Abstract

We propose a simple method for the detection of Bessel beams with arbitrary radial and azimuthal indices, and then demonstrate it in an all-digital setup with a spatial light modulator. We confirm that the fidelity of the detection method is very high, with modal cross-talk below 5%, even for high orbital angular momentum carrying fields with long propagation ranges. To illustrate the versatility of the approach we use it to observe the modal spectrum changes during the self-reconstruction process of Bessel beams after encountering an obstruction, as well as to characterize modal distortions of Bessel beams propagating through atmospheric turbulence.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
    [CrossRef]
  2. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
    [CrossRef] [PubMed]
  3. D. McGloin and K. Dholakai, “Bessel beams: diffraction in new light,” Contemp. Phys. 46(1), 15–28 (2005).
    [CrossRef]
  4. M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: non-diffracting beams,” Laser Photon. Rev. 4(4), 529–547 (2010).
    [CrossRef]
  5. A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel Beams,” Opt. Photon. News,  24(6), 22–29 (2013)
    [CrossRef]
  6. M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
    [CrossRef] [PubMed]
  7. M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams, ” Opt. Express 20(21), 23589–23597 (2012).
    [CrossRef] [PubMed]
  8. H. C. Ramrez, R. R. Alarcón, F. J. Morelos, P. A. Q. Su, J. C. G. Vega, and A. B. U’Ren, “Observation of non-diffracting behavior at the single-photon level,” Opt. Express 20(28), 29761–29768 (2012).
    [CrossRef]
  9. F. Gori and G. Guattari, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
    [CrossRef]
  10. M. A. Mahmoud, M. Y. Shalaby, and D. Khalil, “Propagation of Bessel beams generated using finite-width Durnin ring,” Appl. Opt. 52(2), 256–263 (2013).
    [CrossRef] [PubMed]
  11. R. M. Herman and T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8(6), 932–942 (1991).
    [CrossRef]
  12. J. Alrt and K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177, 277–301 (2000).
  13. A. Vasara, J. Turunen, and A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6(11), 1748–1754 (1989).
    [CrossRef] [PubMed]
  14. C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
    [CrossRef]
  15. R. Bowman, N. Muller, X. Zambrana-Puyalto, O. Jedrikiewicz, P. Di Tramapani, and M. J. Padgett, “Efficient generation of Bessel beam arrays by means of an SLM,” Eur. Phys. J. Special Topics 199, 159–166 (2011).
    [CrossRef]
  16. Z. Y. Rong, Y. J. Han, S. Z. Wang, and C. Guo, “Generation of arbitrary vector beams with cascaded liquid crystal spatial light modulators,” Opt. Express 22(2), 1636–1644 (2014).
    [CrossRef] [PubMed]
  17. M. Bock, S. K. Das, and R. Grunwald, “Programmable ultrashort-pulsed flying images,” Opt. Express 17, 7465–7478 (2009).
    [CrossRef] [PubMed]
  18. R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, “Generating superpositions of higher-order Bessel beams,” Opt. Express 17(26), 23389–23395 (2009).
    [CrossRef]
  19. A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett. 38(17), 3429–3432 (2013).
    [CrossRef] [PubMed]
  20. A. Dudley, T. Mhlanga, M. Lavery, A. McDonald, F. S. Roux, M. J. Padgett, and A. Forbes, “Efficient sorting of Bessel beams, ” Opt. Express 21(1), 165–171 (2013).
    [CrossRef] [PubMed]
  21. A. Mourka, M. Mazilu, E. M. Wright, and K. Dholakia, “Modal characterization using principal component analysis: application to Bessel, higher-order Gaussian beams and their superpositions,” Scientific Reports 3, 1422 (2013).
    [CrossRef]
  22. M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, “Simultaneous determination of the constituent azimuthal and radial mode indices for light fields possessing orbital angular momentum,” Appl. Phys. Lett. 100, 231115 (2012).
    [CrossRef]
  23. I. Litvin, M. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
    [CrossRef]
  24. Z. Bouchal, J. Wanger, and M. Chulpl, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
    [CrossRef]
  25. I. A. Litvin, A. Dudley, F. S. Roux, and A. Forbes, “Azimuthal decomposition with digital holograms,” Opt. Express 20(10), 10996–11004 (2012).
    [CrossRef] [PubMed]
  26. A. Janssen, S. van Haver, P. Dirksen, and J. Braat, “Zernike representation and strehl ratio of optical systems with numerical aperture,”J. Mod. Opt. 55(7), 1127–1157 (2008).
    [CrossRef]
  27. J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
    [CrossRef]
  28. W. Nelson, J. P. Palastro, C. C. Davis, and P. Sprangl, “Propagation of Bessel and Airy beams through atmospheric turbulence,” J. Opt. Soc. Am. A 31(3), 603–609 (2014).
    [CrossRef]

2014 (4)

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[CrossRef] [PubMed]

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[CrossRef]

Z. Y. Rong, Y. J. Han, S. Z. Wang, and C. Guo, “Generation of arbitrary vector beams with cascaded liquid crystal spatial light modulators,” Opt. Express 22(2), 1636–1644 (2014).
[CrossRef] [PubMed]

W. Nelson, J. P. Palastro, C. C. Davis, and P. Sprangl, “Propagation of Bessel and Airy beams through atmospheric turbulence,” J. Opt. Soc. Am. A 31(3), 603–609 (2014).
[CrossRef]

2013 (5)

2012 (4)

2011 (1)

R. Bowman, N. Muller, X. Zambrana-Puyalto, O. Jedrikiewicz, P. Di Tramapani, and M. J. Padgett, “Efficient generation of Bessel beam arrays by means of an SLM,” Eur. Phys. J. Special Topics 199, 159–166 (2011).
[CrossRef]

2010 (1)

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: non-diffracting beams,” Laser Photon. Rev. 4(4), 529–547 (2010).
[CrossRef]

2009 (3)

2008 (1)

A. Janssen, S. van Haver, P. Dirksen, and J. Braat, “Zernike representation and strehl ratio of optical systems with numerical aperture,”J. Mod. Opt. 55(7), 1127–1157 (2008).
[CrossRef]

2005 (1)

D. McGloin and K. Dholakai, “Bessel beams: diffraction in new light,” Contemp. Phys. 46(1), 15–28 (2005).
[CrossRef]

2000 (1)

J. Alrt and K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177, 277–301 (2000).

1998 (1)

Z. Bouchal, J. Wanger, and M. Chulpl, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

1996 (1)

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[CrossRef]

1991 (1)

1989 (1)

1987 (3)

F. Gori and G. Guattari, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
[CrossRef]

Agnew, M.

Alarcón, R. R.

Alrt, J.

J. Alrt and K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177, 277–301 (2000).

Bock, M.

Bouchal, Z.

Z. Bouchal, J. Wanger, and M. Chulpl, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

Bowman, R.

R. Bowman, N. Muller, X. Zambrana-Puyalto, O. Jedrikiewicz, P. Di Tramapani, and M. J. Padgett, “Efficient generation of Bessel beam arrays by means of an SLM,” Eur. Phys. J. Special Topics 199, 159–166 (2011).
[CrossRef]

Boyd, R. W.

Braat, J.

A. Janssen, S. van Haver, P. Dirksen, and J. Braat, “Zernike representation and strehl ratio of optical systems with numerical aperture,”J. Mod. Opt. 55(7), 1127–1157 (2008).
[CrossRef]

Chulpl, M.

Z. Bouchal, J. Wanger, and M. Chulpl, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

Das, S. K.

Davis, C. C.

Dholakai, K.

D. McGloin and K. Dholakai, “Bessel beams: diffraction in new light,” Contemp. Phys. 46(1), 15–28 (2005).
[CrossRef]

Dholakia, K.

A. Mourka, M. Mazilu, E. M. Wright, and K. Dholakia, “Modal characterization using principal component analysis: application to Bessel, higher-order Gaussian beams and their superpositions,” Scientific Reports 3, 1422 (2013).
[CrossRef]

M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, “Simultaneous determination of the constituent azimuthal and radial mode indices for light fields possessing orbital angular momentum,” Appl. Phys. Lett. 100, 231115 (2012).
[CrossRef]

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: non-diffracting beams,” Laser Photon. Rev. 4(4), 529–547 (2010).
[CrossRef]

J. Alrt and K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177, 277–301 (2000).

Di Tramapani, P.

R. Bowman, N. Muller, X. Zambrana-Puyalto, O. Jedrikiewicz, P. Di Tramapani, and M. J. Padgett, “Efficient generation of Bessel beam arrays by means of an SLM,” Eur. Phys. J. Special Topics 199, 159–166 (2011).
[CrossRef]

Dirksen, P.

A. Janssen, S. van Haver, P. Dirksen, and J. Braat, “Zernike representation and strehl ratio of optical systems with numerical aperture,”J. Mod. Opt. 55(7), 1127–1157 (2008).
[CrossRef]

Dudley, A.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Escuti, M.

Forbes, A.

Friberg, A. T.

Gori, F.

F. Gori and G. Guattari, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[CrossRef]

Grunwald, R.

Guattari, G.

F. Gori and G. Guattari, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[CrossRef]

Gunn-Moore, F.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: non-diffracting beams,” Laser Photon. Rev. 4(4), 529–547 (2010).
[CrossRef]

Guo, C.

Han, Y. J.

He, Y.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[CrossRef]

Herman, R. M.

Janssen, A.

A. Janssen, S. van Haver, P. Dirksen, and J. Braat, “Zernike representation and strehl ratio of optical systems with numerical aperture,”J. Mod. Opt. 55(7), 1127–1157 (2008).
[CrossRef]

Jedrikiewicz, O.

R. Bowman, N. Muller, X. Zambrana-Puyalto, O. Jedrikiewicz, P. Di Tramapani, and M. J. Padgett, “Efficient generation of Bessel beam arrays by means of an SLM,” Eur. Phys. J. Special Topics 199, 159–166 (2011).
[CrossRef]

Jiang, Y.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[CrossRef]

Khalil, D.

Khilo, N.

Lavery, M.

Leach, J.

Li, Y.

Liao, J.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[CrossRef]

Litvin, I.

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

Litvin, I. A.

Mahmoud, M. A.

Mazilu, M.

A. Mourka, M. Mazilu, E. M. Wright, and K. Dholakia, “Modal characterization using principal component analysis: application to Bessel, higher-order Gaussian beams and their superpositions,” Scientific Reports 3, 1422 (2013).
[CrossRef]

M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, “Simultaneous determination of the constituent azimuthal and radial mode indices for light fields possessing orbital angular momentum,” Appl. Phys. Lett. 100, 231115 (2012).
[CrossRef]

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: non-diffracting beams,” Laser Photon. Rev. 4(4), 529–547 (2010).
[CrossRef]

McDonald, A.

McGloin, D.

D. McGloin and K. Dholakai, “Bessel beams: diffraction in new light,” Contemp. Phys. 46(1), 15–28 (2005).
[CrossRef]

McLaren, M.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[CrossRef] [PubMed]

M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams, ” Opt. Express 20(21), 23589–23597 (2012).
[CrossRef] [PubMed]

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

Mhlanga, T.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Morelos, F. J.

Mourka, A.

A. Mourka, M. Mazilu, E. M. Wright, and K. Dholakia, “Modal characterization using principal component analysis: application to Bessel, higher-order Gaussian beams and their superpositions,” Scientific Reports 3, 1422 (2013).
[CrossRef]

M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, “Simultaneous determination of the constituent azimuthal and radial mode indices for light fields possessing orbital angular momentum,” Appl. Phys. Lett. 100, 231115 (2012).
[CrossRef]

Muller, N.

R. Bowman, N. Muller, X. Zambrana-Puyalto, O. Jedrikiewicz, P. Di Tramapani, and M. J. Padgett, “Efficient generation of Bessel beam arrays by means of an SLM,” Eur. Phys. J. Special Topics 199, 159–166 (2011).
[CrossRef]

Nelson, W.

Ou, J.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[CrossRef]

Padgett, M.

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel Beams,” Opt. Photon. News,  24(6), 22–29 (2013)
[CrossRef]

Padgett, M. J.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[CrossRef] [PubMed]

A. Dudley, T. Mhlanga, M. Lavery, A. McDonald, F. S. Roux, M. J. Padgett, and A. Forbes, “Efficient sorting of Bessel beams, ” Opt. Express 21(1), 165–171 (2013).
[CrossRef] [PubMed]

M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams, ” Opt. Express 20(21), 23589–23597 (2012).
[CrossRef] [PubMed]

R. Bowman, N. Muller, X. Zambrana-Puyalto, O. Jedrikiewicz, P. Di Tramapani, and M. J. Padgett, “Efficient generation of Bessel beam arrays by means of an SLM,” Eur. Phys. J. Special Topics 199, 159–166 (2011).
[CrossRef]

Palastro, J. P.

Paterson, C.

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[CrossRef]

Ramrez, H. C.

Rong, Z. Y.

Roux, F. S.

Shalaby, M. Y.

Smith, R.

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[CrossRef]

Sprangl, P.

Stevenson, D. J.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: non-diffracting beams,” Laser Photon. Rev. 4(4), 529–547 (2010).
[CrossRef]

Su, P. A. Q.

Tang, H.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[CrossRef]

Turunen, J.

U’Ren, A. B.

van Haver, S.

A. Janssen, S. van Haver, P. Dirksen, and J. Braat, “Zernike representation and strehl ratio of optical systems with numerical aperture,”J. Mod. Opt. 55(7), 1127–1157 (2008).
[CrossRef]

Vasara, A.

Vasilyeu, R.

Vega, J. C. G.

Vettenburg, T.

M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, “Simultaneous determination of the constituent azimuthal and radial mode indices for light fields possessing orbital angular momentum,” Appl. Phys. Lett. 100, 231115 (2012).
[CrossRef]

Wang, S.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[CrossRef]

Wang, S. Z.

Wanger, J.

Z. Bouchal, J. Wanger, and M. Chulpl, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

Wiggins, T. A.

Wright, E. M.

A. Mourka, M. Mazilu, E. M. Wright, and K. Dholakia, “Modal characterization using principal component analysis: application to Bessel, higher-order Gaussian beams and their superpositions,” Scientific Reports 3, 1422 (2013).
[CrossRef]

M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, “Simultaneous determination of the constituent azimuthal and radial mode indices for light fields possessing orbital angular momentum,” Appl. Phys. Lett. 100, 231115 (2012).
[CrossRef]

Zambrana-Puyalto, X.

R. Bowman, N. Muller, X. Zambrana-Puyalto, O. Jedrikiewicz, P. Di Tramapani, and M. J. Padgett, “Efficient generation of Bessel beam arrays by means of an SLM,” Eur. Phys. J. Special Topics 199, 159–166 (2011).
[CrossRef]

Zhang, J.

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Mazilu, A. Mourka, T. Vettenburg, E. M. Wright, and K. Dholakia, “Simultaneous determination of the constituent azimuthal and radial mode indices for light fields possessing orbital angular momentum,” Appl. Phys. Lett. 100, 231115 (2012).
[CrossRef]

Contemp. Phys. (1)

D. McGloin and K. Dholakai, “Bessel beams: diffraction in new light,” Contemp. Phys. 46(1), 15–28 (2005).
[CrossRef]

Eur. Phys. J. Special Topics (1)

R. Bowman, N. Muller, X. Zambrana-Puyalto, O. Jedrikiewicz, P. Di Tramapani, and M. J. Padgett, “Efficient generation of Bessel beam arrays by means of an SLM,” Eur. Phys. J. Special Topics 199, 159–166 (2011).
[CrossRef]

J. Mod. Opt. (1)

A. Janssen, S. van Haver, P. Dirksen, and J. Braat, “Zernike representation and strehl ratio of optical systems with numerical aperture,”J. Mod. Opt. 55(7), 1127–1157 (2008).
[CrossRef]

J. Opt. Soc. Am. A (4)

Laser Photon. Rev. (1)

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: non-diffracting beams,” Laser Photon. Rev. 4(4), 529–547 (2010).
[CrossRef]

Nat. Commun. (1)

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[CrossRef] [PubMed]

Opt. Commun. (6)

J. Alrt and K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177, 277–301 (2000).

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[CrossRef]

F. Gori and G. Guattari, “Bessel-Gauss beams,” Opt. Commun. 64(6), 491–495 (1987).
[CrossRef]

J. Ou, Y. Jiang, J. Zhang, H. Tang, Y. He, S. Wang, and J. Liao, “Spreading of spiral spectrum of Bessel-Gaussian beam in non-Kolmogorov turbulence,” Opt. Commun. 318, 95–99 (2014).
[CrossRef]

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

Z. Bouchal, J. Wanger, and M. Chulpl, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[CrossRef]

Opt. Express (7)

Opt. Lett. (1)

Opt. Photon. News (1)

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel Beams,” Opt. Photon. News,  24(6), 22–29 (2013)
[CrossRef]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Scientific Reports (1)

A. Mourka, M. Mazilu, E. M. Wright, and K. Dholakia, “Modal characterization using principal component analysis: application to Bessel, higher-order Gaussian beams and their superpositions,” Scientific Reports 3, 1422 (2013).
[CrossRef]

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.


Figures (7)

Fig. 1
Fig. 1

A diagram illustrating the generation and the detection of Bessel-Gaussian beams. (a) The BG beam is generated using a programmed hologram of an axicon, illuminating by a Gaussian beam, and exists in a finite region, zmax. An obstacle placed in the center of the BG region obstructed the generated beam for a minimum distance, zmin, after which the BG mode reconstructs. (b–e) experimental beam images of a Bessel beam of order = 1 at four different positions. (f) The BG beam is detected at the far field of a programmed hologram of a second axicon, where the hologram is placed at z = zmax after the first axicon.

Fig. 2
Fig. 2

Experimental images of (a) a digital hologram for the detector of a BG mode with = 3 and (b) a BG mode profile of = 3 and (c) its Fourier transform (annular ring). The signal at the detector is shown for the scenarios of (d) matching kr and and (e) matching in but no matching in kr. The black and white insets show the theoretical results.

Fig. 3
Fig. 3

A schematic of the experimental setup for accomplishing the decomposition of a Bessel field. The Lenses L1, L2, L3, L4 and L5 have focal lengths f1 = 100 mm, f2 = 300 mm, f3 = 500 mm, f4 =500 mm and f5=150 mm, respectively. A is the filtering aperture. SLM1 and SLM2 denote the two spatial light modulators and M represents a mirror. The field from SLM1 was relay imaged with a 1:1 telescope and then allowed to propagate a distance of zmax prior to modulation by SLM2. The resulting signal was measured in the far field of SLM2 using a CCD camera.

Fig. 4
Fig. 4

(a) Bessel beam radial, kr, decomposition for = 1. (b) Bessel beam azimuthal, , decomposition for kr = 0.25 rad/pixel.

Fig. 5
Fig. 5

(a) Azimuthal decomposition ( detection) of the fully obstructed beam and (b) kr decomposition without an obstruction and then at three planes with the obstruction.

Fig. 6
Fig. 6

Images of a Bessel-Gaussian mode profile for = 1 (a) without turbulence, after passing a turbulence of (b) SR=0.2 and (c) SR=0.03.

Fig. 7
Fig. 7

(a) kr = 0.25 rad/pixel decomposition for different strehl ratios. (b) decomposition spectrum without turbulence. (c) and (d) decomposition spectrum for SR=0.2 and SR=0.03, respectively.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E BG ( r , Φ , z ) = 2 π J ( z R k r r z R i z ) exp ( i Φ i k z z ) exp ( i k r 2 z w 0 2 2 k r 2 4 ( z R i z ) ) ,
z max = w 0 k r / k = w 0 2 π λ k r .
z min = 2 π R obs k r λ .
t SLM = exp ( i k ˜ r r i ϕ ) ,
g out = { E BG } { t SLM } ,

Metrics