Abstract

We present dark and antidark diffraction-free beams and discuss their properties. We show that all such beams must be partially spatially coherent. The new beams can be used for optical trapping of atoms.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).
  2. Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
    [CrossRef]
  3. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  4. J. M. Brittingham, J. Appl. Phys. 54, 1179 (1983).
    [CrossRef]
  5. R. W. Ziolkowski, J. Math. Phys. 26, 861 (1985).
    [CrossRef]
  6. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  7. R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, J. Opt. Soc. Am. A 10, 75 (1993).
    [CrossRef]
  8. J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
    [CrossRef]
  9. M. A. Porras, Opt. Lett. 26, 1364 (2001).
    [CrossRef]
  10. D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, Opt. Lett. 29, 1446 (2004).
    [CrossRef] [PubMed]
  11. H. Sonajalg, M. Ratsep, and P. Saari, Opt. Lett. 22, 310 (1997).
    [CrossRef] [PubMed]
  12. S. A. Ponomarenko and G. P. Agrawal, Opt. Commun. 261, 1 (2006).
    [CrossRef]
  13. Such an equation, known as Wolf's equation, was first derived without making the paraxial approximation in E. Wolf, Proc. R. Soc. London, Ser. A 230, 246 (1955).
    [CrossRef]
  14. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  15. J. Turunen, A. Vasara, and A. T. Friberg, J. Opt. Soc. Am. A 8, 282 (1991).
    [CrossRef]
  16. M. W. Kowarz and G. S. Agarwal, J. Opt. Soc. Am. A 12, 1324 (1995).
    [CrossRef]
  17. I. S. Gradstein and I. M. Ryzhik, Tables of Intergrals, Series and Products (Academic, 1980).
  18. D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, Phys. Rev. Lett. 80, 5113 (1998).
    [CrossRef]
  19. R. K. Tyson, Principles of Adaptive Optics (Academic, 1997).
  20. T. H. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Soljacic, and M. Segev, Phys. Rev. Lett. 84, 2374 (2000).
    [CrossRef] [PubMed]

2006

S. A. Ponomarenko and G. P. Agrawal, Opt. Commun. 261, 1 (2006).
[CrossRef]

2004

2001

2000

T. H. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Soljacic, and M. Segev, Phys. Rev. Lett. 84, 2374 (2000).
[CrossRef] [PubMed]

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

1998

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, Phys. Rev. Lett. 80, 5113 (1998).
[CrossRef]

1997

1995

1993

1991

1987

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

1985

R. W. Ziolkowski, J. Math. Phys. 26, 861 (1985).
[CrossRef]

1983

J. M. Brittingham, J. Appl. Phys. 54, 1179 (1983).
[CrossRef]

1955

Such an equation, known as Wolf's equation, was first derived without making the paraxial approximation in E. Wolf, Proc. R. Soc. London, Ser. A 230, 246 (1955).
[CrossRef]

J. Appl. Phys.

J. M. Brittingham, J. Appl. Phys. 54, 1179 (1983).
[CrossRef]

J. Math. Phys.

R. W. Ziolkowski, J. Math. Phys. 26, 861 (1985).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

S. A. Ponomarenko and G. P. Agrawal, Opt. Commun. 261, 1 (2006).
[CrossRef]

Opt. Lett.

Phys. Rep.

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

Phys. Rev. E

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, Phys. Rev. E 62, 4261 (2000).
[CrossRef]

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, Phys. Rev. Lett. 80, 5113 (1998).
[CrossRef]

T. H. Coskun, D. N. Christodoulides, Y. Kim, Z. Chen, M. Soljacic, and M. Segev, Phys. Rev. Lett. 84, 2374 (2000).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A

Such an equation, known as Wolf's equation, was first derived without making the paraxial approximation in E. Wolf, Proc. R. Soc. London, Ser. A 230, 246 (1955).
[CrossRef]

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

I. S. Gradstein and I. M. Ryzhik, Tables of Intergrals, Series and Products (Academic, 1980).

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

R. K. Tyson, Principles of Adaptive Optics (Academic, 1997).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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 (2)

Fig. 1
Fig. 1

Intensity profiles of dark (dashed curve) and antidark (solid curve) diffraction-free beams with α = 1 and 1, respectively.

Fig. 2
Fig. 2

Intensity profile of the ideal ( α = 1 ) dark diffraction-free beam (solid curve), and that of the corresponding dark diffraction-free beam, constructed with N = 25 Bessel modes (dashed curve).

Equations (15)

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

( 2 i k 0 z + 1 2 2 2 ) W ( ρ 1 , ρ 2 , z ) = 0 .
( i k 0 z + r R ) W ( r , R , z ) = 0 .
W d f ( r , R ) = Φ ( r ) + Ψ ( R ) ,
W ( ρ 2 , ρ 1 , z ) = W * ( ρ 1 , ρ 2 , z ) .
Ψ * ( R ) = Ψ ( R ) , Φ * ( r ) = Φ ( r ) .
d ρ 1 d ρ 2 W d f ( ρ 1 , ρ 2 ) f * ( ρ 1 ) f ( ρ 2 ) 0 ,
W d f ( ρ 1 , ρ 2 ) = ν λ ν u ν * ( ρ 1 ) u ν ( ρ 2 ) ,
λ ν 0 .
W d f ( ρ 1 , ρ 2 ) J 0 ( β ρ 1 ρ 2 ) + α J 0 ( β ρ 1 + ρ 2 ) ,
I d f ( ρ ) W d f ( ρ , ρ ) 1 + α J 0 ( 2 β ρ ) .
α * = α , α 1 .
J 0 ( β ρ 1 ρ 2 ) = m = ( ± 1 ) m e i m ( ϕ 2 ϕ 1 ) J m ( β ρ 1 ) J m ( β ρ 2 ) .
W d f ( ρ 1 , ρ 2 ) m = λ m ψ m * ( ρ 1 ) ψ m ( ρ 2 ) ,
ψ m ( ρ ) = J m ( β ρ ) e i m ϕ ,
λ m = 1 + ( 1 ) m α .

Metrics