Abstract

The synthesis of diffraction-free fields with different profiles is described. The synthesis is done by illuminating a screen containing a circular slit with a cosine beam. The treatment is equivalent to the modulation of the slit transfer characteristics and makes possible a tunable interference interaction of Bessel beams with noncommon axes. These results are generalized, and it is shown that coherent diffraction-free fields with arbitrary profiles can be expressed as the superposition of shifted zero-order Bessel beams and temporary parametric representations of the shifted functions. Diffraction-free fields with partially coherent features can be obtained. Experimental results are shown for each case.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Durnin, “Exact solutions for diffraction-free beams I: the scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  2. Z. Bouchal, J. Wagner, M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
    [CrossRef]
  3. W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. 57, 772–778 (1967).
    [CrossRef]
  4. P. Szwaykoski, J. Ojeda-Castañeda, “Nondiffracting beams and the self-imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).
    [CrossRef]
  5. D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
    [CrossRef]
  6. J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
    [CrossRef]
  7. G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1985), p. 561.
  8. Y. Kosaku, Lectures on Differential and Integral Equations (Dover, New York, 1991), pp. 115–157.
  9. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995), pp. 229–237.
  10. C. A. McQueen, J. Arlt, K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
    [CrossRef]

2002 (1)

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[CrossRef]

2001 (1)

J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

1999 (1)

C. A. McQueen, J. Arlt, K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

1998 (1)

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

1991 (1)

P. Szwaykoski, J. Ojeda-Castañeda, “Nondiffracting beams and the self-imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).
[CrossRef]

1987 (1)

1967 (1)

Arfken, G.

G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1985), p. 561.

Arlt, J.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[CrossRef]

J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

C. A. McQueen, J. Arlt, K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

Bouchal, Z.

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

Chlup, M.

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

Dholakia, K.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[CrossRef]

J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

C. A. McQueen, J. Arlt, K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

Durnin, J.

Garces-Chavez, V.

J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Kosaku, Y.

Y. Kosaku, Lectures on Differential and Integral Equations (Dover, New York, 1991), pp. 115–157.

Lancaster, G. P. T.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[CrossRef]

Livesey, J.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[CrossRef]

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995), pp. 229–237.

McGloin, D.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[CrossRef]

McQueen, C. A.

C. A. McQueen, J. Arlt, K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

Montgomery, W. D.

Ojeda-Castañeda, J.

P. Szwaykoski, J. Ojeda-Castañeda, “Nondiffracting beams and the self-imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).
[CrossRef]

Rhodes, D. P.

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[CrossRef]

Sibbett, W.

J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Szwaykoski, P.

P. Szwaykoski, J. Ojeda-Castañeda, “Nondiffracting beams and the self-imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).
[CrossRef]

Wagner, J.

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

Wolf, E.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995), pp. 229–237.

Am. J. Phys. (1)

C. A. McQueen, J. Arlt, K. Dholakia, “An experiment to study a ‘nondiffracting’ light beam,” Am. J. Phys. 67, 912–915 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (4)

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

P. Szwaykoski, J. Ojeda-Castañeda, “Nondiffracting beams and the self-imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).
[CrossRef]

D. P. Rhodes, G. P. T. Lancaster, J. Livesey, D. McGloin, J. Arlt, K. Dholakia, “Guiding a cold atomic beam along a co-propagating and oblique hollow light guide,” Opt. Commun. 214, 247–254 (2002).
[CrossRef]

J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[CrossRef]

Other (3)

G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1985), p. 561.

Y. Kosaku, Lectures on Differential and Integral Equations (Dover, New York, 1991), pp. 115–157.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995), pp. 229–237.

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 (4)

Fig. 1
Fig. 1

Experimental setup for the spatial case. La, He–Ne laser; SF, spatial filter; Le, collimator lens; BS, beam splitter; M1, M2, mirrors; CS, circular slit; L, Fourier transform lens; F, focal length of 15 cm; PF, photographic film.

Fig. 2
Fig. 2

Experimental results. Diffraction-free field for two different values of the parameter α. (a) α=8ϕ; (b) α=14ϕ.

Fig. 3
Fig. 3

Experimental setup for the temporary case. La, laser; SF, spatial filter; Le, collimator lens; RP, rotating plane; RP2, RP, frontal view (observe that the circular slit is out of the rotation axis); P, pulley; M, DC motor; F, photographic film.

Fig. 4
Fig. 4

Diffraction-free field and intensity profile obtained in the rotating configuration along the AA direction.

Equations (19)

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

t(u, v)=δ(ρ-d),
B(x, y, z)--δ(ρ-d)exp[-iπλz(u2+v2)]×exp[i2π(ux+yv)]dudv=exp(-iπλzd2)J0(2πrd),
B(x, y, z)--M(u, v)δ(ρ-d)×exp[-iπλz(u2+v2)]×exp[i2π(ux+yv)]dudv,
B(x, y, z)--cos(2παu)δ(ρ-d)exp[-iπλz×(u2+v2)]exp[i2π(ux+yv)]dudv=12exp(-iπλzd2)J0{2πd[(x-α)2+y2]1/2}+12exp(-iπλzd2)J0{2πd[(x+α)2+y2]1/2}.
I(x, y)=|B(x, y, z)|2=14J02{2πd[(x-α)2+y2]1/2}+14J02{2πd[(x+α)2+y2]1/2}+12J0{2πd[(x-α)2+y2]1/2}×J0{2πd[(x+α)2+y2]1/2}.
J0(a)J0(b)=J0(a+b)-2s=1Js(a)J-s(b);
[(x-α)2+y2]1/2+[(x+α)2+y2]1/2=c.
4x2(4α2-c2)-4c2y2=c2(4α2-c2),
B(x, y, z)=exp(iπλzd2)--A(x0, y0)×J0{2π[(x-x0)2+(y-y0)2]1/2}dx0dy0,
B(x, y, z=0)=--A(x0, y0)J0{2π[(x-x0)2+(y-y0)2]1/2}dx0dy0.
σΨ(x, y)=--Ψ(x0, y0)J0{2π[(x-x0)2+(y-y0)2]1/2}dx0dy0,
Ψnm(x, y){cos(nx)cos(my), sin(nx)sin(my)}.
A(x, y)=n,m[anm cos(nx)cos(my)+bnm sin(nx)sin(my)],
Bˆ(u, v)=Aˆ(u, v)δ(ρ-d),
B(x, y, z)=exp(iπλzd2)-A(t)J0(2π{[x-f(t)]2+[y-g(t)]2}1/2)dt.
Λf(x, y)=-A(t)J0(2π{[x-f(t)]2+[x-g(t)]2}1/2)dt,
A(t)=anδ(t-μn),
fn(x, y)=anJ0(2π{[x-f(μn)]2+[y-g(μn)]2}1/2).
B(x, y)=nanJ0(2π{[x-f(μn)]2+[y-g(μn)]2}1/2).

Metrics