Abstract

This work proposes a simple model of pulse Laguerre-Gaussian Beam (LGB) by chopping the incident continuous wave LGB into ultrashort pulse. The pulse LGB is expanded into a series of LGBs with the same angular quantum number (AQN) but different radial quantum number (RQN). The expansion coefficients may show the time-varying and propagating characteristics of the pulse helical beam. Bigger RQN of the incident LGB will cause more serious mode dispersion. This work discusses emphatically the cases that the incident LGBs have zero RQN, in which the original mode, i.e. the same eigen-mode as the incident beam, can be used to approximate the pulse LGB in short propagating range, e.g. 2zR. The original mode decreases, spreads and delays when propagating, and it’s more evident for incident LGB with larger AQN. These conclusions are important for the optical communication that uses the orbital angular momentum division multiplexing (OAM-DM) technology.

©2010 Optical Society of America

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References

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  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, 8185–8190 (1992).
    [Crossref] [PubMed]
  2. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
    [Crossref] [PubMed]
  3. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
    [Crossref] [PubMed]
  4. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
    [Crossref] [PubMed]
  5. Z. Bouchal and R. Celechovsky, “Mixed vortex states of light as information carriers,” N. J. Phys. 6, 131 (2004).
    [Crossref]
  6. C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
    [Crossref] [PubMed]
  7. Z. Bouchal, V. Kollarova, P. Zemanek, and T. Cizmar, “Orbital angular momentum of mixed vortex beams,” Proc. SPIE 660907, 1–8 (2007).
  8. J. Lin, X.-C. Yuan, S. H. Tao, and R. E. Burge, “Multiplexing free-space optical signals using superimposed collinear orbital angular momentum states,” Appl. Opt. 46, 4680–4685 (2007).
    [Crossref] [PubMed]
  9. Y. D. Liu, C. Gao, X. Qi, and H. Weber, “Orbital angular momentum (OAM) spectrum correction in free space optical communication,” Opt. Express 16, 7091–7101 (2008).
    [Crossref] [PubMed]
  10. J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link,” Appl. Opt. 47, 2414–2429 (2008).
    [Crossref] [PubMed]
  11. G. A. Tyler and R. W. Boyd, “Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum,” Opt. Lett. 34, 142–144 (2009).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  13. H. Wei, X. Xue, J. Leach, M. J. Padgetc, S. M. Barnett, S. Franke-Arnoldd, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
    [Crossref]
  14. S. Feng and H. G. Winful, “Higher-order transverse modes of ultrashort isodiffracting,” Phys. Rev. E 63, 046602 (2001).
    [Crossref]
  15. J. Lekner, “Helical light pulses,” J. Opt. A 6, L29–L32 (2004).
  16. M. A. Porras, “Pulse correction to monochromatic light-beam propagation,” Opt. Lett. 26, 44–46 (2001).
    [Crossref]
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    [Crossref]
  18. http://en.wikipedia.org/wiki/Laguerre_polynomials

2009 (1)

2008 (2)

2007 (2)

J. Lin, X.-C. Yuan, S. H. Tao, and R. E. Burge, “Multiplexing free-space optical signals using superimposed collinear orbital angular momentum states,” Appl. Opt. 46, 4680–4685 (2007).
[Crossref] [PubMed]

Z. Bouchal, V. Kollarova, P. Zemanek, and T. Cizmar, “Orbital angular momentum of mixed vortex beams,” Proc. SPIE 660907, 1–8 (2007).

2005 (1)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref] [PubMed]

2004 (3)

Z. Bouchal and R. Celechovsky, “Mixed vortex states of light as information carriers,” N. J. Phys. 6, 131 (2004).
[Crossref]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref] [PubMed]

J. Lekner, “Helical light pulses,” J. Opt. A 6, L29–L32 (2004).

2003 (1)

H. Wei, X. Xue, J. Leach, M. J. Padgetc, S. M. Barnett, S. Franke-Arnoldd, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

2002 (1)

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

2001 (3)

M. A. Porras, “Pulse correction to monochromatic light-beam propagation,” Opt. Lett. 26, 44–46 (2001).
[Crossref]

S. Feng and H. G. Winful, “Higher-order transverse modes of ultrashort isodiffracting,” Phys. Rev. E 63, 046602 (2001).
[Crossref]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

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, 8185–8190 (1992).
[Crossref] [PubMed]

1986 (1)

Allen, L.

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, 8185–8190 (1992).
[Crossref] [PubMed]

Anguita, J. A.

Barnett, S. M.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref] [PubMed]

H. Wei, X. Xue, J. Leach, M. J. Padgetc, S. M. Barnett, S. Franke-Arnoldd, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Beijersbergen, M. W.

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, 8185–8190 (1992).
[Crossref] [PubMed]

Bouchal, Z.

Z. Bouchal, V. Kollarova, P. Zemanek, and T. Cizmar, “Orbital angular momentum of mixed vortex beams,” Proc. SPIE 660907, 1–8 (2007).

Z. Bouchal and R. Celechovsky, “Mixed vortex states of light as information carriers,” N. J. Phys. 6, 131 (2004).
[Crossref]

Boyd, R. W.

Burge, R. E.

Celechovsky, R.

Z. Bouchal and R. Celechovsky, “Mixed vortex states of light as information carriers,” N. J. Phys. 6, 131 (2004).
[Crossref]

Cizmar, T.

Z. Bouchal, V. Kollarova, P. Zemanek, and T. Cizmar, “Orbital angular momentum of mixed vortex beams,” Proc. SPIE 660907, 1–8 (2007).

Courtial, J.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref] [PubMed]

H. Wei, X. Xue, J. Leach, M. J. Padgetc, S. M. Barnett, S. Franke-Arnoldd, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Feng, S.

S. Feng and H. G. Winful, “Higher-order transverse modes of ultrashort isodiffracting,” Phys. Rev. E 63, 046602 (2001).
[Crossref]

Franke-Arnold, S.

Franke-Arnoldd, S.

H. Wei, X. Xue, J. Leach, M. J. Padgetc, S. M. Barnett, S. Franke-Arnoldd, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

Gao, C.

Gibson, G.

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

Kollarova, V.

Z. Bouchal, V. Kollarova, P. Zemanek, and T. Cizmar, “Orbital angular momentum of mixed vortex beams,” Proc. SPIE 660907, 1–8 (2007).

Leach, J.

H. Wei, X. Xue, J. Leach, M. J. Padgetc, S. M. Barnett, S. Franke-Arnoldd, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Lekner, J.

J. Lekner, “Helical light pulses,” J. Opt. A 6, L29–L32 (2004).

Lin, J.

Liu, Y. D.

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Molina-Terriza, G.

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

Neifeld, M. A.

Padgetc, M. J.

H. Wei, X. Xue, J. Leach, M. J. Padgetc, S. M. Barnett, S. Franke-Arnoldd, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Padgett, M. J.

Pas’ko, V.

Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref] [PubMed]

Porras, M. A.

Qi, X.

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

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, 8185–8190 (1992).
[Crossref] [PubMed]

Tao, S. H.

Torner, L.

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

Torres, J. P.

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

Tyler, G. A.

Vasic, B. V.

Vasnetsov, M.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Weber, H.

Wei, H.

H. Wei, X. Xue, J. Leach, M. J. Padgetc, S. M. Barnett, S. Franke-Arnoldd, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Winful, H. G.

S. Feng and H. G. Winful, “Higher-order transverse modes of ultrashort isodiffracting,” Phys. Rev. E 63, 046602 (2001).
[Crossref]

Woerdman, J. P.

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, 8185–8190 (1992).
[Crossref] [PubMed]

Xue, X.

H. Wei, X. Xue, J. Leach, M. J. Padgetc, S. M. Barnett, S. Franke-Arnoldd, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Yao, E.

H. Wei, X. Xue, J. Leach, M. J. Padgetc, S. M. Barnett, S. Franke-Arnoldd, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Yuan, X.-C.

Zauderer, E.

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Zemanek, P.

Z. Bouchal, V. Kollarova, P. Zemanek, and T. Cizmar, “Orbital angular momentum of mixed vortex beams,” Proc. SPIE 660907, 1–8 (2007).

Appl. Opt. (2)

J. Opt. A (1)

J. Lekner, “Helical light pulses,” J. Opt. A 6, L29–L32 (2004).

J. Opt. Soc. Am. A (1)

N. J. Phys. (1)

Z. Bouchal and R. Celechovsky, “Mixed vortex states of light as information carriers,” N. J. Phys. 6, 131 (2004).
[Crossref]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Opt. Commun. (1)

H. Wei, X. Xue, J. Leach, M. J. Padgetc, S. M. Barnett, S. Franke-Arnoldd, E. Yao, and J. Courtial, “Simplified measurement of the orbital angular momentum of single photons,” Opt. Commun. 223, 117–122 (2003).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (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, 8185–8190 (1992).
[Crossref] [PubMed]

Phys. Rev. E (1)

S. Feng and H. G. Winful, “Higher-order transverse modes of ultrashort isodiffracting,” Phys. Rev. E 63, 046602 (2001).
[Crossref]

Phys. Rev. Lett. (3)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref] [PubMed]

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

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref] [PubMed]

Proc. SPIE (1)

Z. Bouchal, V. Kollarova, P. Zemanek, and T. Cizmar, “Orbital angular momentum of mixed vortex beams,” Proc. SPIE 660907, 1–8 (2007).

Other (1)

http://en.wikipedia.org/wiki/Laguerre_polynomials

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Figures (3)

Fig. 1.
Fig. 1. Model of ultrashort pulse LGBs generation.

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Fig. 2.
Fig. 2. (color online)Time-varying and propagating of decomposed LGBs, |am,n (z, t)|2. Incident LGBs (rows from top to bottom) are ψ 0,0, ψ 0,3, ψ 0,6, and ψ 3,3; RQN of decomposed LGBs (columns from left to right) are m = 0, 1, 2, but m = 2, 3 and 4 in the last row.

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Fig. 3.
Fig. 3. Time-varying of decomposed LGBs, |am,n (z, t)|2, at different distances. Incident LGBs (rows from top to bottom) are ψ 0,0, ψ 0,6, and ψ 3,3; Distances (columns from left to right) are z = zR , 2zR , and 4zR .

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Equations (13)

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

Δ ⊥ ψ + 2 i k 0 ∂ z ψ − 2 c ∂ z ∂ t ψ = 0 ,
Δ ⊥ ψ + 2 i k 0 ∂ z ψ = 0 .
ψ = ∑ m , n a m , n ( z , t ) ψ m , n .
∑ m , n ψ m , n ( ω 0 ∂ z a m , n + i ∂ z ∂ t a m , n ) + i ∂ z ψ m , n ∂ t a m , n = 0 .
∑ m δ m ′ , m ( i ω 0 − ∂ t ) ∂ z a m , n − H m ′ , n ∂ t a m , n = 0 ,
( i ω 0 − ∂ t ) ∂ z X − H ∂ t X = 0 ,
( i ω 0 − ∂ t ) ∂ z Y + i Λ ∂ t Y = 0 ,
( i ω 0 − ∂ t ) ∂ z b m , n + i λ m , n ∂ t b m , n = 0 .
f ( t ) = exp ( − t 2 T 2 ) ,
ψ ( x , z = 0 , t ) = ψ m 0 , n f ( t ) ,
Y ∣ z = 0 = ( U ¯ 1 , m 0 U ¯ 2 , m 0 . . . U ¯ m , m 0 . . . ) T f ( t ) ,
Y ∣ t = − ∞ = 0 .
{ ∂ t ∂ z b m , n − i ω 0 ∂ z b m , n − i λ m , n ∂ t b m , n = 0 b m , n ∣ z = 0 = U ¯ m , m 0 f ( t ) b m , n ∣ t = − ∞ = 0

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