Abstract

In this work we investigate the behavior of the instantaneous Poynting vector of symmetrical paraxial laser beams, namely the modification of the instantaneous Poynting vector and the radiation pattern during propagation in free space for a variety of such beams. As an example, we have investigated in detail the behavior of the instantaneous Poynting vector and the radiation pattern of the paraxial Gaussian and Bessel beams.

© 2012 Optical Society of America

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  1. 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.
  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]
  3. M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121, 36–40 (1995).
    [CrossRef]
  4. L. Allen and M. J. Padgett, “The Poynting vector in Laguerre-Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000).
    [CrossRef]
  5. K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B 4, S82–S89 (2002).
    [CrossRef]
  6. A. V. Novitsky and D. V. Novitsky, “Nondiffracting electromagnetic fields in inhomogeneous isotropic media,” J. Phys. A: Math. Gen. 39, 5227–5231 (2006).
    [CrossRef]
  7. H. I. Sztul and R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express 16, 9411–9416 (2008).
    [CrossRef]
  8. R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
    [CrossRef]
  9. M. W. Beijersbergen, L. Allen, H. E. L. O. Van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and the transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
    [CrossRef]
  10. G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
    [CrossRef]
  11. C. Gao, X. Qi, Y. Liu, J. Xin, and L. Wang, “Sorting and detecting orbital angular momentum states by using a Dove prism embedded Mach–Zehnder interferometer and amplitude gratings,” Opt. Commun. 284, 48–51 (2011).
    [CrossRef]
  12. G. Zhou, R. Chen, and J. Chen, “Propagation of non-paraxial nonsymmetrical vector Gaussian beam,” Opt. Commun. 259, 32–39 (2006).
    [CrossRef]
  13. A. Bekshaev, K. Bliokh, and M. Soskin, “Internal flows and energy circulation in light beams,” J. Opt. 13, 053001 (2011).
    [CrossRef]
  14. A. V. Novitsky and D. V. Novitsky, “Change of the size of vector Bessel beam rings under reflection,” Opt. Commun. 281, 2727–2734 (2008).
    [CrossRef]
  15. I. A. Litvin, A. Dudley, and A. Forbes, “Poynting vector and orbital angular momentum density of superpositions of Bessel beams,” Opt. Express 19, 16760–16771 (2011).
    [CrossRef]
  16. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  17. B. Thidé1, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701(2007).
    [CrossRef]
  18. I. Mokhun and R. Khrobatin, “Shift of application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A 10, 064015 (2008).
    [CrossRef]
  19. I. Mokhun, A. Mokhun, Ju. Viktorovskaya, D. Cojoc, O. Angelsky, and E. Di Fabrizio, “Orbital angular momentum of inhomogeneous electromagnetic field produced by polarized optical beams,” Proc. SPIE 5514, 652–662, (2004).
    [CrossRef]
  20. R. Khrobatin, I. Mokhon, and J. Viktorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9, 182–186 (2008).
    [CrossRef]
  21. I. A. Litvin, M. G. McLarena, and A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
    [CrossRef]
  22. G. Rodríguez-Zurita, N. I. Toto-Arellano, M. L. Arroyo-Carrasco, C. Meneses-Fabian, and J. F. Vazquez Castillo, “Experimental observation of spiral patterns by obstruction of Bessel beams: application of single shot phase-shifting interferometry,” in Proceedings of IEEE Conference on Lasers and Electro-Optics/Pacific Rim (IEEE, 2009), pp. 1–2.
  23. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  24. M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
    [CrossRef]

2011 (3)

C. Gao, X. Qi, Y. Liu, J. Xin, and L. Wang, “Sorting and detecting orbital angular momentum states by using a Dove prism embedded Mach–Zehnder interferometer and amplitude gratings,” Opt. Commun. 284, 48–51 (2011).
[CrossRef]

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

I. A. Litvin, A. Dudley, and A. Forbes, “Poynting vector and orbital angular momentum density of superpositions of Bessel beams,” Opt. Express 19, 16760–16771 (2011).
[CrossRef]

2010 (1)

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

2009 (1)

I. A. Litvin, M. G. McLarena, and A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
[CrossRef]

2008 (4)

I. Mokhun and R. Khrobatin, “Shift of application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A 10, 064015 (2008).
[CrossRef]

A. V. Novitsky and D. V. Novitsky, “Change of the size of vector Bessel beam rings under reflection,” Opt. Commun. 281, 2727–2734 (2008).
[CrossRef]

R. Khrobatin, I. Mokhon, and J. Viktorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9, 182–186 (2008).
[CrossRef]

H. I. Sztul and R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express 16, 9411–9416 (2008).
[CrossRef]

2007 (1)

B. Thidé1, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701(2007).
[CrossRef]

2006 (2)

A. V. Novitsky and D. V. Novitsky, “Nondiffracting electromagnetic fields in inhomogeneous isotropic media,” J. Phys. A: Math. Gen. 39, 5227–5231 (2006).
[CrossRef]

G. Zhou, R. Chen, and J. Chen, “Propagation of non-paraxial nonsymmetrical vector Gaussian beam,” Opt. Commun. 259, 32–39 (2006).
[CrossRef]

2004 (1)

I. Mokhun, A. Mokhun, Ju. Viktorovskaya, D. Cojoc, O. Angelsky, and E. Di Fabrizio, “Orbital angular momentum of inhomogeneous electromagnetic field produced by polarized optical beams,” Proc. SPIE 5514, 652–662, (2004).
[CrossRef]

2002 (1)

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B 4, S82–S89 (2002).
[CrossRef]

2000 (1)

L. Allen and M. J. Padgett, “The Poynting vector in Laguerre-Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000).
[CrossRef]

1995 (1)

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

1993 (1)

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

1992 (1)

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]

1979 (1)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

1975 (1)

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

1936 (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[CrossRef]

Alfano, R. R.

Allen, L.

L. Allen and M. J. Padgett, “The Poynting vector in Laguerre-Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000).
[CrossRef]

M. J. Padgett and 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, and J. P. Woerdman, “Astigmatic laser mode converters and the transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
[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]

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.

Arlt, J.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B 4, S82–S89 (2002).
[CrossRef]

Arroyo-Carrasco, M. L.

G. Rodríguez-Zurita, N. I. Toto-Arellano, M. L. Arroyo-Carrasco, C. Meneses-Fabian, and J. F. Vazquez Castillo, “Experimental observation of spiral patterns by obstruction of Bessel beams: application of single shot phase-shifting interferometry,” in Proceedings of IEEE Conference on Lasers and Electro-Optics/Pacific Rim (IEEE, 2009), pp. 1–2.

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.

Beijersbergen, M. W.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

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

Bekshaev, A.

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

Bergman, J.

B. Thidé1, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701(2007).
[CrossRef]

Berkhout, G. C. G.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Beth, R. A.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[CrossRef]

Bliokh, K.

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

Carozzi, T. D.

B. Thidé1, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701(2007).
[CrossRef]

Chávez-Cerda, S.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B 4, S82–S89 (2002).
[CrossRef]

Chen, J.

G. Zhou, R. Chen, and J. Chen, “Propagation of non-paraxial nonsymmetrical vector Gaussian beam,” Opt. Commun. 259, 32–39 (2006).
[CrossRef]

Chen, R.

G. Zhou, R. Chen, and J. Chen, “Propagation of non-paraxial nonsymmetrical vector Gaussian beam,” Opt. Commun. 259, 32–39 (2006).
[CrossRef]

Courtial, J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

Dholakia, K.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B 4, S82–S89 (2002).
[CrossRef]

Dudley, A.

Forbes, A.

I. A. Litvin, A. Dudley, and A. Forbes, “Poynting vector and orbital angular momentum density of superpositions of Bessel beams,” Opt. Express 19, 16760–16771 (2011).
[CrossRef]

I. A. Litvin, M. G. McLarena, and A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
[CrossRef]

Gao, C.

C. Gao, X. Qi, Y. Liu, J. Xin, and L. Wang, “Sorting and detecting orbital angular momentum states by using a Dove prism embedded Mach–Zehnder interferometer and amplitude gratings,” Opt. Commun. 284, 48–51 (2011).
[CrossRef]

Garcés-Chávez, V.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B 4, S82–S89 (2002).
[CrossRef]

Ibragimov, N. H.

B. Thidé1, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701(2007).
[CrossRef]

Istomin, Ya. N.

B. Thidé1, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701(2007).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Khamitova, R.

B. Thidé1, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701(2007).
[CrossRef]

Khrobatin, R.

I. Mokhun and R. Khrobatin, “Shift of application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A 10, 064015 (2008).
[CrossRef]

R. Khrobatin, I. Mokhon, and J. Viktorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9, 182–186 (2008).
[CrossRef]

Lavery, M. P. J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Lax, M.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Litvin, I. A.

I. A. Litvin, A. Dudley, and A. Forbes, “Poynting vector and orbital angular momentum density of superpositions of Bessel beams,” Opt. Express 19, 16760–16771 (2011).
[CrossRef]

I. A. Litvin, M. G. McLarena, and A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
[CrossRef]

Liu, Y.

C. Gao, X. Qi, Y. Liu, J. Xin, and L. Wang, “Sorting and detecting orbital angular momentum states by using a Dove prism embedded Mach–Zehnder interferometer and amplitude gratings,” Opt. Commun. 284, 48–51 (2011).
[CrossRef]

Louisell, W. H.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

McKnight, W. B.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

McLarena, M. G.

I. A. Litvin, M. G. McLarena, and A. Forbes, “A conical wave approach to calculating Bessel–Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
[CrossRef]

Meneses-Fabian, C.

G. Rodríguez-Zurita, N. I. Toto-Arellano, M. L. Arroyo-Carrasco, C. Meneses-Fabian, and J. F. Vazquez Castillo, “Experimental observation of spiral patterns by obstruction of Bessel beams: application of single shot phase-shifting interferometry,” in Proceedings of IEEE Conference on Lasers and Electro-Optics/Pacific Rim (IEEE, 2009), pp. 1–2.

Mokhon, I.

R. Khrobatin, I. Mokhon, and J. Viktorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9, 182–186 (2008).
[CrossRef]

Mokhun, I.

I. Mokhun and R. Khrobatin, “Shift of application point of angular momentum in the area of elementary polarization singularity,” J. Opt. A 10, 064015 (2008).
[CrossRef]

Novitsky, A. V.

A. V. Novitsky and D. V. Novitsky, “Change of the size of vector Bessel beam rings under reflection,” Opt. Commun. 281, 2727–2734 (2008).
[CrossRef]

A. V. Novitsky and D. V. Novitsky, “Nondiffracting electromagnetic fields in inhomogeneous isotropic media,” J. Phys. A: Math. Gen. 39, 5227–5231 (2006).
[CrossRef]

Novitsky, D. V.

A. V. Novitsky and D. V. Novitsky, “Change of the size of vector Bessel beam rings under reflection,” Opt. Commun. 281, 2727–2734 (2008).
[CrossRef]

A. V. Novitsky and D. V. Novitsky, “Nondiffracting electromagnetic fields in inhomogeneous isotropic media,” J. Phys. A: Math. Gen. 39, 5227–5231 (2006).
[CrossRef]

Padgett, M. J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

L. Allen and M. J. Padgett, “The Poynting vector in Laguerre-Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000).
[CrossRef]

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

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.

Palmer, K.

B. Thidé1, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701(2007).
[CrossRef]

Qi, X.

C. Gao, X. Qi, Y. Liu, J. Xin, and L. Wang, “Sorting and detecting orbital angular momentum states by using a Dove prism embedded Mach–Zehnder interferometer and amplitude gratings,” Opt. Commun. 284, 48–51 (2011).
[CrossRef]

Rodríguez-Zurita, G.

G. Rodríguez-Zurita, N. I. Toto-Arellano, M. L. Arroyo-Carrasco, C. Meneses-Fabian, and J. F. Vazquez Castillo, “Experimental observation of spiral patterns by obstruction of Bessel beams: application of single shot phase-shifting interferometry,” in Proceedings of IEEE Conference on Lasers and Electro-Optics/Pacific Rim (IEEE, 2009), pp. 1–2.

Sjöholm, J.

B. Thidé1, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701(2007).
[CrossRef]

Soskin, M.

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

Sztul, H. I.

Then, H.

B. Thidé1, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701(2007).
[CrossRef]

Thidé1, B.

B. Thidé1, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Ya. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99, 087701(2007).
[CrossRef]

Toto-Arellano, N. I.

G. Rodríguez-Zurita, N. I. Toto-Arellano, M. L. Arroyo-Carrasco, C. Meneses-Fabian, and J. F. Vazquez Castillo, “Experimental observation of spiral patterns by obstruction of Bessel beams: application of single shot phase-shifting interferometry,” in Proceedings of IEEE Conference on Lasers and Electro-Optics/Pacific Rim (IEEE, 2009), pp. 1–2.

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

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

Vazquez Castillo, J. F.

G. Rodríguez-Zurita, N. I. Toto-Arellano, M. L. Arroyo-Carrasco, C. Meneses-Fabian, and J. F. Vazquez Castillo, “Experimental observation of spiral patterns by obstruction of Bessel beams: application of single shot phase-shifting interferometry,” in Proceedings of IEEE Conference on Lasers and Electro-Optics/Pacific Rim (IEEE, 2009), pp. 1–2.

Viktorovskaya, J.

R. Khrobatin, I. Mokhon, and J. Viktorovskaya, “Potentiality of experimental analysis for characteristics of the Poynting vector components,” Ukr. J. Phys. Opt. 9, 182–186 (2008).
[CrossRef]

Volke-Sepulveda, K.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B 4, S82–S89 (2002).
[CrossRef]

Wang, L.

C. Gao, X. Qi, Y. Liu, J. Xin, and L. Wang, “Sorting and detecting orbital angular momentum states by using a Dove prism embedded Mach–Zehnder interferometer and amplitude gratings,” Opt. Commun. 284, 48–51 (2011).
[CrossRef]

Woerdman, J. P.

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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).
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Xin, J.

C. Gao, X. Qi, Y. Liu, J. Xin, and L. Wang, “Sorting and detecting orbital angular momentum states by using a Dove prism embedded Mach–Zehnder interferometer and amplitude gratings,” Opt. Commun. 284, 48–51 (2011).
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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

The Poynting vector behavior in the case of a symmetric linearly polarized beam: (a) Transverse 2D representation; (b), (c) the oscillation of the Poynting vector with arbitrary parameters of a laser beam; (d) a laser beam with a plane phase (the beam waist plane); and (e) the beam in the far field.

Fig. 2.
Fig. 2.

The representation of the behavior of the instantaneous and time-averaged Poynting vector at the waist plane of a Gaussian beam.

Fig. 3.
Fig. 3.

(a) The angular pattern of the electromagnetic radiation of a Gaussian beam at the waist plane for different values of the radial coordinate. The beam width in this case is equivalent to 5 mm. (b) The evolution during the propagation of the radiation energy contained within the divergence angle of a Gaussian beam versus the evolution of the beam width of a similar Gaussian beam during propagation for the beam where the beam width is 1 mm at the waist plane.

Fig. 4.
Fig. 4.

(a) The behavior of the IPV during propagation from the near to the far field. The beam width at the waist plane of the Gaussian beam is 1 mm and the transformation of the beam along the propagation axis is indicated in the shaded region in the background of the ellipses. (b) A graphical explanation of the deviation of the Poynting vector that has a nonzero radial component during propagation and the resulting oscillation behavior of the IPV.

Fig. 5.
Fig. 5.

The behavior of the coefficients A r ( r , z ) , B r ( r , z ) , A ( r , z ) , B ( r , z ) in the far field for a Gaussian beam width of 1 mm at the waist plane.

Fig. 6.
Fig. 6.

(a) The behavior of the FWHM of the radiation pattern of a BB for a cone angle γ , equivalent to 0.06 degrees. (b) The longitudinal cross section of an intensity distribution of an obstructed BB and the dependence of the radiation pattern ellipse on the cone angle of a BB (incept), (bI) is a zoomed in section of the ABC (the region of the double shadow) area of the figure for the following parameters of a BB, namely, γ = 0.06 degrees, the half-width of the obstruction is 1.6 mm and the corresponding reconstruction distance is equal to 1.6 m.

Fig. 7.
Fig. 7.

The behavior of the BB functions with different values for the cone angle (black) and the corresponding approximation function (red). The points on the graph (black and red) show the evolution of the committed point on the BB function graph that corresponds to a half maximum drop for the parameter m = 3 .

Equations (24)

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A ( x , y , z ) = U ( x , y , z ) e i ( k z ω t ) i ,
B ( x , y , z ) = i k ( U ( x , y , z ) j + i k U ( x , y , z ) y j ) e i ( k z ω t ) ,
E ( x , y , z ) = i ω ( U ( x , y , z ) i + i k U ( x , y , z ) x z ) e i ( k z ω t ) ,
P ( t ) = ε 0 c 2 4 ( E + E * ) × ( B + B * ) = P + P i ( t ) ,
P = ε 0 ω c 2 4 ( i ( U τ U * U * τ U ) + 2 k | U | 2 z )
P i ( t ) = i ε 0 ω c 2 4 ( U τ U e 2 i ( k z ω t ) U * τ U * e 2 i ( k z ω t ) ) ε 0 ω k c 2 4 ( U 2 e 2 i ( k z ω t ) + U * 2 e 2 i ( k z ω t ) ) z
P x , y ( z , y , z , t ) = ε 0 ω c 2 ( B ( x , y , z ) cos ( k z ω t ) + A ( x , y , z ) sin ( k z ω t ) ) * ( A 1 x , y ( x , y , z ) cos ( k z ω t ) B 1 x , y ( x , y , z ) sin ( k z ω t ) ) , P z ( x , y , z , t ) = ε 0 ω k c 2 ( B ( x , y , z ) cos ( k z ω t ) + A ( x , y , z ) sin ( k z ω t ) ) 2 ,
A ( x , y , z ) = Re ( U ) and B ( x , y , z ) = Im ( U ) , A 1 x , y ( x , y , z ) = Re ( U ( x , y ) ) and B 1 x , y ( x , y , z ) = Im ( U ( x , y ) ) .
P φ ( r , z , φ , t ) = arctg ( S s ( r , z , t ) cos ( φ ) , S s ( r , z , t ) sin ( φ ) ) , P r ( r , z , t ) = ε 0 ω c 2 | S r ( r , z , t ) S ( r , z , t ) | , P z ( r , z , t ) = ε 0 ω k c 2 S ( r , z , t ) 2 ,
S r ( r , z , t ) = A r ( r , z ) cos ( k z ω t ) B r ( r , z ) sin ( k z ω t ) , S ( r , z , t ) = A ( r , z ) sin ( k z ω t ) + B ( r , z ) cos ( k z ω t ) , S s ( r , z , t ) = sign ( S r ( r , z , t ) S ( r , z , t ) ) ;
A ( r , z ) = Re ( U ( r , z ) ) and B ( r , z ) = Im ( U ( r , z ) ) , A r ( r , z ) = Re ( U ( r , z ) r ) and B r ( r , z ) = Im ( U ( r , z ) r ) .
P ( α , r ) = ε 0 ω k c 2 A ( r ) 2 A r ( r ) 2 A r ( r ) 2 + A ( r ) 2 k 2 α 2 .
α FWHM GB ( r ) = 2 r k w 2 .
t 0 ( r , z ) = arctg ( B ( r , z ) / A ( r , z ) ) ω .
P r ( r , z , t 1 , 2 ( r , z ) + t 0 ( r , z ) ) P z ( r , z , t 1 , 2 ( r , z ) + t 0 ( r , z ) ) = ± φ .
E φ ( z ) = 2 ω 0 r t 1 ( r , z ) + t 0 ( r , z ) t 2 ( r , z ) + t 0 ( r , z ) P z ( r , z , t ) d t d r .
Re ( U ) = Im ( U e i π 2 )
Re ( U r ) = Im ( U r e i π 2 ) .
P BB ( α , r ) = ε 0 ω k c 2 σ 2 q 2 J 1 ( q r ) 2 J 0 ( q r ) 2 q 2 J 1 ( q r ) 2 + J 0 ( q r ) 2 k 2 α 2 ,
α FWHM BB ( r ) = γ | J 1 ( q r ) J 0 ( q r ) | γ 1 sin ( 2 q r ) 1 + sin ( 2 q r ) .
δ ( r c BB , γ ) = t 1 ( r c BB , γ ) t 1 ( r c BB , γ ) P z BB ( r c BB , γ , t ) d t 0 π / ω P z BB ( r c BB , γ , t ) d t ,
r c BB ( γ , b ) = π + 2 n π + 4 arccos ( b ) 4 q ( γ ) + 2 m π q ( γ ) ,
δ ( b , m ) = 2 ( π + 2 ar ctg ( F ( b , m ) ) sin ( 2 arctg ( F ( b , m ) ) ) )
F ( b , m ) = J 0 ( 1 4 ( 1 + 8 m ) π + arccos ( b ) ) J 1 ( 1 4 ( 1 + 8 m ) π + arccos ( b ) ) ,

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