Abstract

Laguerre–Gaussian beams with a nonzero azimuthal index are known to carry orbital angular momentum (OAM), and are routinely created external to laser cavities. The few reports of obtaining such beams from laser cavities suffer from inconclusive evidence of the real electromagnetic field. In this Letter we revisit this question and show that an observed doughnut beam from a laser cavity may not be a pure Laguerre–Gaussian azimuthal mode but can be an incoherent sum of petal modes, which do not carry OAM. We point out the requirements for future analysis of such fields from laser resonators.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  2. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
    [CrossRef]
  3. E. Yao, S. Franke-Arnold, J. Courtial, M. Padgett, and S. Barnett, Opt. Express 14, 13089 (2006).
    [CrossRef]
  4. A. Shevchenko, S. Buchter, N. Tabiryan, and M. Kaivola, Opt. Commun. 77, 232 (2004).
  5. C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
    [CrossRef]
  6. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
    [CrossRef]
  7. G. Machavariani, Y. Lumer, I. Moshe, A. Meir, S. Jackel, and N. Davidson, Appl. Opt. 46, 3304 (2007).
    [CrossRef]
  8. M. Okida, Y. Hayashi, T. Omatsu, J. Hamazaki, and R. Morita, Appl. Phys. B 97, 275 (2009).
    [CrossRef]
  9. G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, Opt. Commun. 281, 732 (2008).
    [CrossRef]
  10. J. Kim and W. Clarkson, Opt. Commun. 296, 109 (2013).
    [CrossRef]
  11. Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K. Ueda, Opt. Rev. 19, 201 (2012).
    [CrossRef]
  12. S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2283 (2013).
    [CrossRef]
  13. V. Arrizon, Opt. Lett. 28, 2521 (2003).
    [CrossRef]
  14. S. Ngcobo, K. Ait-Ameur, I. A. Litvin, A. Hasnaoui, and A. Forbes, Opt. Express 21, 21113 (2013).
    [CrossRef]
  15. D. Naidoo, K. Ait-Ameur, M. Brunel, and A. Forbes, Appl. Phys. B 106, 683 (2012).
    [CrossRef]
  16. M. Harris, C. A. Hill, P. R. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
    [CrossRef]
  17. I. A. Litvin, A. Dudley, F. S. Roux, and A. Forbes, Opt. Express 20, 10996 (2012).
    [CrossRef]
  18. C. Schulze, S. Ngcobo, M. Duparre, and A. Forbes, Opt. Express 20, 27866 (2012).
    [CrossRef]
  19. I. A. Litvin, L. Burger, and A. Forbes, Opt. Lett. 38, 3363 (2013).
    [CrossRef]
  20. I. A. Litvin, L. Burger, and A. Forbes, Opt. Express 15, 14065 (2007).
    [CrossRef]

2013 (4)

2012 (4)

D. Naidoo, K. Ait-Ameur, M. Brunel, and A. Forbes, Appl. Phys. B 106, 683 (2012).
[CrossRef]

I. A. Litvin, A. Dudley, F. S. Roux, and A. Forbes, Opt. Express 20, 10996 (2012).
[CrossRef]

C. Schulze, S. Ngcobo, M. Duparre, and A. Forbes, Opt. Express 20, 27866 (2012).
[CrossRef]

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

2009 (1)

M. Okida, Y. Hayashi, T. Omatsu, J. Hamazaki, and R. Morita, Appl. Phys. B 97, 275 (2009).
[CrossRef]

2008 (1)

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, Opt. Commun. 281, 732 (2008).
[CrossRef]

2007 (2)

2006 (1)

2004 (1)

A. Shevchenko, S. Buchter, N. Tabiryan, and M. Kaivola, Opt. Commun. 77, 232 (2004).

2003 (1)

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

1996 (1)

C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
[CrossRef]

1994 (1)

M. Harris, C. A. Hill, P. R. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
[CrossRef]

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

1992 (1)

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Ait-Ameur, K.

S. Ngcobo, K. Ait-Ameur, I. A. Litvin, A. Hasnaoui, and A. Forbes, Opt. Express 21, 21113 (2013).
[CrossRef]

D. Naidoo, K. Ait-Ameur, M. Brunel, and A. Forbes, Appl. Phys. B 106, 683 (2012).
[CrossRef]

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Arrizon, V.

Barnett, S.

Beijersbergen, M.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Bisson, J. F.

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

Brunel, M.

D. Naidoo, K. Ait-Ameur, M. Brunel, and A. Forbes, Appl. Phys. B 106, 683 (2012).
[CrossRef]

Buchter, S.

A. Shevchenko, S. Buchter, N. Tabiryan, and M. Kaivola, Opt. Commun. 77, 232 (2004).

Burger, L.

Clarkson, W.

J. Kim and W. Clarkson, Opt. Commun. 296, 109 (2013).
[CrossRef]

Courtial, J.

Davidson, N.

Dudley, A.

Duparre, M.

Forbes, A.

Franke-Arnold, S.

Hamazaki, J.

M. Okida, Y. Hayashi, T. Omatsu, J. Hamazaki, and R. Morita, Appl. Phys. B 97, 275 (2009).
[CrossRef]

Harris, M.

M. Harris, C. A. Hill, P. R. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
[CrossRef]

Hasnaoui, A.

Hayashi, Y.

M. Okida, Y. Hayashi, T. Omatsu, J. Hamazaki, and R. Morita, Appl. Phys. B 97, 275 (2009).
[CrossRef]

Hill, C. A.

M. Harris, C. A. Hill, P. R. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
[CrossRef]

Jackel, S.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, Opt. Commun. 281, 732 (2008).
[CrossRef]

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, S. Jackel, and N. Davidson, Appl. Opt. 46, 3304 (2007).
[CrossRef]

Kaivola, M.

A. Shevchenko, S. Buchter, N. Tabiryan, and M. Kaivola, Opt. Commun. 77, 232 (2004).

Kim, J.

J. Kim and W. Clarkson, Opt. Commun. 296, 109 (2013).
[CrossRef]

Li, J.

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

Litvin, I.

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2283 (2013).
[CrossRef]

Litvin, I. A.

Lumer, Y.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, Opt. Commun. 281, 732 (2008).
[CrossRef]

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, S. Jackel, and N. Davidson, Appl. Opt. 46, 3304 (2007).
[CrossRef]

Machavariani, G.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, Opt. Commun. 281, 732 (2008).
[CrossRef]

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, S. Jackel, and N. Davidson, Appl. Opt. 46, 3304 (2007).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Meir, A.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, Opt. Commun. 281, 732 (2008).
[CrossRef]

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, S. Jackel, and N. Davidson, Appl. Opt. 46, 3304 (2007).
[CrossRef]

Morita, R.

M. Okida, Y. Hayashi, T. Omatsu, J. Hamazaki, and R. Morita, Appl. Phys. B 97, 275 (2009).
[CrossRef]

Moshe, I.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, Opt. Commun. 281, 732 (2008).
[CrossRef]

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, S. Jackel, and N. Davidson, Appl. Opt. 46, 3304 (2007).
[CrossRef]

Naidoo, D.

D. Naidoo, K. Ait-Ameur, M. Brunel, and A. Forbes, Appl. Phys. B 106, 683 (2012).
[CrossRef]

Ngcobo, S.

Okida, M.

M. Okida, Y. Hayashi, T. Omatsu, J. Hamazaki, and R. Morita, Appl. Phys. B 97, 275 (2009).
[CrossRef]

Omatsu, T.

M. Okida, Y. Hayashi, T. Omatsu, J. Hamazaki, and R. Morita, Appl. Phys. B 97, 275 (2009).
[CrossRef]

Padgett, M.

Paterson, C.

C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
[CrossRef]

Roux, F. S.

Schulze, C.

Senatsky, Y.

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

Shevchenko, A.

A. Shevchenko, S. Buchter, N. Tabiryan, and M. Kaivola, Opt. Commun. 77, 232 (2004).

Shirakawa, A.

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

Smith, R.

C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
[CrossRef]

Spreeuw, R.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Tabiryan, N.

A. Shevchenko, S. Buchter, N. Tabiryan, and M. Kaivola, Opt. Commun. 77, 232 (2004).

Tapster, P. R.

M. Harris, C. A. Hill, P. R. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
[CrossRef]

Thirugnanasambandam, M.

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

Ueda, K.

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

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

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Vaughan, J. M.

M. Harris, C. A. Hill, P. R. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Woerdman, J.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Woerdman, J. P.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

Yao, E.

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (2)

M. Okida, Y. Hayashi, T. Omatsu, J. Hamazaki, and R. Morita, Appl. Phys. B 97, 275 (2009).
[CrossRef]

D. Naidoo, K. Ait-Ameur, M. Brunel, and A. Forbes, Appl. Phys. B 106, 683 (2012).
[CrossRef]

Nat. Commun. (1)

S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, Nat. Commun. 4, 2283 (2013).
[CrossRef]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Opt. Commun. (5)

A. Shevchenko, S. Buchter, N. Tabiryan, and M. Kaivola, Opt. Commun. 77, 232 (2004).

C. Paterson and R. Smith, Opt. Commun. 124, 121 (1996).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, Opt. Commun. 281, 732 (2008).
[CrossRef]

J. Kim and W. Clarkson, Opt. Commun. 296, 109 (2013).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Opt. Rev. (1)

Y. Senatsky, J. F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K. Ueda, Opt. Rev. 19, 201 (2012).
[CrossRef]

Phys. Rev. A (2)

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

M. Harris, C. A. Hill, P. R. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).
[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) Schematic of the digital laser concept for the generation of a doughnut mode showing the spatial light modulator (SLM), Brewster window (BW), high reflectivity (HR) mirror at an angle of 45°, Nd:YAG gain medium pumped by an external laser diode (P) source, and the output coupler (OC). (b) Schematic of the experimental setup of the modal decomposition technique.

Fig. 2.
Fig. 2.

Slope efficiency graph for generation of the doughnut mode by the digital laser setup.

Fig. 3.
Fig. 3.

Doughnut beam obtained by inserting an intracavity circular aperture into the conventional plano–concave stable cavity for implemention of the digital laser setup.

Fig. 4.
Fig. 4.

Intensities of the modes with the highest eigenvalue, equivalent to 0.987, which was obtained through the Fox–Li method.

Fig. 5.
Fig. 5.

Doughnut beam produced by a coherent and an incoherent superposition of the two petal beams.

Fig. 6.
Fig. 6.

Azimuthal modal decomposition of the doughnut mode.

Fig. 7.
Fig. 7.

Interference of the field produced by selecting two portions of the doughnut beam through two pinholes (b). The pinholes correspond to the lobes of the superimposed field (c), where we interfere either two lobes of the same petal beam [1 and 3, (a)] or two lobes with one from each petal beam [1 and 2, (d)]. (e) Schematic of the interference experiment.

Equations (5)

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

ueven(r,ϕ,z)=LG(r,ϕ,z)[exp(iϕ)+exp(iϕ)],
uodd(r,ϕ,z)=iLG(r,ϕ,z)[exp(iϕ)exp(iϕ)],
LG(r,z,ϕ)=2πw(z)2||!(2rw(z))||exp(r2w(z)2+ik0r22R(z))exp(i(1+||)α(z)),
Di(r,z)=uodd(r,ϕ,z)+iueven(r,ϕ,z),
Dc(r,z)=iuodd(r,ϕ,z)+cueven(r,ϕ,z),

Metrics