CrossRef] [PubMed]

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

Marienko, I. G.

I. V. Basistiy, L. V. Kreminskaya, I. G. Marienko, M. S. Soskin, M. V. Vasnetsov, “Experimental observation of rotation and diffraction of a “singular” light beam,” in International Conference on Singular Optics, M. S. Soskin, ed., Proc. SPIE3487, 34–38 (1998).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (4) ( 2002).
[CrossRef] [PubMed]

G. Molina-Terriza, E. M. Wright, L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26, 163–165 (2001).
[CrossRef]

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (4) ( 2002).
[CrossRef] [PubMed]

Padgett, M. J.

A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (4) ( 2002).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (4) ( 2002).
[CrossRef] [PubMed]

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

M. J. Padgett, L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[CrossRef]

Popov, A. Yu.

A. Ya. Bekshaev, A. Yu. Popov, “Measurement of the orbital angular momentum of an optical beam with the help of space-angle intensity moments,” in Selected Papers from Fifth International Conference on Correlation Optics, O. V. Angelsky, ed., Proc. SPIE4607, 90–98 (2002).
[CrossRef]

A. Ya. Bekshaev, A. Yu. Popov, “Optical system for Laguerre-Gaussian/Hermite-Gaussian mode conversion,” in 2nd International Conference on Singular Optics (Optical Vortices): Fundamentals and Applications, M. S. Soskin, M. V. Vasnetsov, eds., Proc. SPIE4403, 296–301 (2001).

Rubinsztein-Dunlop, H.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. Heckenberg, “Optical angular momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

Ryzhevich, A. A.

N. S. Kazak, N. A. Khilo, A. A. Ryzhevich, “Generation of Bessel light beams under the conditions of internal conical refraction,” Quantum Electron. 29, 1020–1024 (1999).
[CrossRef]

Shvartsman, N.

I. Freund, N. Shvartsman, V. Freilikher, “Optical dislocation network in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

Siegman, A. E.

A. E. Siegman, “Handbook of laser beam propagation and beam quality formulas using the spatial-frequency and intensity-moment analysis,” (draft version, 7/2/1991). Manuscript available from A. E. Siegman, Stanford University, 550 Junipero Serra Blvd., Stanford, Calif. 94305; e-mail, siegman@stanford.edu.

Soskin, M. S.

A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of the orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Letters 75, 127–130 (2002).
[CrossRef]

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

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

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

I. V. Basistiy, L. V. Kreminskaya, I. G. Marienko, M. S. Soskin, M. V. Vasnetsov, “Experimental observation of rotation and diffraction of a “singular” light beam,” in International Conference on Singular Optics, M. S. Soskin, ed., Proc. SPIE3487, 34–38 (1998).
[CrossRef]

M. S. Soskin, M. V. Vasnetsov, I. V. Basistiy, “Optical wavefront dislocations,” in International Conference on Holography and Correlation Optics, O. V. Angelsky, ed., Proc. SPIE2647, 57–62 (1995).
[CrossRef]

Spreuw, R. J. C.

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

Torner, L.

G. Molina-Terriza, J. P. Torres, L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (4) ( 2002).
[CrossRef] [PubMed]

G. Molina-Terriza, E. M. Wright, L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26, 163–165 (2001).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (4) ( 2002).
[CrossRef] [PubMed]

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

Vasnetsov, M. V.

A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of the orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Letters 75, 127–130 (2002).
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M. S. Soskin, M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
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M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
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I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
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I. V. Basistiy, L. V. Kreminskaya, I. G. Marienko, M. S. Soskin, M. V. Vasnetsov, “Experimental observation of rotation and diffraction of a “singular” light beam,” in International Conference on Singular Optics, M. S. Soskin, ed., Proc. SPIE3487, 34–38 (1998).
[CrossRef]

M. S. Soskin, M. V. Vasnetsov, I. V. Basistiy, “Optical wavefront dislocations,” in International Conference on Holography and Correlation Optics, O. V. Angelsky, ed., Proc. SPIE2647, 57–62 (1995).
[CrossRef]

Volostnikov, V. G.

E. G. Abramochkin, V. G. Volostnikov, “Light beams with phase singularities: some aspects of analysis and synthesis,” in 2nd International Conference on Singular Optics (Optical Vortices): Fundamentals and Applications, M. S. Soskin, M. V. Vasnetsov, eds., Proc. SPIE4403, 43–48 (2001).
[CrossRef]

Woerdman, J. P.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
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L. Allen, M. W. Beijersbergen, R. J. C. Spreuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian modes,” Phys. Rev. A 45, 8185–8189 (1992).
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Appl. Phys. B (1)

J. Arlt, T. Hitomi, K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549–554 (2000).
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Fotoelektronika (Odessa) (1)

A. Ya. Bekshaev, “Intensity moments of the laser beam formed by superposition of Hermit-Gaussian modes,” Fotoelektronika (Odessa) 8, 22–25 (1999); in Russian.

J. Mod. Opt. (1)

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

JETP Letters (1)

A. Ya. Bekshaev, M. V. Vasnetsov, V. G. Denisenko, M. S. Soskin, “Transformation of the orbital angular momentum of a beam with optical vortex in an astigmatic optical system,” JETP Letters 75, 127–130 (2002).
[CrossRef]

Opt. Commun. (4)

M. J. Padgett, L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[CrossRef]

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

I. Freund, N. Shvartsman, V. Freilikher, “Optical dislocation network in highly random media,” Opt. Commun. 101, 247–264 (1993).
[CrossRef]

Opt. Lett. (1)

Opt. Spectrosc. (1)

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

Phys. Rev. A (3)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, N. Heckenberg, “Optical angular momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593–1596 (1996).
[CrossRef] [PubMed]

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

Phys. Rev. Lett. (3)

A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601 (4) ( 2002).
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G. Molina-Terriza, J. P. Torres, L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (4) ( 2002).
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J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (4) ( 2002).
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Prog. Opt. (2)

L. Allen, M. J. Padgett, M. Babiker, “Orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
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M. S. Soskin, M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

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N. S. Kazak, N. A. Khilo, A. A. Ryzhevich, “Generation of Bessel light beams under the conditions of internal conical refraction,” Quantum Electron. 29, 1020–1024 (1999).
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Other (10)

M. S. Soskin, M. V. Vasnetsov, I. V. Basistiy, “Optical wavefront dislocations,” in International Conference on Holography and Correlation Optics, O. V. Angelsky, ed., Proc. SPIE2647, 57–62 (1995).
[CrossRef]

A. Ya. Bekshaev, A. Yu. Popov, “Optical system for Laguerre-Gaussian/Hermite-Gaussian mode conversion,” in 2nd International Conference on Singular Optics (Optical Vortices): Fundamentals and Applications, M. S. Soskin, M. V. Vasnetsov, eds., Proc. SPIE4403, 296–301 (2001).

I. V. Basistiy, L. V. Kreminskaya, I. G. Marienko, M. S. Soskin, M. V. Vasnetsov, “Experimental observation of rotation and diffraction of a “singular” light beam,” in International Conference on Singular Optics, M. S. Soskin, ed., Proc. SPIE3487, 34–38 (1998).
[CrossRef]

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

M. V. Vasnetsov, K. Staliunas, eds., Optical Vortices (Nova Science, New York, 1999).

R. Bellman, Introduction to Matrix Analysis (McGraw-Hill, New York, 1960).

A. E. Siegman, “Handbook of laser beam propagation and beam quality formulas using the spatial-frequency and intensity-moment analysis,” (draft version, 7/2/1991). Manuscript available from A. E. Siegman, Stanford University, 550 Junipero Serra Blvd., Stanford, Calif. 94305; e-mail, siegman@stanford.edu.

E. G. Abramochkin, V. G. Volostnikov, “Light beams with phase singularities: some aspects of analysis and synthesis,” in 2nd International Conference on Singular Optics (Optical Vortices): Fundamentals and Applications, M. S. Soskin, M. V. Vasnetsov, eds., Proc. SPIE4403, 43–48 (2001).
[CrossRef]

A. Ya. Bekshaev, “Mechanical properties of the light wave with phase singularity,” in Fourth International Conference on Correlation Optics, O. V. Angelsky, ed., Proc. SPIE3904, 131–139 (1999).
[CrossRef]

A. Ya. Bekshaev, A. Yu. Popov, “Measurement of the orbital angular momentum of an optical beam with the help of space-angle intensity moments,” in Selected Papers from Fifth International Conference on Correlation Optics, O. V. Angelsky, ed., Proc. SPIE4607, 90–98 (2002).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Evolution of the beam with anisotropic screw wave-front dislocation (Subsection 4.A), with γ=π/6 [see Eq. (26)]. (a) The initial beam pattern (z=0); (b) near field (z<zR); (c) transient region (zzR); (d) far field. The beam shape does not change, but scaling varies.

Fig. 2
Fig. 2

Evolution of the LG01 mode after passing an astigmatic lens (Subsection 4.B) with fx=200 cm, fy=80 cm (a) immediately behind the lens (the intensity distribution retains circular symmetry); (b) plane of the first OV sign inversion; (c), (d) between the first and second inversion planes; (e) second OV inversion plane; (f) far field. At z80 cm (b) and z200 cm (e), a screw WF dislocation and the VOAM disappear; in (c) and (d) the VOAM sign is opposite to the initial one but the total OAM remains constant due to the high value of the AOAM, which corresponds to relatively quick rotation of the beam pattern [∼80% of the total intensity-ellipse revolution happens between the inversion planes (b) and (e)].

Fig. 3
Fig. 3

Beam pattern variation during the propagation of the astigmatic LG01 mode (Subsection 4.C) with the initial beam sizes bx=0.1 cm and by=0.0577 cm. (a), (b) Near field; (c)–(e) transient region; (f) far field.

Fig. 4
Fig. 4

Beam pattern variation for the LG01 mode transformed by the Gaussian diaphragm (Subsection 4.D) with d=0.07 cm. (a) Initial spot shape immediately behind the diaphragm (beam sizes bx=0.1 cm, by=0.0577 cm); (b) near field; (c)–(e) transient region; (f) far field. In (d)–(f) the beam pattern transforms as it changes direction of rotation in contrast to the monotonic rotation of the intensity ellipse.

Fig. 5
Fig. 5

Spot evolution for the Gaussian–LG01 mode superposition (Subsection 4.E) for b0=b=0.1 cm, A/B=tgγ=0.3. The beam shape is invariant except for scaling and rotation.

Equations (61)

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M=M11M12M˜12M22,
M12(z)=mxxmxymyxmyy
Λ=Φc2 (mxy-myx)=-Φc2Sp(M12J)
=Φ2c2Sp[(M˜12-M12)J],
MS=M+R0R˜0.
ΛS=Λ+Φc2 (x0qy0-y0qx0)=Λ+Φc2 |r0×q0|.
upl(r)=1b8Φcp!(p+l)!rb|l|Lp|l|r2b2×exp-r22b2+ilϕ,
M=M11M12M˜12M22=12Qb2Ilk  J-lk  JQk2b2  I,
Λ=Φc2k l.
u(r)=8kΦc (det Di)1/4expik2 (rDr),
M=M11M12M˜12M22=12kDi-1Di-1DrDrDi-1DrDi-1Dr+Di,
Λ=Φ2c2Sp[(DrDi-1-Di-1Dr)J].
M12(Ω)=M12-M11Ω,
ΔΛ(Ω)=Φc2Sp(M11ΩJ).
Ω=M11-1M12+JSp(M12M11J)Sp M11.
M12(Ω)=-JSp(M12M11J)Sp M11=-M11M˜21-M12M11Sp M11.
Λv=-2Φc2Sp(M12M11J)Sp M11.
Λa=Λ-Λv=Φc22 Sp(M12M11J)Sp M11-Sp(M12J).
M11(z)=M11+(M12+M˜12)z+M22z2,
M12(z)=M12+M22z,M22(z)=M22.
Λv(z)
=-2Φc2Sp{[M12M11+(M122+M22M11)z+M22M12z2]J}Sp[M11+(M12+M˜12)z+M22z2].
Λv()=-2Φc2Sp(M22M12J)SpM22,
Λv=2Φc2ayymxy-axxmyx+axy(mxx-myy)axx+ayy,
Λa=Φc2(axx-ayy)(mxy+myx)-2axy(mxx-myy)axx+ayy.
(rM11-1r)=ayyx2+axxy2-2axyxydet M11=1.
θ=12arccotaxx-ayy2axy,
dθdz=(axx-ayy)(mxy+myx)-2axy(mxx-myy)(Sp M11)2-4 det M11.
Λa=Φc2(Sp M11)2-4 det M11Sp M11dθdz,
Λa=Φc2(b12-b22)2b12+b22dθdz=Φc2 b1242-2dθdz,
A-A+=cos γ-sin γcos γ+sin γ,
u(r)=4b2Φc (x cos γ+iy sin γ)exp-x2+y22b2.
M11(z)=b221+z2zR2(I+S),
M12(z)=12kzzR (I+S)+Jsin 2γ,
M22(z)=12kzR (I+S),
Λ(z)=Λv(z)=Φc2ksin 2γ,Λa(z)=0.
Λ(z)=Φc2k l,
Λv(z)=Φlc2kzzR2+1-zfx1-zfyzzR2+121-zfx2+121-zfy2,
Λa(z)=Φlc2kzfx-zfy22zzR2+1-zfx2+1-zfy2.
u(r)=2bxby2Φcxbx+i ybyexp-x22bx2-y22by2.
Λ(z)=Φc2k12bxby+bybx,
Λv(z)=2Φc2kbxby+bybx-1,
Λa(z)=Φc2k(bx2-by2)22bxby(bx2+by2).
u(r)(x+iy)exp-x22bx2-y22by2bxu10(x, y)+ibyu01(x, y),
Λa(z)
=Φc2k(bx2-by2)23+z2k2bx2by23(bx4+by4)+2bx2by2+z2k2bx2by2+by2bx2+6,
Λv(z)
=Φc2k8bx2by2+z2k23(bx4+by4)+2bx2by2+z2k2bx2by2+by2bx2+6.
u(r)=A exp-x2+y22b02+Bb (x+iy)exp-x2+y22b2,
M11=A2b04+2B2b42(A2b02+B2b2)  I,
M12=B2b22k(A2b02+B2b2)  J,
M22=A2+2B22k2(A2b02+B2b2)  I.
Λ=Λv=Φc2kB2b2A2b02+B2b2=ΦLGc2k,
M11(z)=b221+z2zR2(1+cos2 γ)I,
M12(z)=12kzzR (1+cos2 γ)I+Jcos2 γ,
M22(z)=1+cos2 γ2k2b2  I,
Λ(z)=Λv(z)=Φc2kcos2 γ.
x0=b sin γ cos γ,y0=0, qx0=0,
qy0=sin γ cos γkb
Λ(z)=Φc2kcos4 γ,Λv(z)=Φc2k2 cos6 γ1+cos4 γ,
Λa(z)=Φc2k(sin γ cos γ)41+cos4 γ.

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