Abstract

We study the self-reconstruction property of a fractional Bessel beam (FBB), where the FBB is described in terms of a Bessel beam of a fractional order for both amplitude and azimuthal phase components. The simulation and experimental results show that the FBB can overcome a block of obstacles and regenerate itself after a characteristic distance. As a comparison, the propagation of a Gaussian beam and an integer-order Bessel beam (IBB) through the same obstacles are also studied.

© 2004 Optical Society of America

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References

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  1. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  2. J. Arlt, V. Garces-Chavez, W. Sibbett, K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
    [CrossRef]
  3. V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
    [CrossRef] [PubMed]
  4. K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B Quantum Semiclassical Opt. 4, s82–s89 (2002).
    [CrossRef]
  5. R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun. 122, 169–177 (1996).
    [CrossRef]
  6. S. Sogomonian, S. Klewitz, S. Herminghaus, “Self-reconstruction of a Bessel beam in a nonlinear medium,” Opt. Commun. 139, 313–319 (1997).
    [CrossRef]
  7. Z. Bouchal, J. Wagner, M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
    [CrossRef]
  8. S. H. Tao, W. M. Lee, X.-C. Yuan, “Dynamic optical manipulation using higher-order fractional Bessel beam generated from a spatial light modulator,” Opt. Lett. 28, 1867–1869 (2003).
    [CrossRef] [PubMed]
  9. J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
    [CrossRef]
  10. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  11. S. H. Tao, W. M. Lee, X. Yuan, “Experimental study of holographic generation of fractional Bessel beams,” Appl. Opt. 43, 122–126 (2004).
    [CrossRef] [PubMed]

2004

2003

2002

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B Quantum Semiclassical Opt. 4, s82–s89 (2002).
[CrossRef]

2001

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

2000

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

1998

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

1997

S. Sogomonian, S. Klewitz, S. Herminghaus, “Self-reconstruction of a Bessel beam in a nonlinear medium,” Opt. Commun. 139, 313–319 (1997).
[CrossRef]

1996

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun. 122, 169–177 (1996).
[CrossRef]

1987

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

Arlt, J.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B Quantum Semiclassical Opt. 4, s82–s89 (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]

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

Boothroyd, S. A.

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun. 122, 169–177 (1996).
[CrossRef]

Bouchal, Z.

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

Chavez-Cerda, S.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B Quantum Semiclassical Opt. 4, s82–s89 (2002).
[CrossRef]

Chlup, M.

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

Chrostowski, J.

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun. 122, 169–177 (1996).
[CrossRef]

Dholakia, K.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B Quantum Semiclassical Opt. 4, s82–s89 (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]

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

Durnin, J.

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

Eberly, J. H.

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

Garces-Chavez, V.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B Quantum Semiclassical Opt. 4, s82–s89 (2002).
[CrossRef]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

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

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Herminghaus, S.

S. Sogomonian, S. Klewitz, S. Herminghaus, “Self-reconstruction of a Bessel beam in a nonlinear medium,” Opt. Commun. 139, 313–319 (1997).
[CrossRef]

Klewitz, S.

S. Sogomonian, S. Klewitz, S. Herminghaus, “Self-reconstruction of a Bessel beam in a nonlinear medium,” Opt. Commun. 139, 313–319 (1997).
[CrossRef]

Lee, W. M.

MacDonald, R. P.

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun. 122, 169–177 (1996).
[CrossRef]

McGloin, D.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

Melville, H.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

Miceli, J. J.

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

Okamoto, T.

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun. 122, 169–177 (1996).
[CrossRef]

Sibbett, W.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

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

Sogomonian, S.

S. Sogomonian, S. Klewitz, S. Herminghaus, “Self-reconstruction of a Bessel beam in a nonlinear medium,” Opt. Commun. 139, 313–319 (1997).
[CrossRef]

Syrett, B. A.

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun. 122, 169–177 (1996).
[CrossRef]

Tao, S. H.

Volke-Sepulveda, K.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B Quantum Semiclassical Opt. 4, s82–s89 (2002).
[CrossRef]

Wagner, J.

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

Yuan, X.

Yuan, X.-C.

Appl. Opt.

J. Opt. B Quantum Semiclassical Opt.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B Quantum Semiclassical Opt. 4, s82–s89 (2002).
[CrossRef]

Nature

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[CrossRef] [PubMed]

Opt. Commun.

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

R. P. MacDonald, S. A. Boothroyd, T. Okamoto, J. Chrostowski, B. A. Syrett, “Interboard optical data distribution by Bessel beam shadowing,” Opt. Commun. 122, 169–177 (1996).
[CrossRef]

S. Sogomonian, S. Klewitz, S. Herminghaus, “Self-reconstruction of a Bessel beam in a nonlinear medium,” Opt. Commun. 139, 313–319 (1997).
[CrossRef]

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

J. Arlt, K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

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

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

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Figures (12)

Fig. 1
Fig. 1

Intensity pattern of an FBB of order 4.5 at (a) z=0 mm, (b) z=300 mm.

Fig. 2
Fig. 2

Intensity patterns of the FBB propagation from z=1 to 100 mm, with n=4.5, at z=(a) 1 mm, (b) 5 mm, (c) 10 mm, (d) 100 mm.

Fig. 3
Fig. 3

Schematic diagram of the obstruction and propagation of a light beam.

Fig. 4
Fig. 4

(a) Cross section of a Gaussian beam with no obstacle. (b) Gaussian beam’s cross section at z=190 mm. (c) Gaussian beam is blocked by two obstacles at z=65 mm. (d) Gaussian beam’s propagation at z=190 mm after the blocks.

Fig. 5
Fig. 5

(a) Cross section of a fourth-order Bessel beam with no obstacle. (b) Bessel beam’s cross section at z=190 mm. (c) fourth-order Bessel beam is blocked by two obstacles at z=65 mm. (d) Bessel beam’s propagation at z=190 mm after the blocks.

Fig. 6
Fig. 6

(a) Cross section of an FBB of order 4.5 with no obstacle. (b) FBB’s cross section at z=190 mm; (c) the FBB is blocked by two obstacles at z=65 mm. (d) FBB’s propagation at z=190 mm after the blocks.

Fig. 7
Fig. 7

Three-dimensional views of the Gaussian beam’s intensity versus propagation distance. An obstacle is positioned at z=25 mm. (a) View toward the z direction, (b) planar view.

Fig. 8
Fig. 8

Three-dimensional views of the IBB’s intensity versus propagation distance. An obstacle is positioned at z=25 mm. (a) View toward the z direction, (b) planar view.

Fig. 9
Fig. 9

Three-dimensional views of FBB’s intensity versus propagation distance. An obstacle is positioned at z=25 mm. (a) View toward the z direction, (b) planar view.

Fig. 10
Fig. 10

Snapshots of the FBB’s phase with and without obstruction. With the obstacles, the phase cross sections of the FBB are shown at z=(a) 65, (b) 90, (c) 140, (d) 190 mm. Without obstruction, the phase cross sections of the FBB are shown at z=(e) 65, (f) 90, (g) 140, (h) 190 mm.

Fig. 11
Fig. 11

Phase evolutions of the FBB (a) without obstructions at propagation distance ranging from z=65 mm to z=190 mm, (b) with obstructions at the same range of propagation distance as in (a).

Fig. 12
Fig. 12

Experimental results with (a) the particle used in the experiment positioned 200 mm behind the hologram: The captured intensity profiles of the obstructed FBB are shown for z=(b) 300, (c) 500, (d) 550, (e) 600, (f) 700 mm from the hologram.  

Equations (3)

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2-1c22t2E(r, t)=0.
En(r, ϕ, z)=A exp(ikzz)Jn(krr)exp(inϕ),
A(x, y, z)=FT-1{FT[A(x, y, z-Δz)]exp(-ikzΔz)},

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